From 49d1867c0a29154eeed9b254aa5e5be5022c97d7 Mon Sep 17 00:00:00 2001 From: hansenpei Date: Sat, 23 Jan 2021 14:36:26 -0500 Subject: [PATCH 001/103] C-vine copula class 1. Create the C-vine copula class housing all functionalities needed for the trading module. 2. Not unittested yet but it can be done soon. 3. No trading yet. --- .../copula_approach/vinecop_generate.py | 277 ++++++++++++++++++ 1 file changed, 277 insertions(+) create mode 100644 arbitragelab/copula_approach/vinecop_generate.py diff --git a/arbitragelab/copula_approach/vinecop_generate.py b/arbitragelab/copula_approach/vinecop_generate.py new file mode 100644 index 00000000..f493dcc6 --- /dev/null +++ b/arbitragelab/copula_approach/vinecop_generate.py @@ -0,0 +1,277 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html +""" +Module that generates vine copulas. + +Built on top of the :code:`pyvinecoplib` package. See https://github.com/vinecopulib/pyvinecopulib for more details. +""" + +from abc import ABC, abstractmethod +from typing import List, Union +from scipy.optimize import minimize +from itertools import permutations +import numpy as np +import pandas as pd +import pyvinecopulib as pv +import scipy.integrate as integrate + +class CVineCop(): + """ + Class for C-vine copulas. + + This is a wrapper class of pv.Vinecop that provides useful methods for statistical arbitrage. One key note is + that, to keep the notaion consistent with literature consensus, all variables started with pv are indexed from + 1, not 0. In this way it is easier to see the nodes of the tree. + """ + + def __init__(self, cvine_cop: pv.Vinecop = None): + """ + Initiate a C-vine copula class. + + :param cvine_cop: (pv.Vinecop) Optional. A fitted C-vine copula. Defaults to None. + """ + + # All the bivariate classes used to construct the vine copula. + self._bicop_family = [pv.BicopFamily.bb1, pv.BicopFamily.bb6, pv.BicopFamily.bb7, pv.BicopFamily.bb8, + pv.BicopFamily.clayton, pv.BicopFamily.student, pv.BicopFamily.frank, + pv.BicopFamily.gaussian, pv.BicopFamily.gumbel, pv.BicopFamily.indep] + # The pv.Vinecop being wrapped + self.cvine_cop = cvine_cop + + def fit(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = True): + """ + Fit data to the C-vine copula by selecting the center stock. + + The method will loop through all possible C-vine structures and choose the best fit by AIC. The targeted + stock will never show up in the center of the tree, thus some C-vine structures need not be included. This + method is relatively slow, and the complexity is O(n!) with n being the number of stocks. Hence please keep + n <= 7. + + The original pv.Vinecop will be returned just in case there is some usage not covered by this class. + + :param data: (pd.DataFrame) The quantile data to be used to fit the C-vine copula. + :param pv_target_idx: (int) Optional. The stock to be targeted for trading. This is indexed from 1, hence + 1 corresponds to the 0th column data in the data frame. Defalts to 1. + :param if_renew: (bool) Optional. Whether to update the class attribute cvine_cop. Defaults to True. + :return: (pv.Vinecop) The fitted pv.Vinecop object. + """ + + # Initializing. + data_np = data.to_numpy() # pyvinecopulib uses numpy arrays for fitting. + data_dim = len(data.columns) # Number of stocks. + # List of all possible C-vine structures, a list of tuples. + possible_cvine_structures = self._get_possible_cvine_structs(data_dim, pv_target_idx) + + # Fit among all possible structures. + controls = pv.FitControlsVinecop(family_set = self._bicop_family) # Bivar copula constituents for the C-vine. + aics = dict() # Dictionary for AIC values for all candidate C-vine copulas. + cvine_cops = dict() # Dictionary for storing all candiate C-vine copulas. + for cvine_structure in possible_cvine_structures: + temp_cvine_struct = pv.CVineStructure(order=cvine_structure) # Specific C-vine structure + temp_cvine_cop = pv.Vinecop(structure=temp_cvine_struct) # Construct the C-vine copula + temp_cvine_cop.select(data=data_np, controls=controls) # Fit to data + aics[cvine_structure] = temp_cvine_cop.aic(data_np) # Calculate AIC + cvine_cops[cvine_structure] = temp_cvine_cop # Store the C-vine copula candidate + + # Select the structure that has the lowest aics + aics = pd.Series(aics) + fitted_cvine_strcture = aics.idxmin() # aics indexed by the structure (tuple) + + # Generate a C-vine copula for the system + fitted_cvine_cop = cvine_cops[fitted_cvine_strcture] + + if if_renew: # Whether to renew the class C-vine copula. + self.cvine_cop = fitted_cvine_cop + + return fitted_cvine_cop + + @staticmethod + def _get_possible_cvine_structs(data_dim: int, pv_target_idx: int) -> List[tuple]: + """ + Get all possible C-vine structures specified by the dimension and the targeted node. + + A C-vine copula is uniquelly determined by an ordered tuple, listing the center of each tree at every level + read backwards. For example, for a 4-dim C-vine characterized by (4, 2, 1, 3), node 3 is the center for the + 0th tree, node 1 is the center for the 1st tree and so on. The targeted node representing the stock of + interest, cannot be the at the center of every tree (except the last) and thus has to be the 0th element in the + tuple, as claimed in [Stubinger et al. 2016]. For a tuple (4, 2, 1, 3), it says stock 4 is the targeted stock. + + :param data_dim: (int) The number of stocks. + :param pv_target_idx: (int). The stock to be targeted for trading. This is indexed from 1, hence 1 corresponds + to the 0th column data in a pandas data frame. + :return: (List[tuple]) The list of all possible C-vine structures stored as tuples. + """ + + # Initiating + all_items = list(range(1, data_dim+1)) # All the nodes, indexed from 1 + all_structures = permutations(all_items) # All the possible stuctures, as permutations of the nodes + + # Loop thourgh all the structures + valid_structures = [] + for structure in all_structures: + if structure[0] == pv_target_idx: # Only keep the ones where the targeted index is the 0-th element + valid_structures.append(structure) + + return valid_structures + + def get_condi_prob(self, u: pd.Series, pv_target_idx: int = 1, eps: float = 1e-4) -> float: + r""" + Get the conditional probability of the C-vine copula. + + For example, if we have 5 stocks and pv_target_idx = 2, then this method calculates: + P(U2 <= u2 | U1=u1, U3=u3, U4=u2, U5=u5) + + The calculation is numerical by integrating along the margin. By default it uses the 0th element of u as the + target. Also this function's value is wrapped within [eps, 1-eps] to avoid potential edge values by default. + + :param u: (pd.Series) The vector value of quantiles. + :param pv_target_idx: (int) Optional. The stock to be targeted for trading. This is indexed from 1, hence 1 + corresponds to the 0th column data in a pandas data frame. In this case it is the only variable not + conditioned on. Defaults to 1. + :param eps: (float) Optional. The small value that keeps results within [eps, 1-eps]. Defaults to 1e-4. + :return: (float) The calculated conditional probability. + """ + + # Initiating + u = np.array(u) # Casting to 1D numpy array + target_idx = pv_target_idx - 1 # Indexing from 0 + target = u[target_idx] # Upper lim of the integration + others = np.delete(u, target_idx) # Those will be served as arguments in quad + + # The integrand function is the pdf + def pdf_func(target, others): + # the pv.Vinecop.pdf only takes 2D arrays as input. Here it is assembled back + u_vec = np.insert(arr=others, obj=target_idx, values=target).reshape((1, 4)) + pdf = self.cvine_cop.pdf(u_vec)[0] + + return pdf + + # Integrating along the margin and normalizing the conditional probability + sum_prob = integrate.quad(pdf_func, 0, target, args=others)[0] + total_prob = integrate.quad(pdf_func, 0, 1, args=others)[0] + condi_prob = sum_prob / total_prob + + # Map the condi prob into [eps, 1-eps] + wrapped_condi_prob = max(min(condi_prob, 1-eps), eps) + + return wrapped_condi_prob + + def get_cop_densities(self, u: Union[pd.DataFrame, np.array], num_threads: int = 1) -> Union[pd.Series, float]: + """ + Calculate probability density of the vine copula. + + Result is analytical. You may also take advantage of multi-thread calculation. The result will be either a + pandas series of numbers or a single number depends on the dimension of the input. + + :param u: (Union[pd.DataFrame, np.array]) The quantiles data to be used. The input can be a pandas dataframe, + or a numpy array vector. The formal case yields the result with in pandas series in matching indices, and + the latter yields a single float number. + :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. + :return: (Union[pd.Series, float]) The calculated pdf. If the input is a dataframe then the result is a series + with matching indices. If the input is a 1D np.array then the result is a float. + """ + + # When the input is a 1D np.array + if isinstance(u, np.ndarray) and u.ndim == 1: + u_np = u.reshape((1, -1)) + pdf = self.cvine_cop.pdf(u_np, num_threads)[0] + # The output is a float + return pdf + + # When tne input is a pd.Dataframe + u_np = np.array(u) + pdfs = self.cvine_cop.pdf(u_np, num_threads) + pdfs_series = pd.Series(pdfs, index=u.index) + # The result is a pd.Series with matching indices + return pdfs_series + + def get_cop_evals(self, u: pd.DataFrame, mcn: int = 1e4, num_threads: int = 1) -> pd.Series: + """ + Calculate cumulative density of the vine copula. + + Result is numerical through Monte-Carlo integration. You may also take advantage of multi-thread calculation. + The result will be either a pandas series of numbers or a single number depends on the dimension of the input. + + :param u: (Union[pd.DataFrame, np.array]) The quantiles data to be used. The input can be a pandas dataframe, + or a numpy array vector. The formal case yields the result with in pandas series in matching indices, and + the latter yields a single float number. + :param mcn: (int) Integer for the number of quasi-random numbers to draw to evaluate the distribution for the + Monte-Carlo integration. Defaults to 1e4. + :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. + :return: (Union[pd.Series, float]) The calculated cdf. If the input is a dataframe then the result is a series + with matching indices. If the input is a 1D np.array then the result is a float. + """ + + # When the input is a 1D np.array + if isinstance(u, np.ndarray) and u.ndim == 1: + u_np = u.reshape((1, -1)) + cdf = self.cvine_cop.cdf(u_np, mcn, num_threads)[0] + # The output is a float + return cdf + + # When tne input is a pd.Dataframe + u_np = np.array(u) + cdfs = self.cvine_cop.cdf(u_np, mcn, num_threads) + cdfs_series = pd.Series(cdfs, index=u.index) + # The result is a pd.Series with matching indices + return cdfs_series + + def simulate(self, n: int, qrn: bool = False, num_threads: int = 1, seeds: List[int] = []) -> np.ndarray: + """ + Simulate from a vine copula model. + + :param n: (int) Number of observations. + :param qrn: (bool) Optional. Set to True for quasi-random numbers. Defaults to False. + :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. + :param seeds: (List[int]) Optional. Seeds of the random number generator. If empty then the random generator + will be seeded randomly. Defaults to False. + :return: (pd.ndarray) The generated random samples from the vine copula. + """ + + simulated_samples = self.cvine_cop.simulate(n, qrn, num_threads, seeds) + + return simulated_samples + + def aic(self, u: pd.Dataframe, num_threads: int = 1) -> float: + """ + Evaluates the Akaike information criterion (AIC). + + :param u: (pd.DataFrame) The quantile data used for evaluation. + :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. + :return: (float) calculated AIC value. + """ + + u_np = u.to_numpy() # Transit to numpy ndarrays + aic_value = self.cvine_cop.aic(u_np, num_threads) + + return aic_value + + def bic(self, u: pd.Dataframe, num_threads: int = 1) -> float: + """ + Evaluates the Bayesian information criterion (BIC). + + :param u: (pd.DataFrame) The quantile data used for evaluation. + :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. + :return: (float) calculated BIC value. + """ + + u_np = u.to_numpy() # Transit to numpy ndarrays + bic_value = self.cvine_cop.bic(u_np, num_threads) + + return bic_value + + def loglik(self, u: pd.Dataframe, num_threads: int = 1) -> float: + """ + Evaluates the Sum of log-likelihood. + + :param u: (pd.DataFrame) The quantile data used for evaluation. + :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. + :return: (float) calculated sum of log-likelihood. + """ + + u_np = u.to_numpy() # Transit to numpy ndarrays + loglik_value = self.cvine_cop.loglik(u_np, num_threads) + + return loglik_value + From bd51756eef8c77db46433b3147c78e69b980b9b1 Mon Sep 17 00:00:00 2001 From: hansenpei Date: Tue, 26 Jan 2021 10:48:11 -0500 Subject: [PATCH 002/103] Functionality code for vine copula module Back up on Git just in case, will clean up soon. --- .../copula_approach/vinecop_generate.py | 84 ++++- .../copula_approach/vinecop_strategy.py | 343 ++++++++++++++++++ 2 files changed, 418 insertions(+), 9 deletions(-) create mode 100644 arbitragelab/copula_approach/vinecop_strategy.py diff --git a/arbitragelab/copula_approach/vinecop_generate.py b/arbitragelab/copula_approach/vinecop_generate.py index f493dcc6..06825101 100644 --- a/arbitragelab/copula_approach/vinecop_generate.py +++ b/arbitragelab/copula_approach/vinecop_generate.py @@ -9,14 +9,23 @@ from abc import ABC, abstractmethod from typing import List, Union -from scipy.optimize import minimize from itertools import permutations +import numba import numpy as np import pandas as pd import pyvinecopulib as pv import scipy.integrate as integrate -class CVineCop(): +class RVineCop(): + """ + R-Vine copula class, housing C-vine copula and D-vine copula as special subcases. + """ + + def __init__(self): + pass + + +class CVineCop(RVineCop): """ Class for C-vine copulas. @@ -39,9 +48,9 @@ def __init__(self, cvine_cop: pv.Vinecop = None): # The pv.Vinecop being wrapped self.cvine_cop = cvine_cop - def fit(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = True): + def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = True): """ - Fit data to the C-vine copula by selecting the center stock. + Auto fit data to the C-vine copula by selecting the center stock. The method will loop through all possible C-vine structures and choose the best fit by AIC. The targeted stock will never show up in the center of the tree, thus some C-vine structures need not be included. This @@ -115,9 +124,42 @@ def _get_possible_cvine_structs(data_dim: int, pv_target_idx: int) -> List[tuple return valid_structures - def get_condi_prob(self, u: pd.Series, pv_target_idx: int = 1, eps: float = 1e-4) -> float: + def get_condi_probs(self, u: Union[pd.DataFrame, np.array], pv_target_idx: int = 1, + eps: float = 1e-4) -> Union[pd.Series, float]: r""" - Get the conditional probability of the C-vine copula. + Get the conditional probabilities of the C-vine copula for a target. + + For example, if we have 5 stocks and pv_target_idx = 2, then this method calculates: + P(U2 <= u2 | U1=u1, U3=u3, U4=u2, U5=u5) + + The calculation is numerical by integrating along the margin. By default it uses the 0th element of u as the + target. Also this function's value is wrapped within [eps, 1-eps] to avoid potential edge values by default. + + :param u: (Union[pd.DataFrame, np.array]) The quantiles data to be used. The input can be a pandas dataframe, + or a numpy array vector. The formal case yields the result with in pandas series in matching indices, and + the latter yields a single float number. + :param pv_target_idx: (int) Optional. The stock to be targeted for trading. This is indexed from 1, hence 1 + corresponds to the 0th column data in a pandas data frame. In this case it is the only variable not + conditioned on. Defaults to 1. + :param eps: (float) Optional. The small value that keeps results within [eps, 1-eps]. Defaults to 1e-4. + :return: (Union[pd.Series, float]) The calculated pdf. If the input is a dataframe then the result is a series + with matching indices. If the input is a 1D np.array then the result is a float. + """ + # When the input is a 1D np.array + if isinstance(u, np.ndarray) and u.ndim == 1: + u_srs = pd.Series(u) + condi_prob = self._get_condi_prob(u_srs, pv_target_idx, eps) + # The output is a float + return condi_prob + + # When tne input is a pd.Dataframe + condi_probs = u.apply(lambda row: self._get_condi_prob(row, pv_target_idx, eps), axis=1) + # The result is a pd.Series with matching indices + return condi_probs + + def _get_condi_prob(self, u: pd.Series, pv_target_idx: int = 1, eps: float = 1e-4) -> float: + r""" + Get the conditional probability of the C-vine copula for a target. For example, if we have 5 stocks and pv_target_idx = 2, then this method calculates: P(U2 <= u2 | U1=u1, U3=u3, U4=u2, U5=u5) @@ -233,7 +275,7 @@ def simulate(self, n: int, qrn: bool = False, num_threads: int = 1, seeds: List[ return simulated_samples - def aic(self, u: pd.Dataframe, num_threads: int = 1) -> float: + def aic(self, u: pd.DataFrame, num_threads: int = 1) -> float: """ Evaluates the Akaike information criterion (AIC). @@ -247,7 +289,7 @@ def aic(self, u: pd.Dataframe, num_threads: int = 1) -> float: return aic_value - def bic(self, u: pd.Dataframe, num_threads: int = 1) -> float: + def bic(self, u: pd.DataFrame, num_threads: int = 1) -> float: """ Evaluates the Bayesian information criterion (BIC). @@ -261,7 +303,7 @@ def bic(self, u: pd.Dataframe, num_threads: int = 1) -> float: return bic_value - def loglik(self, u: pd.Dataframe, num_threads: int = 1) -> float: + def loglik(self, u: pd.DataFrame, num_threads: int = 1) -> float: """ Evaluates the Sum of log-likelihood. @@ -275,3 +317,27 @@ def loglik(self, u: pd.Dataframe, num_threads: int = 1) -> float: return loglik_value + + +# #%% +# print(cvine_cop.families) +# #%% +# test_quantiles = np.array([[0.1, 0.2, 0.3, 0.4], +# [0.5, 0.2, 0.3, 0.4], +# [1, 0.2, 0.3, 0.4]]) +# lower_input = np.array([[0.099, 0.2, 0.3, 0.4], +# [0.499, 0.6, 0.7, 0.8], +# [0.199, 0.3, 0.4, 0.8]]) +# upper_input = np.array([[0.101, 0.2, 0.3, 0.4], +# [0.501, 0.6, 0.7, 0.8], +# [0.201, 0.3, 0.4, 0.8]]) +# print(cvine_cop.pdf(u=test_quantiles)) +#%% + +# u = np.array([0, 0.2, 0.3, 0.4]) +# print(cvinecop._get_condi_prob(u, pv_target_idx = 1, eps=1e-4)) + +#%% + +#%% +#%% diff --git a/arbitragelab/copula_approach/vinecop_strategy.py b/arbitragelab/copula_approach/vinecop_strategy.py new file mode 100644 index 00000000..dc5e79bb --- /dev/null +++ b/arbitragelab/copula_approach/vinecop_strategy.py @@ -0,0 +1,343 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html +""" +Module that generates vine copulas. + +Built on top of the :code:`pyvinecoplib` package. See https://github.com/vinecopulib/pyvinecopulib for more details. +""" + +from typing import List, Union, Callable, Tuple +from itertools import permutations +from arbitragelab.copula_approach.vinecop_generate import CVineCop +import numpy as np +import pandas as pd +import pyvinecopulib as pv + +class CVineCopStrat(): + """ + Trading strategy class using vine copulas. + """ + def __init__(self, cvinecop: CVineCop = None): + """ + Create the trading strategy class. + """ + self.cvine_cop = cvinecop + self.past_obs = None + self.threshold_std = None + # Signal to position table: Row indexed by previous position, column indexed by signal + # Refer to doc string of self._signal_to_position() for more detail + self.signal_to_position_table = pd.DataFrame({1: {0: 1, 1: 1, -1: 0}, + -1: {0: -1, 1: 0, -1: -1}, + 0: {0: 0, 1: 0, -1: 0}, + 2: {0: 0, 1: 1, -1: -1}}) + + def calc_mpi(self, returns: pd.DataFrame, cdfs: List[Callable], pv_target_idx: int = 1, + subtract_mean: bool = False) -> pd.Series: + """ + Calculate mispricing indices from returns for the target stock. + + Mispricing indices are technically cumulative conditional probabilities calculated from a copula based on + returns data. + """ + + # 1. Map all the returns to quantiles + quantiles = pd.DataFrame(data=0, index=returns.index, columns=returns.columns) + for i, column_name in enumerate(returns): + quantiles[column_name] = returns[column_name].apply(cdfs[i]) + + # 2. Calculate the conditional probabilities + mpis = self.cvine_cop.get_condi_probs(quantiles, pv_target_idx) + + if subtract_mean: + mpis = mpis.subtract(0.5) + + return mpis + + def select_candidates(self): + pass + + def get_positions_bollinger(self, returns: pd.DataFrame, cdfs: List[Callable], pv_target_idx: int = 1, + init_pos: int = 0, past_obs: int = 20, threshold_std: float = 1.0, + mpis: pd.Series = None, if_return_bollinger_band = False) -> pd.Series: + """ + Get positions based on the strategy suggested by [Bollinger, 1992]. + + Calculate the running mean and standard deviation of Cumulative mispricing index (CMPI) for the past 20 + observations (one month if it is daily data) and create the running Bollinger band as + (mean - k*std, mean + k*std), k is the threshold_std variable. Trading logic is as follows: + + - Long if the CMPI crosses its lower Bollinger band (undervalued) + - Short if the CMPI crosses its upper Bollinger band (overvalued) + - Exit if the CMPI crosses the running mean of the Bollinger band (reversion to equilibrium) + + This is used for backtesting when one has access to all testing data at once. The first 20 observations + ([0, 19]) will be used for calculating the Bollinger band and the trading signal generation starts from + observation 20. For live data feed please use self.get_cur_pos_bollinger(). + """ + + self.past_obs = past_obs + self.threshold_std = threshold_std + + # 1. Get the initial mean and std of CMPI + if mpis is None: + cmpis = self.calc_mpi(returns, cdfs, pv_target_idx, subtract_mean=True).cumsum() + else: + cmpis = mpis.cumsum() + + init_mean = cmpis.iloc[:past_obs].mean() + init_std = cmpis.iloc[:past_obs].std() + + # 2. Get positions + # Initiating + trading_cmpis = cmpis.iloc[past_obs-1:] + bollinger_band = pd.DataFrame(data=0, index=trading_cmpis.index, columns=['LowerBound', 'Mean', 'UpperBound']) + bollinger_band.iloc[0] = [init_mean - threshold_std*init_std, init_mean, init_mean + threshold_std*init_std] + positions = pd.Series(data=0, index=trading_cmpis.index) + positions.iloc[0] = init_pos + # Loop through trading_cmpis to calculate positions + for idx in range(1, len(trading_cmpis)): + # Get signal + signal = self.get_cur_signal_bollinger( + past_pos=positions.iloc[idx-1], past_cmpi=trading_cmpis[idx-1], cur_cmpi=trading_cmpis[idx], + running_mean=bollinger_band['Mean'].iloc[idx-1], + upper_threshold=bollinger_band['UpperBound'].iloc[idx-1], + lower_threshold=bollinger_band['LowerBound'].iloc[idx-1]) + # Translate signal to current position + positions.iloc[idx] = self._signal_to_position(past_pos=positions.iloc[idx-1], signal=signal) + + # Update the bollinger band + cur_returns_slice = cmpis.iloc[idx: idx+past_obs] + cur_mean = cur_returns_slice.mean() + cur_std = cur_returns_slice.std() + # Format: LowerBound, Mean, UpperBound + bollinger_band.iloc[idx] = [cur_mean - threshold_std*cur_std, cur_mean, cur_mean + threshold_std*cur_std] + + # 3. Return positions (and the bollinger band) + if if_return_bollinger_band: + return positions, bollinger_band + + return positions + + @staticmethod + def get_cur_signal_bollinger(past_pos: int, past_cmpi: float, cur_cmpi: float, running_mean: float, + upper_threshold: float, lower_threshold: float) -> int: + """ + Get the currrent trading signal based. + + Signal types {1: long, -1: short, 0: exit, 2: do nothing} + """ + + signal = 2 # By default do nothing + + # Open signal + if_long = (cur_cmpi < lower_threshold) + if_short = (cur_cmpi > upper_threshold) + + # Exit signal: when the cmpi crosses with the running mean + if_exit = ((past_cmpi - running_mean) * (cur_cmpi - running_mean) < 0) + + # Assemble the signal together + if_any_signal = any([if_long, if_short, if_exit]) + if if_any_signal: + signal = (int(if_long) - int(if_short)) * int(not if_exit) + # Return the updated signal + return signal + # Return the default signal, which is do nothing + return signal + + def _signal_to_position(self, past_pos: int, signal: int, signal_to_position_table: pd.DataFrame = None) -> int: + """ + Map the signal to position, given the past position. + + The default map is: + signal [long, short, exit, do-nothing], acting on previous positions being [0, 1, -1] respectively + + * long signal: {0: 1, 1: 1, -1: 0} + * short signal: {0: -1, 1: 0, -1: 0} + * exit signal: {0: 0, 1: 0, -1: 0} + * do-nothing signal: {0: 0, 1: 1, -1: -1} + """ + + if signal_to_position_table is not None: + self.signal_to_position_table = signal_to_position_table + + table = self.signal_to_position_table + + new_position = table.loc[past_pos, signal] + + return new_position + + def get_cur_pos_bollinger(self, returns_slice: pd.DataFrame, cdfs: List[Callable], past_pos: int, + pv_target_idx: int = 1, past_cmpi: float = 0, threshold_std: float = 1.0) -> Tuple: + """ + Get the suggested position and updated bollinger band from cur_returns pandas DataFrame. + + If the dataframe has 21 rows, then the first 20 rows will be used to calculate the Bollinger band, then the + position will be generated based on the last row. Then we calculate the updated Bollinger band. This is used + for live data feed. + """ + + # 1. Calculate the Bollinger band: mean and std + cmpis = past_cmpi + self.calc_mpi(returns_slice, cdfs, subtract_mean=True).cumsum() + init_mean = cmpis.iloc[: -1].mean() + init_std = cmpis.iloc[: -1].std() + + # 2. Get positions from the last row of the dataframe + past_cmpi = cmpis.iloc[-2] + cur_cmpi = cmpis.iloc[-1] + signal = self.get_cur_signal_bollinger(past_pos, past_cmpi, cur_cmpi, running_mean=init_mean, + upper_threshold=init_mean + threshold_std*init_std, + lower_threshold=init_mean - threshold_std*init_std) + new_position = self._signal_to_position(past_pos, signal) + + return new_position, cur_mpi + + @staticmethod + def positions_to_units_cohort(prices_df: pd.DataFrame, positions: pd.Series, pv_target_idx: int = 1, + multiplier: float = 1) -> pd.DataFrame: + """ + Change the positions series into units held for each security for a dollar neutral strategy. + + For example., for 1 dollar investment of a 4-stock-cohort, long the target stock by 1/2 dollar and short every + other 3 by 1/6 dollar each. + + Originally the positions calculated by this strategy is given with values in {0, 1, -1}. To be able to actually + trade using the dollar neutral strategy as given by the authors in the paper, one needs to know at any given + time how much units to hold for each stock. The result will be returned in a pd.DataFrame. The user can also + multiply the final result by changing the multiplier input. It means by default it uses 1 dollar for + calculation unless changed. It also means there is no reinvestment on gains. + + Note: This method assumes the 0th column in prices_df is the long unit (suppose it is called stock 1), 1st + column the shrot unit (suppose it is called stock 2). For example, 1 in positions means buy stock 1 with 0.5 + dollar and sell stock 2 to gain 0.5 dollar. + + Note2: The short units will be given in its actual value. i.e., short 0.54 units is given as -0.54 in the + output. + + :param prices_df: (pd.DataFrame) Prices data frame for the two securities. + :param positions: (pd.Series) The suggested positions with values in {0, 1, -1}. Need to have the same length + as prices_df. + :param multiplier: (float) Optional. Multiply the calculated result by this amount. Defalts to 1. + :return: (pd.DataFrame) The calculated positions for each security. The row and column index will be taken + from prices_df. + """ + + target_stock_prices = prices_df.iloc[:, pv_target_idx-1] + other_stocks_prices = prices_df.drop(columns=prices_df.columns[pv_target_idx-1]) + num_of_others = len(other_stocks_prices.columns) + target_stock_prices_np = target_stock_prices.to_numpy(dtype=np.float16) + other_stocks_prices_np = other_stocks_prices.to_numpy(dtype=np.float16) + + target_stock_units = pd.Series(data=0, index=target_stock_prices.index) + other_stocks_units = pd.DataFrame(data=0, index=other_stocks_prices.index, columns=other_stocks_prices.columns) + target_stock_units_np = target_stock_units.to_numpy(dtype=np.float16) + other_stocks_units_np = other_stocks_units.to_numpy(dtype=np.float16) + + target_stock_units_np[0] = 0.5 / target_stock_prices_np[0] * positions[0] + other_stocks_units_np[0, :] = - 0.5 / num_of_others /other_stocks_prices_np[0, :] * positions[0] + + nums = len(positions) + for i in range(1, nums): + # By default the new amount of units to be held is the same as the previous step. + target_stock_units_np[i] = target_stock_units_np[i-1] + other_stocks_units_np[i, :] = other_stocks_units_np[i-1, :] + # Updating if there are position changes. + # From not short to short. + if positions[i-1] != -1 and positions[i] == -1: # Short target, long cohort + long_units = 0.5 / num_of_others / other_stocks_prices_np[i, :] + short_units = 0.5 / target_stock_prices_np[i] + target_stock_units_np[i] = - short_units + other_stocks_units_np[i, :] = long_units + # From not long to long. + if positions[i-1] != 1 and positions[i] == 1: # Short cohort, long target + long_units = 0.5 / target_stock_prices_np[i] + short_units = 0.5 / num_of_others / other_stocks_prices_np[i, :] + target_stock_units_np[i] = long_units + other_stocks_units_np[i, :] = - short_units + # From long/short to none. + if positions[i-1] != 0 and positions[i] == 0: # Exiting + target_stock_units_np[i] = 0 + other_stocks_units_np[i, :] = 0 + + return target_stock_units_np * multiplier, other_stocks_units_np * multiplier + +#%% test +import time +import arbitragelab.copula_approach.copula_strategy_basic as csb + +cvinecop = CVineCop() +stocks_universe = pd.read_csv(r'D:\Apprenticeship\data\dow_stocks.csv', parse_dates=True, + index_col='Date') +# Fit a vine copula +# Change to returns +returns_universe = stocks_universe.pct_change() +returns_universe.iloc[0] = 0 + +returns_sample = returns_universe[['AAPL', 'MSFT', 'BA', 'V']] + +train_returns = returns_sample.iloc[:1200] +test_returns = returns_sample.iloc[1200:] + +start_time = time.time() +# Change returns to pct +CSB = csb.BasicCopulaStrategy() +train_quantiles, cdfs = CSB.to_quantile(data=train_returns) +cvine_cop = cvinecop.fit_auto(train_quantiles) +print("--- %s seconds ---" % (time.time() - start_time)) +#%% +cvinecop = CVineCop(cvine_cop) +#%% Test mpi generation +import time +start_time = time.time() +cvcs = CVineCopStrat(cvinecop=cvinecop) +# mpis = cvcs.calc_mpi(returns=test_returns, cdfs=cdfs, subtract_mean=True) +print("--- %s seconds ---" % (time.time() - start_time)) +#%% +start_time = time.time() +positions, bband = cvcs.get_positions_bollinger( + returns=test_returns, cdfs=cdfs, pv_target_idx=1, + init_pos=0, past_obs=20, threshold_std=2.0, mpis=mpis, + if_return_bollinger_band = True) +print("--- %s seconds ---" % (time.time() - start_time)) +#%% +import matplotlib.pyplot as plt +fig, ax = plt.subplots(nrows=3, dpi=300, figsize=(10, 7), gridspec_kw={'height_ratios': [0.5, 0.2, 0.7]}, sharex=True) +ax[0].plot(stocks_universe['AAPL'].iloc[1200:] / stocks_universe['AAPL'].iloc[1200], label='Target Stock Price') +ax[0].plot(stocks_universe['MSFT'].iloc[1200:] / stocks_universe['MSFT'].iloc[1200], label='Cohort Stock 2', linewidth=1) +ax[0].plot(stocks_universe['BA'].iloc[1200:] / stocks_universe['BA'].iloc[1200], label='Cohort Stock 3', linewidth=1) +ax[0].plot(stocks_universe['V'].iloc[1200:] / stocks_universe['V'].iloc[1200], label='Cohort Stock 4',linewidth=1) +ax[1].plot(positions, label='positions') +ax[2].plot(mpis.cumsum(), label='CMPI') +ax[2].plot(bband['LowerBound'], label='B Band Lower Bound', linewidth=1, color='brown') +ax[2].plot(bband['Mean'], label='B Band Mean') +ax[2].plot(bband['UpperBound'], label='B Band Upper Bound', linewidth=1, color='brown') +plt.tight_layout() +ax[0].legend() +ax[2].legend() +fig.show() + +#%% Positions to units +shifted_positions = positions.shift(1) +shifted_positions.iloc[0] = 0 +target_units, others_units = cvcs.positions_to_units_cohort( + prices_df=stocks_universe[['AAPL', 'MSFT', 'BA', 'V']].iloc[1219:], positions=shifted_positions, multiplier=4) + +#%% Equity curve plot +portfolio_pnl = (returns_sample['AAPL'].iloc[1219:].to_numpy() * target_units + + (returns_sample[['MSFT', 'BA', 'V']].iloc[1219:].to_numpy() * others_units).sum(axis=1)) +equity_pnl = pd.Series(data=portfolio_pnl.cumsum(), index=returns_sample['AAPL'].iloc[1219:].index) + +import matplotlib.pyplot as plt +fig, ax = plt.subplots(nrows=3, dpi=300, figsize=(10, 7), gridspec_kw={'height_ratios': [0.5, 0.2, 0.7]}, sharex=True) +ax[0].plot(stocks_universe['AAPL'].iloc[1200:] / stocks_universe['AAPL'].iloc[1200], label='Target Stock Price') +ax[0].plot(stocks_universe['MSFT'].iloc[1200:] / stocks_universe['MSFT'].iloc[1200], label='Cohort Stock 2', linewidth=1) +ax[0].plot(stocks_universe['BA'].iloc[1200:] / stocks_universe['BA'].iloc[1200], label='Cohort Stock 3', linewidth=1) +ax[0].plot(stocks_universe['V'].iloc[1200:] / stocks_universe['V'].iloc[1200], label='Cohort Stock 4',linewidth=1) +ax[1].plot(positions, label='positions') +ax[2].plot(equity_pnl, label='P&L', linewidth=1) + +plt.tight_layout() +ax[0].legend() +ax[2].legend() +fig.show() \ No newline at end of file From 1e79d3e252d0c91d98268c9f02eb5692eaba283d Mon Sep 17 00:00:00 2001 From: hansenpei Date: Wed, 17 Feb 2021 11:23:20 -0500 Subject: [PATCH 003/103] Update comments --- arbitragelab/copula_approach/vinecop_strategy.py | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/arbitragelab/copula_approach/vinecop_strategy.py b/arbitragelab/copula_approach/vinecop_strategy.py index dc5e79bb..6d36302b 100644 --- a/arbitragelab/copula_approach/vinecop_strategy.py +++ b/arbitragelab/copula_approach/vinecop_strategy.py @@ -191,7 +191,7 @@ def get_cur_pos_bollinger(self, returns_slice: pd.DataFrame, cdfs: List[Callable lower_threshold=init_mean - threshold_std*init_std) new_position = self._signal_to_position(past_pos, signal) - return new_position, cur_mpi + return new_position, cur_cmpi @staticmethod def positions_to_units_cohort(prices_df: pd.DataFrame, positions: pd.Series, pv_target_idx: int = 1, @@ -291,7 +291,7 @@ def positions_to_units_cohort(prices_df: pd.DataFrame, positions: pd.Series, pv_ import time start_time = time.time() cvcs = CVineCopStrat(cvinecop=cvinecop) -# mpis = cvcs.calc_mpi(returns=test_returns, cdfs=cdfs, subtract_mean=True) +mpis = cvcs.calc_mpi(returns=test_returns, cdfs=cdfs, subtract_mean=True) print("--- %s seconds ---" % (time.time() - start_time)) #%% start_time = time.time() @@ -302,6 +302,7 @@ def positions_to_units_cohort(prices_df: pd.DataFrame, positions: pd.Series, pv_ print("--- %s seconds ---" % (time.time() - start_time)) #%% import matplotlib.pyplot as plt +plt.style.use('seaborn') fig, ax = plt.subplots(nrows=3, dpi=300, figsize=(10, 7), gridspec_kw={'height_ratios': [0.5, 0.2, 0.7]}, sharex=True) ax[0].plot(stocks_universe['AAPL'].iloc[1200:] / stocks_universe['AAPL'].iloc[1200], label='Target Stock Price') ax[0].plot(stocks_universe['MSFT'].iloc[1200:] / stocks_universe['MSFT'].iloc[1200], label='Cohort Stock 2', linewidth=1) @@ -309,9 +310,9 @@ def positions_to_units_cohort(prices_df: pd.DataFrame, positions: pd.Series, pv_ ax[0].plot(stocks_universe['V'].iloc[1200:] / stocks_universe['V'].iloc[1200], label='Cohort Stock 4',linewidth=1) ax[1].plot(positions, label='positions') ax[2].plot(mpis.cumsum(), label='CMPI') -ax[2].plot(bband['LowerBound'], label='B Band Lower Bound', linewidth=1, color='brown') +ax[2].plot(bband['LowerBound'], label='B Band Bound', linewidth=1, color='brown') ax[2].plot(bband['Mean'], label='B Band Mean') -ax[2].plot(bband['UpperBound'], label='B Band Upper Bound', linewidth=1, color='brown') +ax[2].plot(bband['UpperBound'], linewidth=1, color='brown') plt.tight_layout() ax[0].legend() ax[2].legend() From fc46e320b011a25d9904739df51d94d9b18d718e Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 2 Mar 2021 19:36:23 +0530 Subject: [PATCH 004/103] First Commit with working Partner Selection Implementation --- .../vine_copula_partner_selection.py | 324 ++++++++++++++++++ .../vine_copula_partner_selection_utils.py | 166 +++++++++ tests/test_data/sp500_2016_test.csv | 250 ++++++++++++++ tests/test_partner_selection.py | 41 +++ 4 files changed, 781 insertions(+) create mode 100644 arbitragelab/copula_approach/vine_copula_partner_selection.py create mode 100644 arbitragelab/copula_approach/vine_copula_partner_selection_utils.py create mode 100644 tests/test_data/sp500_2016_test.csv create mode 100644 tests/test_partner_selection.py diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py new file mode 100644 index 00000000..620563fd --- /dev/null +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -0,0 +1,324 @@ +import itertools +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +import seaborn as sns + +from statsmodels.distributions.empirical_distribution import ECDF +from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, multivariate_rho, diagonal_measure, extremal_measure, get_co_variance_matrix + + +class PartnerSelection: + """ + Implementation of the Partner Selection procedures proposed in Section 3.1.1 in the following paper. + + 3 partner stocks are selected for a target stock based on four different approaches namely, Traditional approach, + Extended approach,Geometric approach and Extremal approach. + https://www.econstor.eu/bitstream/10419/147450/1/870932616.pdf + """ + + def __init__(self, prices: pd.DataFrame): + """ + Inputs the price series required for further calculations. + Also includes preprocessing steps described in the paper, before starting the Partner Selection procedures. + These steps include, finding the returns and ranked returns of the stocks, and calculating the top 50 + correlated stocks for each stock in the universe. + + :param prices: (pd.DataFrame): Contains price series of all stocks in universe + """ + + if len(prices) == 0: + raise Exception("Input does not contain any data") + + if not isinstance(prices, pd.DataFrame): + raise Exception("Partner Selection Class requires a pandas DataFrame as input") + + self.universe = prices # Contains daily prices for all stocks in universe. + self.returns, self.ranked_returns = self._get_returns() # Daily returns and corresponding ranked returns. + + # Correlation matrix containing all stocks in universe + self.correlation_matrix = self._correlation() + # For each stock in universe, tickers of top 50 most correlated stocks are stored + self.top_50_correlations = self._top_50_tickers() + # Quadruple combinations for all stocks in universe + self.all_quadruples = self._generate_all_quadruples() + + def _correlation(self) -> pd.DataFrame: + """ + Calculates correlation between all stocks in universe. + + :return: (pd.DataFrame) : Correlation Matrix + """ + + return self.ranked_returns.corr(method='pearson') # Pearson or spearman,we get same results as input is ranked + + def _get_returns(self) -> (pd.DataFrame, pd.DataFrame): + """ + Calculating daily returns and ranked daily returns of the stocks. + + :return (tuple): + returns_df : (pd.DataFrame) : Dataframe consists of daily returns + returns_df_ranked : (pd.DataFrame) : Dataframe consists of ranked daily returns between [0,1] + """ + + returns_df = self.universe.pct_change() + returns_df = returns_df.replace([np.inf, -np.inf], np.nan).ffill().dropna() + + # Calculating rank of daily returns for each stock. 'first' method is used to assign ranks in order they appear + returns_df_ranked = returns_df.rank(axis=0, method='first', pct=True) + return returns_df, returns_df_ranked + + def _top_50_tickers(self) -> pd.DataFrame: + """ + Calculates the top 50 correlated stocks for each target stock. + + :return: (pd.DataFrame) : Dataframe consisting of 50 columns for each stock in the universe + """ + + def tickers_list(col): + """ + Returns list of tickers ordered according to correlations with target. + """ + # Sort the column data in descending order and return the index of top 50 rows. + return col.sort_values(ascending=False)[1:51].index.to_list() + + # Returns DataFrame with all stocks as indices and their respective top 50 correlated stocks as columns. + return self.correlation_matrix.apply(tickers_list, axis=0).T + + def _generate_all_quadruples(self) -> pd.DataFrame: + """ + Method generates unique quadruples for all target stocks in universe. + + :return: (pd.DataFrame) : consists of all quadruples for every target stock + """ + + return self.top_50_correlations.apply(self._generate_all_quadruples_helper, axis=1) + + @staticmethod + def _generate_all_quadruples_helper(row: pd.Series) -> list: + """ + Helper function which generates unique quadruples for each target stock. + + :param row: (pd.Series) : list of 50 partner stocks + :return: (list) : quadruples + """ + + target = row.name + quadruples = [] + for triple in itertools.combinations(row, 3): + quadruples.append([target] + list(triple)) + return quadruples + + # Method 1 + def traditional(self, n_targets=5) -> list: + """ + This method implements the first procedure described in Section 3.1.1. + For all possible quadruples of a given stock, we calculate the sum of all pairwise correlations. + For every target stock the quadruple with the highest sum is returned. + + :param n_targets: (int) : number of target stocks to select + :return output_matrix: list: List of all selected quadruples + """ + + output_matrix = [] # Stores the final set of quadruples. + # Iterating on the top 50 indices for each target stock. + for target in self.top_50_correlations.index[:n_targets]: + max_sum_correlations = 0 # Variable used to extract the desired maximum value + final_quadruple = None # Stores the final desired quadruple + + # Iterating on all unique quadruples generated for a target + for quadruple in self.all_quadruples[target]: + sum_correlations = get_sum_correlations(self.correlation_matrix, quadruple) + if sum_correlations > max_sum_correlations: + max_sum_correlations = sum_correlations + final_quadruple = quadruple + + print(final_quadruple) + # Appending the final quadruple for each target to the output matrix + output_matrix.append(final_quadruple) + + return output_matrix + + # Method 2 + def extended(self, n_targets=5) -> list: + """ + This method implements the second procedure described in Section 3.1.1. + It involves calculating the multivariate version of Spearman's correlation + for all possible quadruples of a given stock. + For every target stock the quadruple with the highest correlation is returned. + + :param n_targets: (int) : number of target stocks to select + :return output_matrix: list: List of all selected quadruples + """ + + u = self.returns.copy() # Generating ranked returns from quantiles using statsmodels ECDF + for column in self.returns.columns: + ecdf = ECDF(self.returns.loc[:, column]) + u[column] = ecdf(self.returns.loc[:, column]) + + output_matrix = [] # Stores the final set of quadruples. + # Iterating on the top 50 indices for each target stock. + for target in self.top_50_correlations.index[:n_targets]: + max_correlation = -np.inf # Variable used to extract the desired maximum value + final_quadruple = None # Stores the final desired quadruple + + # Iterating on all unique quadruples generated for a target + for quadruple in self.all_quadruples[target]: + correlation = multivariate_rho(u[quadruple]) + if correlation > max_correlation: + max_correlation = correlation + final_quadruple = quadruple + + print(final_quadruple) + # Appending the final quadruple for each target to the output matrix + output_matrix.append(final_quadruple) + + return output_matrix + + # Method 3 + def geometric(self, n_targets=5) -> list: + """ + This method implements the third procedure described in Section 3.1.1. + It involves calculating the four dimensional diagonal measure for all possible quadruples of a given stock. + For every target stock the quadruple with the lowest diagonal measure is returned. + + :param n_targets: (int) : number of target stocks to select + :return output_matrix: list: List of all selected quadruples + """ + + output_matrix = [] # Stores the final set of quadruples. + # Iterating on the top 50 indices for each target stock. + for target in self.top_50_correlations.index[:n_targets]: + min_measure = np.inf # Variable used to extract the desired minimum value + final_quadruple = None # Stores the final desired quadruple + + # Iterating on all unique quadruples generated for a target + for quadruple in self.all_quadruples[target]: + measure = diagonal_measure(self.ranked_returns[quadruple]) + if measure < min_measure: + min_measure = measure + final_quadruple = quadruple + print(final_quadruple) + # Appending the final quadruple for each target to the output matrix + output_matrix.append(final_quadruple) + + return output_matrix + + # Method 4 + def extremal(self, n_targets=5) -> list: + """ + This method implements the fourth procedure described in Section 3.1.1. + It involves calculating a non-parametric test statistic based on Mangold (2015) to measure the + degree of deviation from independence. Main focus of this measure is the occurrence of joint extreme events. + + :param n_targets: (int) : number of target stocks to select + :return output_matrix: list: List of all selected quadruples + """ + + co_variance_matrix = get_co_variance_matrix() + output_matrix = [] # Stores the final set of quadruples. + # Iterating on the top 50 indices for each target stock. + for target in self.top_50_correlations.index[:n_targets]: + max_measure = -np.inf # Variable used to extract the desired maximum value + final_quadruple = None # Stores the final desired quadruple + + # Iterating on all unique quadruples generated for a target + for quadruple in self.all_quadruples[target]: + measure = extremal_measure(self.ranked_returns[quadruple], co_variance_matrix) + if measure > max_measure: + max_measure = measure + final_quadruple = quadruple + print(final_quadruple) + # Appending the final quadruple for each target to the output matrix + output_matrix.append(final_quadruple) + + return output_matrix + + def plot_selected_pairs(self, quadruples: list): + """ + Plots the final selection of quadruples. + :param quadruples: List of quadruples + """ + + if quadruples is None: + raise Exception("Input list is empty") + + fig, axs = plt.subplots(len(quadruples), + figsize=(15, 3 * len(quadruples))) + + plt.subplots_adjust(hspace=0.6) + for i, quadruple in enumerate(quadruples): + data = self.universe.loc[:, quadruple].apply(lambda x: np.log(x).diff()).cumsum() + sns.lineplot(ax=axs[i], data=data, legend=quadruple) + axs[i].set_title(f'Final Quadruple of stocks with {quadruple[0]} as target') + axs[i].set_ylabel('Cumulative Daily Returns') + plt.show() + + def plot_all_target_measures(self, target: str, procedure: str): + """ + Plots a scatterplot showing measures calculated for all possible quadruples of a given target stock. + :param target: (str) : target stock ticker + :param procedure: (str) : name of procedure for calculating measure + """ + + if procedure not in ('traditional', 'extended', 'geometric', 'extremal'): + raise Exception("Please enter a valid procedure name, i.e ('traditional', 'extended', 'geometric', " + "'extremal') ") + + measures_list = [] + quadruples = self.all_quadruples[target] # List of all quadruples + final_quadruple = None + final_measure = -np.inf + + co_variance_matrix = None + u = None + + # Preprocessing steps for some approaches + if procedure == 'extremal': + co_variance_matrix = get_co_variance_matrix() + if procedure == 'extended': + u = self.returns.copy() # Generating ranked returns from quantiles using statsmodels ECDF + for column in self.returns.columns: + ecdf = ECDF(self.returns.loc[:, column]) + u[column] = ecdf(self.returns.loc[:, column]) + if procedure == 'geometric': + final_measure = np.inf + + for quadruple in quadruples: + # Separate functionality for geometric approach because here the minimum measure is required. + if procedure == 'geometric': + measure = diagonal_measure(self.ranked_returns[quadruple]) + measures_list.append(measure) + if measure < final_measure: + final_measure = measure + final_quadruple = quadruple + continue + + measure = 0 + if procedure == 'traditional': + measure = get_sum_correlations(self.correlation_matrix, quadruple) + elif procedure == 'extended': + measure = multivariate_rho(u[quadruple]) + elif procedure == 'extremal': + measure = extremal_measure(self.ranked_returns[quadruple], co_variance_matrix) + + measures_list.append(measure) # Storing all calculated measures + if measure > final_measure: + final_measure = measure + final_quadruple = quadruple + + print(final_quadruple) + + # Code for plotting the final list of calculated measures + plt.figure(figsize=(20, 6)) + data = pd.DataFrame(measures_list, columns=['measure']) + data['indices'] = range(len(measures_list)) + data['hue'] = [0] * len(data) + if procedure == 'geometric': + data.loc[data['measure'].idxmin(), 'hue'] = 1 + else: + data.loc[data['measure'].idxmax(), 'hue'] = 1 + sns.scatterplot(x='indices', y='measure', data=data, alpha=0.5, hue='hue', size='hue', + sizes={0: 5, 1: 40}, legend=False) + plt.title(f"Measures calculated from {procedure} approach for all quadruples of target {target}") + plt.show() diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py new file mode 100644 index 00000000..5c7d5da2 --- /dev/null +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -0,0 +1,166 @@ +import itertools +import numpy as np +import pandas as pd +import scipy + + +def get_sector_data(quadruple, constituents): + """ + Function returns Sector and Sub sector information from tickers. + """ + try: + return constituents.loc[quadruple, ['Security', 'GICS Sector', 'GICS Sub-Industry']] + except KeyError: + return None + + +def get_sum_correlations(corr_matrix, quadruple: list) -> float: + """ + Helper function for traditional approach to partner selection. + Calculates sum of pairwise correlations between all stocks in the quadruple. + + :param corr_matrix: Correlation Matrix + :param quadruple: (list) : list of 4 stock tickers + :return: (float) : sum of correlations + """ + + return (corr_matrix.loc[quadruple, quadruple].sum().sum() - len(quadruple)) / 2 + + +def multivariate_rho(u: pd.DataFrame) -> float: + """ + Helper function for extended approach to partner selection. Calculates 3 proposed estimators for + high dimensional generalization for Spearman's rho. These implementations are present in + Schmid, F., Schmidt, R., 2007. Multivariate extensions of Spearman’s rho and related statis-tics. + + :param u: (pd.DataFrame) : ranked returns of quadruple + :return: (float) : mean of the three estimators of multivariate rho + """ + + n, d = u.shape # n : Number of samples, d : Number of stocks + h_d = (d + 1) / ((2 ** d) - d - 1) + + # # Calculating the first estimator of multivariate rho + sum_1 = np.prod(1 - u, axis=1).sum() + rho_1 = h_d * (-1 + (((2 ** d) / n) * sum_1)) + + # # Calculating the second estimator of multivariate rho + sum_2 = np.prod(u, axis=1).sum() + rho_2 = h_d * (-1 + (((2 ** d) / n) * sum_2)) + + # Calculating the third estimator of multivariate rho + pairs = [x for x in itertools.combinations(range(u.shape[-1]), 2)] + sum_3 = np.sum([(1 - u.iloc[:, k]) * (1 - u.iloc[:, l]) for (k, l) in pairs]) + dc2 = scipy.special.comb(d, 2, exact=True) + rho_3 = -3 + (12 / (n * dc2)) * sum_3 + + return (rho_1 + rho_2 + rho_3) / 3 + + +def distance_calc(a, ba, x): + """ + Helper function to calculate Euclidean distance between Point and diagonal used to calculate diagonal measure. + :param a: Origin (0,0,0,0) + :param ba: d-dimensional Diagonal + :param x: list of points on d-dimensions + :return: + """ + pa = x - a # Shape : (n,d), pa represents vector from point p to point a + t = np.dot(pa, ba) / np.dot(ba.T, ba) + return np.linalg.norm(pa - np.dot(t, ba.T), ord=2, axis=1) + + +def diagonal_measure(points) -> float: + """ + Helper function for geometric approach to partner selection. Calculates the sum of Euclidean distances + from the relative ranks to the (hyper-)diagonal in four dimensional space for a given target stock. + + Reference for calculating the euclidean distance from a point to diagonal + https://in.mathworks.com/matlabcentral/answers/76727-how-can-i-calculate-distance-between-a-point-and-a-line-in-4d-or-space-higer-than-3d + + :param points: (pd.DataFrame) : ranked returns of 4 stock tickers + :return total_distance: (float) : total euclidean distance + """ + n, d = points.shape # n : Number of samples, d : Number of stocks + a = np.zeros((1, d)) # Point a denotes origin which is present on hyper-diagonal + b = np.ones((1, d)) # Point b denotes point (1,1,1,1) on hyper-diagonal + ba = (b - a).T # ba represents the hyper-diagonal + total_distance = distance_calc(a, ba, points).sum() + return total_distance + + +def extremal_measure(u, co_variance_matrix): + """ + Helper function to calculate chi-squared test statistic based on p-dimensional Nelsen copulas. + Specifically, proposition 3.3 from Mangold (2015) is implemented for 4 dimensions. + :param u: (pd.DataFrame) : ranked returns of stocks in quadruple. + :param co_variance_matrix: (np.array) : Covariance matrix + :return: test statistic + """ + u = u.to_numpy() + n = u.shape[0] + + # Calculating array T_(4,n) from proposition 3.3 + t = t_calc(u).mean(axis=1).reshape(-1, 1) # Shape : (16, 1), Taking the mean w.r.t n + # Calculating the final test statistic + t_test_statistic = n * np.matmul(t.T, np.matmul(co_variance_matrix, t)) + return t_test_statistic[0, 0] + + +def get_co_variance_matrix(): + """ + Calculates 16x16 dimensional covariance matrix. Since the matrix is symmetric, only the integrals + in the upper triangle are calculated. The remaining values are filled from the transpose. + """ + co_variance_matrix = np.zeros((16, 16)) + for i, l1 in enumerate(itertools.product([1, 2], [1, 2], [1, 2], [1, 2])): + for j, l2 in enumerate(itertools.product([1, 2], [1, 2], [1, 2], [1, 2])): + if j < i: + # Integrals in lower triangle are skipped. + continue + + # Numerical Integration of 4 dimensions + co_variance_matrix[i, j] = scipy.integrate.nquad(variance_integral_func, [(0, 1)] * 4, args=(l1, l2))[0] + + inds = np.tri(16, k=-1, dtype=bool) # Storing the indices of elements in lower triangle. + co_variance_matrix[inds] = co_variance_matrix.T[inds] + return np.linalg.inv(co_variance_matrix) + + +def t_calc(u): + """ + Calculates T_(4,n) as seen in proposition 3.3. Each of the 16 rows in the array are appended to output and + returned as numpy array. + :param u: + :return: (np.array) of Shape (16, n) + """ + output = [] + for l in itertools.product([1, 2], [1, 2], [1, 2], [1, 2]): + # Equation form for each one of u1,u2,u3,u4 after partial differentials are calculated and multiplied + # together. + res = func(u[:, 0], l[0]) * func(u[:, 1], l[1]) * func(u[:, 2], l[2]) * func(u[:, 3], l[3]) + output.append(res) + + return np.array(output) # Shape (16, n) + + +def func(t, value): + """ + Function returns equation form of respective variable after partial differentiation. + All variables in the differential equations are in one of two forms. + :param t: (np.array) Variable + :param value: (int) Flag denoting equation form of variable + :return: + """ + if value == 1: + return (t - 1) * (3 * t - 1) + if value == 2: + return t * (2 - 3 * t) + + +def variance_integral_func(u1, u2, u3, u4, l1, l2): + """ + Calculates Integrand for covariance matrix 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+2016-12-30,45.56000137329102,46.68999862670898,169.1199951171875,28.95499992370605 diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py new file mode 100644 index 00000000..ccaee195 --- /dev/null +++ b/tests/test_partner_selection.py @@ -0,0 +1,41 @@ +import os +import pandas as pd +import unittest + +from statsmodels.distributions.empirical_distribution import ECDF +from arbitragelab.copula_approach.vine_copula_partner_selection import PartnerSelection +from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, multivariate_rho, diagonal_measure, extremal_measure, get_co_variance_matrix + + +class PartnerSelectionTests(unittest.TestCase): + + @classmethod + def setUpClass(cls) -> None: + + project_path = os.path.dirname(__file__) + data_path = project_path + '/test_data/sp500_2016_test.csv' + cls.quadruple = ['A', 'AAL', 'AAP', 'AAPL'] + df = pd.read_csv(data_path, parse_dates=True, index_col='Date').dropna() + cls.ps = PartnerSelection(df) + + cls.u = cls.ps.returns.copy() + for column in cls.ps.returns.columns: + ecdf = ECDF(cls.ps.returns.loc[:, column]) + cls.u[column] = ecdf(cls.ps.returns.loc[:, column]) + + cls.co_variance_matrix = get_co_variance_matrix() + + def test_sum_correlations(self): + self.assertEqual(round(get_sum_correlations(self.ps.correlation_matrix, self.quadruple), 4), 1.9678) + + def test_multivariate_rho(self): + self.assertEqual(round(multivariate_rho(self.u[self.quadruple]), 4), 0.3114) + + def test_diagonal_measure(self): + self.assertEqual(round(diagonal_measure(self.ps.ranked_returns[self.quadruple]), 4), 91.9374) + + def test_extremal_measure(self): + self.assertEqual(round(extremal_measure(self.ps.ranked_returns[self.quadruple], self.co_variance_matrix), 4), 108.5128) + +if __name__ == '__main__': + unittest.main() From 3339c54ec593a6bfd8b7494e4670259a590a10c9 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 3 Mar 2021 15:46:04 +0530 Subject: [PATCH 005/103] Added first draft of sphinx documentation for partner selection --- .../copula_approach/partner_selection.rst | 72 +++++++++++++++++++ docs/source/index.rst | 1 + 2 files changed, 73 insertions(+) create mode 100644 docs/source/copula_approach/partner_selection.rst diff --git a/docs/source/copula_approach/partner_selection.rst b/docs/source/copula_approach/partner_selection.rst new file mode 100644 index 00000000..06efd7b4 --- /dev/null +++ b/docs/source/copula_approach/partner_selection.rst @@ -0,0 +1,72 @@ +.. _copula_approach-partner_selection: + +.. Note:: + These descriptions closely follow the following papers: + + `Statistical Arbitrage with Vine Copulas. (2016) `__ by Stübinger, Mangold, and Krauss. + + `Multivariate extensions of Spearman’s rho and related statistics. (2007) `__ by Schmid, F., Schmidt, R. + + `A multivariate linear rank test of independence based on a multiparametric copula with cubic sections. (2015) `__ by Mangold, B. + +======================================== +Vine Copula Partner Selection Approaches +======================================== + +This module contains implementation of the four partner selection approaches mentioned in Section 3.1.1 of Statistical Arbitrage with Vine Copulas. + +In this paper[1], Stubinger, Mangold and Krauss developed a multivariate statistical arbitrage strategy based on vine copulas - a highly flexible instrument for linear and nonlinear multivariate dependence modeling. Pairs trading is a relative-value arbitrage strategy, where an investor seeks to profit from mean-reversion properties of the price spread between two co-moving securities. Existing literature focused on using bivariate copulas to model the dependence structure between two stock return time series, and to identify mispricings that can potentially be exploited in a pairs trading application. + +This paper proposes a multivariate copula-based statistical arbitrage framework, where specifically, for each stock in the S&P 500 data base, the three most suitable partners are selected by leveraging different selection criteria. Then, the multivariate copula models are benchmarked to capture the dependence structure of the selected quadruples. Later on, the paper focusses on the generation of trading signals and backtesting. + +Introduction +############ + +This module will focus on the various Partner Selection procedures and their implementations, as described in the paper. For every stock in the S&P 500, a partner triple is identified based on adequate measures of association. The following four partner selection approaches are implemented : + +- Traditional Approach - baseline approach where the high dimensional relation between the four stocks is approximated by their pairwise bivariate correlations via Spearman’s :math:`\rho`; + +- Extended Approach - calculating the multivariate version of Spearman’s :math:`\rho` based on Schmid and Schmidt (2007)[2]; + +- Geometric Approach - involves calculating the sum of euclidean distances from the 4-dimensional hyper-diagonal; + +- Extremal Approach - involves calculating a non-parametric :math:`\chi^2` test statistic based on Mangold (2015)[3] to measure the degree of deviation from independence. + +Firstly, all measures of association are calculated using the ranks of the daily discrete returns of our samples. Ranked transformation provides robustness against outliers. Secondly, only the top 50 most highly correlated stocks are taken into consideration for each target stock, to reduce the computational burden. + +Traditional Approach +******************** + +Extended Approach +******************** + +Geometric Approach +******************** + +Extremal Approach +******************** + + +Implementation +############## + + + + +Research Notebooks +################## + +The following research notebook can be used to better understand the partner selection approaches described above. + +* `Vine Copula Partner Selection Approaches`_ + +.. _`Vine Copula Partner Selection Approaches`: + +References +########## + +* `Stübinger, Johannes; Mangold, Benedikt; Krauss, Christopher; 2016. Statistical Arbitrage with Vine Copulas. `__ +* `Schmid, F., Schmidt, R., 2007. Multivariate extensions of Spearman’s rho and related statis-tics. Statistics & Probability Letters 77 (4), 407–416. `__ +* `Mangold, B., 2015. A multivariate linear rank test of independence based on a multipara-metric copula with cubic sections. IWQW Discussion Paper Series, University of Erlangen-N ̈urnberg. `__ + + diff --git a/docs/source/index.rst b/docs/source/index.rst index 6051154f..c2bf26f4 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -106,6 +106,7 @@ This project is licensed under an all rights reserved licence. copula_approach/basic_trading_strategy copula_approach/mispricing_index_strategy copula_approach/utility_functions + copula_approach/partner_selection .. toctree:: :maxdepth: 2 From 160b31ab59990c53353c95bed774eb2a2cb44a40 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 3 Mar 2021 16:46:53 +0530 Subject: [PATCH 006/103] Code Changes for pylint 10/10 --- .../vine_copula_partner_selection.py | 24 ++++++++++++--- .../vine_copula_partner_selection_utils.py | 16 +++++++--- tests/test_partner_selection.py | 30 ++++++++++++++++--- 3 files changed, 58 insertions(+), 12 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 620563fd..07ba5805 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -1,3 +1,7 @@ +""" +Module for implementing partner selection approaches for vine copulas. +""" +# pylint: disable = invalid-name import itertools import matplotlib.pyplot as plt import numpy as np @@ -5,7 +9,8 @@ import seaborn as sns from statsmodels.distributions.empirical_distribution import ECDF -from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, multivariate_rho, diagonal_measure, extremal_measure, get_co_variance_matrix +from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, \ + multivariate_rho, diagonal_measure, extremal_measure, get_co_variance_matrix class PartnerSelection: @@ -243,7 +248,7 @@ def plot_selected_pairs(self, quadruples: list): if quadruples is None: raise Exception("Input list is empty") - fig, axs = plt.subplots(len(quadruples), + _, axs = plt.subplots(len(quadruples), figsize=(15, 3 * len(quadruples))) plt.subplots_adjust(hspace=0.6) @@ -276,12 +281,12 @@ def plot_all_target_measures(self, target: str, procedure: str): # Preprocessing steps for some approaches if procedure == 'extremal': co_variance_matrix = get_co_variance_matrix() - if procedure == 'extended': + elif procedure == 'extended': u = self.returns.copy() # Generating ranked returns from quantiles using statsmodels ECDF for column in self.returns.columns: ecdf = ECDF(self.returns.loc[:, column]) u[column] = ecdf(self.returns.loc[:, column]) - if procedure == 'geometric': + elif procedure == 'geometric': final_measure = np.inf for quadruple in quadruples: @@ -309,6 +314,17 @@ def plot_all_target_measures(self, target: str, procedure: str): print(final_quadruple) + self._plot_all_target_measures_helper(measures_list, target, procedure) + + @staticmethod + def _plot_all_target_measures_helper(measures_list: list, target:str, procedure: str): + """ + Helper Method for self.plot_all_target_measures. + :measures_list: (list) : List of calculated measures for all quadruples of a target + :param target: (str) : target stock ticker + :param procedure: (str) : name of procedure for calculating measure + """ + # Code for plotting the final list of calculated measures plt.figure(figsize=(20, 6)) data = pd.DataFrame(measures_list, columns=['measure']) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index 5c7d5da2..4ac40204 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -1,3 +1,7 @@ +""" +Utils for implementing partner selection approaches for vine copulas. +""" +# pylint: disable = invalid-name import itertools import numpy as np import pandas as pd @@ -49,7 +53,7 @@ def multivariate_rho(u: pd.DataFrame) -> float: rho_2 = h_d * (-1 + (((2 ** d) / n) * sum_2)) # Calculating the third estimator of multivariate rho - pairs = [x for x in itertools.combinations(range(u.shape[-1]), 2)] + pairs = itertools.combinations(range(u.shape[-1]), 2) sum_3 = np.sum([(1 - u.iloc[:, k]) * (1 - u.iloc[:, l]) for (k, l) in pairs]) dc2 = scipy.special.comb(d, 2, exact=True) rho_3 = -3 + (12 / (n * dc2)) * sum_3 @@ -81,7 +85,7 @@ def diagonal_measure(points) -> float: :param points: (pd.DataFrame) : ranked returns of 4 stock tickers :return total_distance: (float) : total euclidean distance """ - n, d = points.shape # n : Number of samples, d : Number of stocks + d = points.shape[-1] # d : Number of stocks a = np.zeros((1, d)) # Point a denotes origin which is present on hyper-diagonal b = np.ones((1, d)) # Point b denotes point (1,1,1,1) on hyper-diagonal ba = (b - a).T # ba represents the hyper-diagonal @@ -152,10 +156,14 @@ def func(t, value): :param value: (int) Flag denoting equation form of variable :return: """ + + res = None if value == 1: - return (t - 1) * (3 * t - 1) + res = (t - 1) * (3 * t - 1) if value == 2: - return t * (2 - 3 * t) + res = t * (2 - 3 * t) + + return res def variance_integral_func(u1, u2, u3, u4, l1, l2): diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py index ccaee195..42dc01df 100644 --- a/tests/test_partner_selection.py +++ b/tests/test_partner_selection.py @@ -1,22 +1,32 @@ +""" +Tests for the partner selection approaches from the Copula module. +""" import os -import pandas as pd import unittest +import pandas as pd from statsmodels.distributions.empirical_distribution import ECDF from arbitragelab.copula_approach.vine_copula_partner_selection import PartnerSelection -from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, multivariate_rho, diagonal_measure, extremal_measure, get_co_variance_matrix +from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, multivariate_rho, \ + diagonal_measure, extremal_measure, get_co_variance_matrix class PartnerSelectionTests(unittest.TestCase): + """ + Tests Partner Selection Approaches. + """ @classmethod def setUpClass(cls) -> None: + """ + Creates dataframes with returns and quantile data to work with corresponding test cases. + """ project_path = os.path.dirname(__file__) data_path = project_path + '/test_data/sp500_2016_test.csv' cls.quadruple = ['A', 'AAL', 'AAP', 'AAPL'] - df = pd.read_csv(data_path, parse_dates=True, index_col='Date').dropna() - cls.ps = PartnerSelection(df) + prices = pd.read_csv(data_path, parse_dates=True, index_col='Date').dropna() + cls.ps = PartnerSelection(prices) cls.u = cls.ps.returns.copy() for column in cls.ps.returns.columns: @@ -26,15 +36,27 @@ def setUpClass(cls) -> None: cls.co_variance_matrix = get_co_variance_matrix() def test_sum_correlations(self): + """ + Tests Traditional Approach. + """ self.assertEqual(round(get_sum_correlations(self.ps.correlation_matrix, self.quadruple), 4), 1.9678) def test_multivariate_rho(self): + """ + Tests Extended Approach. + """ self.assertEqual(round(multivariate_rho(self.u[self.quadruple]), 4), 0.3114) def test_diagonal_measure(self): + """ + Tests Geometric Approach. + """ self.assertEqual(round(diagonal_measure(self.ps.ranked_returns[self.quadruple]), 4), 91.9374) def test_extremal_measure(self): + """ + Tests Extremal Approach. + """ self.assertEqual(round(extremal_measure(self.ps.ranked_returns[self.quadruple], self.co_variance_matrix), 4), 108.5128) if __name__ == '__main__': From e8dff5bf4045111a2d2fc74d14c67a1019137b76 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 3 Mar 2021 18:12:29 +0530 Subject: [PATCH 007/103] Added unittests for plotting methods. Made necessary changes to plotting methods. --- .../vine_copula_partner_selection.py | 26 +- .../vine_copula_partner_selection_utils.py | 2 +- .../test_data/sp500_constituents-detailed.csv | 506 ++++++++++++++++++ tests/test_partner_selection.py | 24 +- 4 files changed, 548 insertions(+), 10 deletions(-) create mode 100644 tests/test_data/sp500_constituents-detailed.csv diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 07ba5805..447b9d72 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -252,12 +252,21 @@ def plot_selected_pairs(self, quadruples: list): figsize=(15, 3 * len(quadruples))) plt.subplots_adjust(hspace=0.6) - for i, quadruple in enumerate(quadruples): + + if len(quadruples) == 1: + quadruple = quadruples[0] data = self.universe.loc[:, quadruple].apply(lambda x: np.log(x).diff()).cumsum() - sns.lineplot(ax=axs[i], data=data, legend=quadruple) - axs[i].set_title(f'Final Quadruple of stocks with {quadruple[0]} as target') - axs[i].set_ylabel('Cumulative Daily Returns') - plt.show() + sns.lineplot(ax=axs, data=data, legend=quadruple) + axs.set_title(f'Final Quadruple of stocks with {quadruple[0]} as target') + axs.set_ylabel('Cumulative Daily Returns') + else: + for i, quadruple in enumerate(quadruples): + data = self.universe.loc[:, quadruple].apply(lambda x: np.log(x).diff()).cumsum() + sns.lineplot(ax=axs[i], data=data, legend=quadruple) + axs[i].set_title(f'Final Quadruple of stocks with {quadruple[0]} as target') + axs[i].set_ylabel('Cumulative Daily Returns') + + return axs def plot_all_target_measures(self, target: str, procedure: str): """ @@ -314,7 +323,7 @@ def plot_all_target_measures(self, target: str, procedure: str): print(final_quadruple) - self._plot_all_target_measures_helper(measures_list, target, procedure) + return self._plot_all_target_measures_helper(measures_list, target, procedure) @staticmethod def _plot_all_target_measures_helper(measures_list: list, target:str, procedure: str): @@ -334,7 +343,8 @@ def _plot_all_target_measures_helper(measures_list: list, target:str, procedure: data.loc[data['measure'].idxmin(), 'hue'] = 1 else: data.loc[data['measure'].idxmax(), 'hue'] = 1 - sns.scatterplot(x='indices', y='measure', data=data, alpha=0.5, hue='hue', size='hue', + ax = sns.scatterplot(x='indices', y='measure', data=data, alpha=0.5, hue='hue', size='hue', sizes={0: 5, 1: 40}, legend=False) plt.title(f"Measures calculated from {procedure} approach for all quadruples of target {target}") - plt.show() + + return ax diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index 4ac40204..b2232216 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -15,7 +15,7 @@ def get_sector_data(quadruple, constituents): try: return constituents.loc[quadruple, ['Security', 'GICS Sector', 'GICS Sub-Industry']] except KeyError: - return None + return pd.DataFrame() def get_sum_correlations(corr_matrix, quadruple: list) -> float: diff --git a/tests/test_data/sp500_constituents-detailed.csv b/tests/test_data/sp500_constituents-detailed.csv new file mode 100644 index 00000000..a74c09c8 --- /dev/null +++ b/tests/test_data/sp500_constituents-detailed.csv @@ -0,0 +1,506 @@ +Symbol,Security,SEC filings,GICS Sector,GICS Sub-Industry,Headquarters Location,Date first added,CIK,Founded +MMM,3M Company,reports,Industrials,Industrial Conglomerates,"St. Paul, Minnesota",1976-08-09,0000066740,1902 +ABT,Abbott Laboratories,reports,Health Care,Health Care Equipment,"North Chicago, Illinois",1964-03-31,0000001800,1888 +ABBV,AbbVie Inc.,reports,Health Care,Pharmaceuticals,"North Chicago, Illinois",2012-12-31,0001551152,2013 (1888) +ABMD,Abiomed,reports,Health Care,Health Care Equipment,"Danvers, Massachusetts",2018-05-31,0000815094,1981 +ACN,Accenture plc,reports,Information Technology,IT Consulting & Other Services,"Dublin, Ireland",2011-07-06,0001467373,1989 +ATVI,Activision Blizzard,reports,Communication Services,Interactive Home Entertainment,"Santa Monica, California",2015-08-31,0000718877,2008 +ADBE,Adobe Inc.,reports,Information Technology,Application Software,"San Jose, California",1997-05-05,0000796343,1982 +AMD,Advanced Micro Devices,reports,Information Technology,Semiconductors,"Santa Clara, California",2017-03-20,0000002488,1969 +AAP,Advance Auto Parts,reports,Consumer Discretionary,Automotive Retail,"Raleigh, North Carolina",2015-07-09,0001158449,1932 +AES,AES Corp,reports,Utilities,Independent Power Producers & Energy Traders,"Arlington, Virginia",1998-10-02,0000874761,1981 +AFL,Aflac,reports,Financials,Life & Health Insurance,"Columbus, Georgia",1999-05-28,0000004977,1955 +A,Agilent Technologies,reports,Health Care,Health Care Equipment,"Santa Clara, California",2000-06-05,0001090872,1999 +APD,Air Products & Chemicals,reports,Materials,Industrial Gases,"Allentown, Pennsylvania",1985-04-30,0000002969,1940 +AKAM,Akamai Technologies,reports,Information Technology,Internet Services & Infrastructure,"Cambridge, Massachusetts",2007-07-12,0001086222,1998 +ALK,Alaska Air Group Inc,reports,Industrials,Airlines,"Seattle, Washington",2016-05-13,0000766421,1985 +ALB,Albemarle Corp,reports,Materials,Specialty Chemicals,"Charlotte, North Carolina",2016-07-01,0000915913,1994 +ARE,Alexandria Real Estate Equities,reports,Real Estate,Office REITs,"Pasadena, California",2017-03-20,0001035443,1994 +ALXN,Alexion Pharmaceuticals,reports,Health Care,Pharmaceuticals,"Boston, Massachusetts",2012-05-25,0000899866,1992 +ALGN,Align Technology,reports,Health Care,Health Care Supplies,"San Jose, California",2017-06-19,0001097149,1997 +ALLE,Allegion,reports,Industrials,Building Products,"Dublin, Ireland",2013-12-02,0001579241,1908 +LNT,Alliant Energy Corp,reports,Utilities,Electric Utilities,"Madison, Wisconsin",2016-07-01,0000352541,1917 +ALL,Allstate Corp,reports,Financials,Property & Casualty Insurance,"Northfield Township, Illinois",1995-07-13,0000899051,1931 +GOOGL,Alphabet Inc. (Class A),reports,Communication Services,Interactive Media & Services,"Mountain View, California",2014-04-03,0001652044,1998 +GOOG,Alphabet Inc. (Class C),reports,Communication Services,Interactive Media & Services,"Mountain View, California",2006-04-03,0001652044,1998 +MO,Altria Group Inc,reports,Consumer Staples,Tobacco,"Richmond, Virginia",1957-03-04,0000764180,1985 +AMZN,Amazon.com Inc.,reports,Consumer Discretionary,Internet & Direct Marketing Retail,"Seattle, Washington",2005-11-18,0001018724,1994 +AMCR,Amcor plc,reports,Materials,Paper Packaging,"Warmley, Bristol, United Kingdom",2019-06-07,0001748790,2019 (1860) +AEE,Ameren Corp,reports,Utilities,Multi-Utilities,"St. Louis, Missouri",1991-09-19,0001002910,1902 +AAL,American Airlines Group,reports,Industrials,Airlines,"Fort Worth, Texas",2015-03-23,0000006201,1934 +AEP,American Electric Power,reports,Utilities,Electric Utilities,"Columbus, Ohio",1957-03-04,0000004904,1906 +AXP,American Express Co,reports,Financials,Consumer Finance,"New York, New York",1976-06-30,0000004962,1850 +AIG,American International Group,reports,Financials,Property & Casualty Insurance,"New York, New York",1980-03-31,0000005272,1919 +AMT,American Tower Corp.,reports,Real Estate,Specialized REITs,"Boston, Massachusetts",2007-11-19,0001053507,1995 +AWK,American Water Works Company Inc,reports,Utilities,Water Utilities,"Camden, New Jersey",2016-03-04,0001410636,1886 +AMP,Ameriprise Financial,reports,Financials,Asset Management & Custody Banks,"Minneapolis, Minnesota",2005-10-03,0000820027,1894 +ABC,AmerisourceBergen Corp,reports,Health Care,Health Care Distributors,"Chesterbrook, Pennsylvania",2001-08-30,0001140859,1985 +AME,AMETEK Inc.,reports,Industrials,Electrical Components & Equipment,"Berwyn, Pennsylvania",2013-09-23,0001037868,1930 +AMGN,Amgen Inc.,reports,Health Care,Biotechnology,"Thousand Oaks, California",1992-01-02,0000318154,1980 +APH,Amphenol Corp,reports,Information Technology,Electronic Components,"Wallingford, Connecticut",2008-09-30,0000820313,1932 +ADI,"Analog Devices, Inc.",reports,Information Technology,Semiconductors,"Norwood, Massachusetts",1999-10-12,0000006281,1965 +ANSS,"ANSYS, Inc.",reports,Information Technology,Application Software,"Canonsburg, Pennsylvania",2017-06-19,0001013462,1969 +ANTM,Anthem,reports,Health Care,Managed Health Care,"Indianapolis, Indiana",2002-07-25,0001156039,2014 (1946) +AON,Aon plc,reports,Financials,Insurance Brokers,"London, United Kingdom",1996-04-23,0000315293,1982 (1919) +AOS,A.O. Smith Corp,reports,Industrials,Building Products,"Milwaukee, Wisconsin",2017-07-26,0000091142,1916 +APA,Apache Corporation,reports,Energy,Oil & Gas Exploration & Production,"Houston, Texas",1997-07-28,0000006769,1954 +AAPL,Apple Inc.,reports,Information Technology,"Technology Hardware, Storage & Peripherals","Cupertino, California",1982-11-30,0000320193,1977 +AMAT,Applied Materials Inc.,reports,Information Technology,Semiconductor Equipment,"Santa Clara, California",1995-03-16,0000006951,1967 +APTV,Aptiv PLC,reports,Consumer Discretionary,Auto Parts & Equipment,"Dublin, Ireland",2012-12-24,0001521332,1994 +ADM,Archer-Daniels-Midland Co,reports,Consumer Staples,Agricultural Products,"Chicago, Illinois",1981-07-29,0000007084,1902 +ANET,Arista Networks,reports,Information Technology,Communications Equipment,"Santa Clara, California",2018-08-28,0001596532,2004 +AJG,Arthur J. Gallagher & Co.,reports,Financials,Insurance Brokers,"Rolling Meadows, Illinois",2016-05-31,0000354190,1927 +AIZ,Assurant,reports,Financials,Multi-line Insurance,"New York, New York",2007-04-10,0001267238,1892 +T,AT&T Inc.,reports,Communication Services,Integrated Telecommunication Services,"Dallas, Texas",1983-11-30 (1957-03-04),0000732717,1983 (1885) +ATO,Atmos Energy,reports,Utilities,Gas Utilities,"Dallas, Texas",2019-02-15,0000731802,1906 +ADSK,Autodesk Inc.,reports,Information Technology,Application Software,"San Rafael, California",1989-12-01,0000769397,1982 +ADP,Automatic Data Processing,reports,Information Technology,Data Processing & Outsourced Services,"Roseland, New Jersey",1981-03-31,0000008670,1949 +AZO,AutoZone Inc,reports,Consumer Discretionary,Specialty Stores,"Memphis, Tennessee",1997-01-02,0000866787,1979 +AVB,AvalonBay Communities,reports,Real Estate,Residential REITs,"Arlington, Virginia[3]",2007-01-10,0000915912,1978 +AVY,Avery Dennison Corp,reports,Materials,Paper Packaging,"Glendale, California",1987-12-31,0000008818,1990 +BKR,Baker Hughes Co,reports,Energy,Oil & Gas Equipment & Services,"Houston, Texas",2017-07-07,0001701605,2017 +BLL,Ball Corp,reports,Materials,Metal & Glass Containers,"Broomfield, Colorado",1984-10-31,0000009389,1880 +BAC,Bank of America Corp,reports,Financials,Diversified Banks,"Charlotte, North Carolina",1976-06-30,0000070858,1998 (1923 / 1874) +BK,The Bank of New York Mellon,reports,Financials,Asset Management & Custody Banks,"New York, New York",1995-03-31,0001390777,1784 +BAX,Baxter International Inc.,reports,Health Care,Health Care Equipment,"Deerfield, Illinois",1972-09-30,0000010456,1931 +BDX,Becton Dickinson,reports,Health Care,Health Care Equipment,"Franklin Lakes, New Jersey",1972-09-30,0000010795,1897 +BRK.B,Berkshire Hathaway,reports,Financials,Multi-Sector Holdings,"Omaha, Nebraska",2010-02-16,0001067983,1839 +BBY,Best Buy Co. Inc.,reports,Consumer Discretionary,Computer & Electronics Retail,"Richfield, Minnesota",1999-06-29,0000764478,1966 +BIO,Bio-Rad Laboratories,reports,Health Care,Life Sciences Tools & Services,"Hercules, California",2020-06-22,0000012208,1952 +BIIB,Biogen Inc.,reports,Health Care,Biotechnology,"Cambridge, Massachusetts",2003-11-13,0000875045,1978 +BLK,BlackRock,reports,Financials,Asset Management & Custody Banks,"New York, New York",2011-04-04,0001364742,1988 +BA,Boeing Company,reports,Industrials,Aerospace & Defense,"Chicago, Illinois",1957-03-04,0000012927,1916 +BKNG,Booking Holdings Inc,reports,Consumer Discretionary,Internet & Direct Marketing Retail,"Norwalk, Connecticut",2009-11-06,0001075531,1996 +BWA,BorgWarner,reports,Consumer Discretionary,Auto Parts & Equipment,"Auburn Hills, Michigan",2011-12-19,0000908255,1880 +BXP,Boston Properties,reports,Real Estate,Office REITs,"Boston, Massachusetts",2006-04-03,0001037540,1970 +BSX,Boston Scientific,reports,Health Care,Health Care Equipment,"Marlborough, Massachusetts[4]",1995-02-24,0000885725,1979 +BMY,Bristol-Myers Squibb,reports,Health Care,Health Care Distributors,"New York, New York",1957-03-04,0000014272,1989 +AVGO,Broadcom Inc.,reports,Information Technology,Semiconductors,"San Jose, California",2014-05-08,0001730168,1961 +BR,Broadridge Financial Solutions,reports,Information Technology,Data Processing & Outsourced Services,"Lake Success, New York",2018-06-18,0001383312,1962 +BF.B,Brown-Forman Corp.,reports,Consumer Staples,Distillers & Vintners,"Louisville, Kentucky",1982-10-31,0000014693,1870 +CHRW,C. H. Robinson Worldwide,reports,Industrials,Air Freight & Logistics,"Eden Prairie, Minnesota",2007-03-02,0001043277,1905 +COG,Cabot Oil & Gas,reports,Energy,Oil & Gas Exploration & Production,"Houston, Texas",2008-06-23,0000858470,1989 +CDNS,Cadence Design Systems,reports,Information Technology,Application Software,"San Jose, California",2017-09-18,0000813672,1988 +CPB,Campbell Soup,reports,Consumer Staples,Packaged Foods & Meats,"Camden, New Jersey",1957-03-04,0000016732,1869 +COF,Capital One Financial,reports,Financials,Consumer Finance,"Tysons Corner, Virginia",1998-07-01,0000927628,1935 +CAH,Cardinal Health Inc.,reports,Health Care,Health Care Distributors,"Dublin, Ohio",1997-05-27,0000721371,1971 +KMX,Carmax Inc,reports,Consumer Discretionary,Specialty Stores,"Richmond, Virginia",2010-06-28,0001170010,1993 +CCL,Carnival Corp.,reports,Consumer Discretionary,"Hotels, Resorts & Cruise Lines","Miami, Florida",1998-12-22,0000815097,1972 +CARR,Carrier Global,reports,Industrials,Building Products,"Palm Beach Gardens, Florida",2020-04-03,0001783180,2020 (1915) +CTLT,Catalent,reports,Health Care,Pharmaceuticals,"Somerset, New Jersey",2020-09-21,0001596783,2007 +CAT,Caterpillar Inc.,reports,Industrials,Construction Machinery & Heavy Trucks,"Deerfield, Illinois",1957-03-04,0000018230,1925 +CBOE,Cboe Global Markets,reports,Financials,Financial Exchanges & Data,"Chicago, Illinois",2017-03-01,0001374310,1973 +CBRE,CBRE Group,reports,Real Estate,Real Estate Services,"Dallas, Texas",2006-11-10,0001138118,1906 +CDW,CDW,reports,Information Technology,Technology Distributors,"Lincolnshire, Illinois",2019-09-23,0001402057,1984 +CE,Celanese,reports,Materials,Specialty Chemicals,"Irving, Texas",2018-12-24,0001306830,1918 +CNC,Centene Corporation,reports,Health Care,Managed Health Care,"St. Louis, Missouri",2016-03-30,0001071739,1984 +CNP,CenterPoint Energy,reports,Utilities,Multi-Utilities,"Houston, Texas",1985-07-31,0001130310,1882 +CERN,Cerner,reports,Health Care,Health Care Technology,"North Kansas City, Missouri",2010-04-30,0000804753,1979 +CF,CF Industries Holdings Inc,reports,Materials,Fertilizers & Agricultural Chemicals,"Deerfield, Illinois",2008-08-27,0001324404,1946 +SCHW,Charles Schwab Corporation,reports,Financials,Investment Banking & Brokerage,"Westlake, Texas",1997-06-02,0000316709,1971 +CHTR,Charter Communications,reports,Communication Services,Cable & Satellite,"Stamford, Connecticut",2016-09-08,0001091667,1993 +CVX,Chevron Corp.,reports,Energy,Integrated Oil & Gas,"San Ramon, California",1957-03-04,0000093410,1879 +CMG,Chipotle Mexican Grill,reports,Consumer Discretionary,Restaurants,"Newport Beach, California",2011-04-28,0001058090,1993 +CB,Chubb Limited,reports,Financials,Property & Casualty Insurance,"Zurich, Switzerland",2010-07-15,0000896159,1985 +CHD,Church & Dwight,reports,Consumer Staples,Household Products,"Ewing, New Jersey",2015-12-29,0000313927,1847 +CI,CIGNA Corp.,reports,Health Care,Managed Health Care,"Bloomfield, Connecticut",1976-06-30,0001739940,1982 +CINF,Cincinnati Financial,reports,Financials,Property & Casualty Insurance,"Fairfield, Ohio",1997-12-18,0000020286,1950 +CTAS,Cintas Corporation,reports,Industrials,Diversified Support Services,"Mason, Ohio",2001-03-01,0000723254,1929 +CSCO,Cisco Systems,reports,Information Technology,Communications Equipment,"San Jose, California",1993-12-01,0000858877,1984 +C,Citigroup Inc.,reports,Financials,Diversified Banks,"New York, New York",1988-05-31,0000831001,1998 +CFG,Citizens Financial Group,reports,Financials,Regional Banks,"Providence, Rhode Island",2016-01-29,0000759944,1828 +CTXS,Citrix Systems,reports,Information Technology,Application Software,"Fort Lauderdale, Florida",1999-12-01,0000877890,1989 +CLX,The Clorox Company,reports,Consumer Staples,Household Products,"Oakland, California",1969-03-31,0000021076,1913 +CME,CME Group Inc.,reports,Financials,Financial Exchanges & Data,"Chicago, Illinois",2006-08-11,0001156375,1848 +CMS,CMS Energy,reports,Utilities,Multi-Utilities,"Jackson, Michigan",1999-05-03,0000811156,1886 +KO,Coca-Cola Company,reports,Consumer Staples,Soft Drinks,"Atlanta, Georgia",1957-03-04,0000021344,1886 +CTSH,Cognizant Technology Solutions,reports,Information Technology,IT Consulting & Other Services,"Teaneck, New Jersey",2006-11-17,0001058290,1994 +CL,Colgate-Palmolive,reports,Consumer Staples,Household Products,"New York, New York",1957-03-04,0000021665,1806 +CMCSA,Comcast Corp.,reports,Communication Services,Cable & Satellite,"Philadelphia, Pennsylvania",2002-11-19,0001166691,1963 +CMA,Comerica Inc.,reports,Financials,Diversified Banks,"Dallas, Texas",1995-12-01,0000028412,1849 +CAG,Conagra Brands,reports,Consumer Staples,Packaged Foods & Meats,"Chicago, Illinois",1983-08-31,0000023217,1919 +COP,ConocoPhillips,reports,Energy,Oil & Gas Exploration & Production,"Houston, Texas",1957-03-04,0001163165,2002 +ED,Consolidated Edison,reports,Utilities,Electric Utilities,"New York, New York",,0001047862,1823 +STZ,Constellation Brands,reports,Consumer Staples,Distillers & Vintners,"Victor, New York",2005-07-01,0000016918,1945 +COO,The Cooper Companies,reports,Health Care,Health Care Supplies,"San Ramon, California",2016-09-23,0000711404,1958 +CPRT,Copart Inc,reports,Industrials,Diversified Support Services,"Dallas, Texas",2018-07-02,0000900075,1982 +GLW,Corning Inc.,reports,Information Technology,Electronic Components,"Corning, New York",,0000024741,1851 +CTVA,Corteva,reports,Materials,Fertilizers & Agricultural Chemicals,"Wilmington, Delaware",2019-06-03,0001755672,2019 +COST,Costco Wholesale Corp.,reports,Consumer Staples,Hypermarkets & Super Centers,"Issaquah, Washington",1993-10-01,0000909832,1976 +CCI,Crown Castle International Corp.,reports,Real Estate,Specialized REITs,"Houston, Texas",2012-03-14,0001051470,1994 +CSX,CSX Corp.,reports,Industrials,Railroads,"Jacksonville, Florida",1967-09-30,0000277948,1980 +CMI,Cummins Inc.,reports,Industrials,Industrial Machinery,"Columbus, Indiana",1965-03-31,0000026172,1919 +CVS,CVS Health,reports,Health Care,Health Care Services,"Woonsocket, Rhode Island",1957-03-04,0000064803,1996 +DHI,D. R. Horton,reports,Consumer Discretionary,Homebuilding,"Fort Worth, Texas",2005-06-22,0000882184,1978 +DHR,Danaher Corp.,reports,Health Care,Health Care Equipment,"Washington, D.C.",,0000313616,1969 +DRI,Darden Restaurants,reports,Consumer Discretionary,Restaurants,"Orlando, Florida",,0000940944,1938 +DVA,DaVita Inc.,reports,Health Care,Health Care Facilities,"Denver, Colorado",2008-07-31,0000927066,1979 +DE,Deere & Co.,reports,Industrials,Agricultural & Farm Machinery,"Moline, Illinois",1957-03-04,0000315189,1837 +DAL,Delta Air Lines Inc.,reports,Industrials,Airlines,"Atlanta, Georgia",2013-09-11,0000027904,1929 +XRAY,Dentsply Sirona,reports,Health Care,Health Care Supplies,"Charlotte, North Carolina",2008-11-14,0000818479,2016 (1969) +DVN,Devon Energy,reports,Energy,Oil & Gas Exploration & Production,"Oklahoma City, Oklahoma",2000-08-30,0001090012,1971 +DXCM,DexCom,reports,Health Care,Health Care Equipment,"San Diego, California",2020-05-12,0001093557,1999 +FANG,Diamondback Energy,reports,Energy,Oil & Gas Exploration & Production,"Midland, Texas",2018-12-03,0001539838,2007 +DLR,Digital Realty Trust Inc,reports,Real Estate,Specialized REITs,"Austin, Texas",2016-05-18,0001297996,2004 +DFS,Discover Financial Services,reports,Financials,Consumer Finance,"Riverwoods, Illinois",2007-07-02,0001393612,1985 +DISCA,"Discovery, Inc. (Series A)",reports,Communication Services,Broadcasting,"New York, New York",2010-03-01,0001437107,1985 +DISCK,"Discovery, Inc. (Series C)",reports,Communication Services,Broadcasting,"New York, New York",2014-08-07,0001437107,1985 +DISH,Dish Network,reports,Communication Services,Cable & Satellite,"Meridian, Colorado",2017-03-13,0001001082,1980 +DG,Dollar General,reports,Consumer Discretionary,General Merchandise Stores,"Goodlettsville, Tennessee",2012-12-03,0000029534,1939 +DLTR,Dollar Tree,reports,Consumer Discretionary,General Merchandise Stores,"Chesapeake, Virginia",2011-12-19,0000935703,1986 +D,Dominion Energy,reports,Utilities,Electric Utilities,"Richmond, Virginia",,0000715957,1983 +DPZ,Domino's Pizza,reports,Consumer Discretionary,Restaurants,"Ann Arbor, Michigan",2020-05-12,0001286681,1960 +DOV,Dover Corporation,reports,Industrials,Industrial Machinery,"Downers Grove, Illinois",1985-10-31,0000029905,1955 +DOW,Dow Inc.,reports,Materials,Commodity Chemicals,"Midland, Michigan",2019-04-01,0001751788,2019 +DTE,DTE Energy Co.,reports,Utilities,Multi-Utilities,"Detroit, Michigan",1957-03-04,0000936340,1995 +DUK,Duke Energy,reports,Utilities,Electric Utilities,"Charlotte, North Carolina",1976-06-30,0001326160,1904 +DRE,Duke Realty Corp,reports,Real Estate,Industrial REITs,"Indianapolis, Indiana",2017-07-26,0000783280,1972 +DD,DuPont de Nemours Inc,reports,Materials,Specialty Chemicals,"Wilmington, Delaware",2019-04-02,0001666700,2017 +DXC,DXC Technology,reports,Information Technology,IT Consulting & Other Services,"Tysons Corner, Virginia",2017-04-04,0001688568,2017 +EMN,Eastman Chemical,reports,Materials,Diversified Chemicals,"Kingsport, Tennessee",1994-01-01,0000915389,1920 +ETN,Eaton Corporation,reports,Industrials,Electrical Components & Equipment,"Dublin, Ireland",,0001551182,1911 +EBAY,eBay Inc.,reports,Consumer Discretionary,Internet & Direct Marketing Retail,"San Jose, California",,0001065088,1995 +ECL,Ecolab Inc.,reports,Materials,Specialty Chemicals,"St. Paul, Minnesota",1989-01-31,0000031462,1923 +EIX,Edison Int'l,reports,Utilities,Electric Utilities,"Rosemead, California",1957-03-04,0000827052,1886 +EW,Edwards Lifesciences,reports,Health Care,Health Care Equipment,"Irvine, California",2011-04-01,0001099800,1958 +EA,Electronic Arts,reports,Communication Services,Interactive Home Entertainment,"Redwood City, California",2002-07-22,0000712515,1982 +EMR,Emerson Electric Company,reports,Industrials,Electrical Components & Equipment,"Ferguson, Missouri",1965-03-31,0000032604,1890 +ENPH,Enphase Energy,reports,Information Technology,Semiconductor Equipment,"Fremont, California",2021-01-07,0001463101,2006 +ETR,Entergy Corp.,reports,Utilities,Electric Utilities,"New Orleans, Louisiana",1957-03-04,0000065984,1913 +EOG,EOG Resources,reports,Energy,Oil & Gas Exploration & Production,"Houston, Texas",2000-11-02,0000821189,1999 +EFX,Equifax Inc.,reports,Industrials,Research & Consulting Services,"Atlanta, Georgia",1997-06-19,0000033185,1899 +EQIX,Equinix,reports,Real Estate,Specialized REITs,"Redwood City, California",2015-03-20,0001101239,1998 +EQR,Equity Residential,reports,Real Estate,Residential REITs,"Chicago, Illinois",2001-12-03,0000906107,1969 +ESS,"Essex Property Trust, Inc.",reports,Real Estate,Residential REITs,"San Mateo, California",2014-04-02,0000920522,1971 +EL,Estée Lauder Companies,reports,Consumer Staples,Personal Products,"New York, New York",2006-01-05,0001001250,1946 +ETSY,Etsy,reports,Consumer Discretionary,Internet & Direct Marketing Retail,"Brooklyn, New York",2020-09-21,0001370637,2005 +EVRG,Evergy,reports,Utilities,Electric Utilities,"Kansas City, Missouri",2018-06-05,0001711269,1909 +ES,Eversource Energy,reports,Utilities,Multi-Utilities,"Hartford, Connecticut",,0000072741,1966 +RE,Everest Re Group Ltd.,reports,Financials,Reinsurance,"Hamilton, Bermuda",2017-06-19,0001095073,1973 +EXC,Exelon Corp.,reports,Utilities,Multi-Utilities,"Chicago, Illinois",1957-03-04,0001109357,2000 +EXPE,Expedia Group,reports,Consumer Discretionary,Internet & Direct Marketing Retail,"Seattle, Washington",2007-10-02,0001324424,1996 +EXPD,Expeditors,reports,Industrials,Air Freight & Logistics,"Seattle, Washington",2007-10-10,0000746515,1979 +EXR,Extra Space Storage,reports,Real Estate,Specialized REITs,"Salt Lake City, Utah",2016-01-19,0001289490,1977 +XOM,Exxon Mobil Corp.,reports,Energy,Integrated Oil & Gas,"Irving, Texas",1957-03-04,0000034088,1999 +FFIV,F5 Networks,reports,Information Technology,Communications Equipment,"Seattle, Washington",2010-12-20,0001048695,1996 +FB,"Facebook, Inc.",reports,Communication Services,Interactive Media & Services,"Menlo Park, California",2013-12-23,0001326801,2004 +FAST,Fastenal Co,reports,Industrials,Building Products,"Winona, Minnesota",2008-09-15,0000815556,1967 +FRT,Federal Realty Investment Trust,reports,Real Estate,Retail REITs,"Rockville, Maryland",2016-02-01,0000034903,1962 +FDX,FedEx Corporation,reports,Industrials,Air Freight & Logistics,"Memphis, Tennessee",1980-12-31,0001048911,1971 +FIS,Fidelity National Information Services,reports,Information Technology,Data Processing & Outsourced Services,"Jacksonville, Florida",2006-11-10,0001136893,1968 +FITB,Fifth Third Bancorp,reports,Financials,Regional Banks,"Cincinnati, Ohio",,0000035527,1858 +FE,FirstEnergy Corp,reports,Utilities,Electric Utilities,"Akron, Ohio",,0001031296,1997 +FRC,First Republic Bank,reports,Financials,Regional Banks,"San Francisco, California",2019-01-02,0001132979,1985 +FISV,Fiserv Inc,reports,Information Technology,Data Processing & Outsourced Services,"Brookfield, Wisconsin",2001-04-02,0000798354,1984 +FLT,FleetCor Technologies Inc,reports,Information Technology,Data Processing & Outsourced Services,"Norcross, Georgia",2018-06-20,0001175454,2000 +FLIR,FLIR Systems,reports,Information Technology,Electronic Equipment & Instruments,"Wilsonville, Oregon",2009-01-02,0000354908,1978 +FLS,Flowserve Corporation,reports,Industrials,Industrial Machinery,"Irving, Texas",2008-10-02,0000030625,1997 +FMC,FMC Corporation,reports,Materials,Fertilizers & Agricultural Chemicals,"Philadelphia, Pennsylvania",2009-08-19,0000037785,1883 +F,Ford Motor Company,reports,Consumer Discretionary,Automobile Manufacturers,"Dearborn, Michigan",1957-03-04,0000037996,1903 +FTNT,Fortinet,reports,Information Technology,Systems Software,"Sunnyvale, California",2018-10-11,0001262039,2000 +FTV,Fortive Corp,reports,Industrials,Industrial Machinery,"Everett, Washington",2016-07-01,0001659166,2016 +FBHS,Fortune Brands Home & Security,reports,Industrials,Building Products,"Deerfield, Illinois",2016-06-22,0001519751,2011 (1969) +FOXA,Fox Corporation (Class A),reports,Communication Services,Movies & Entertainment,"New York, New York",2013-07-01,0001754301,2019 +FOX,Fox Corporation (Class B),reports,Communication Services,Movies & Entertainment,"New York, New York",2015-09-18,0001754301,2019 +BEN,Franklin Resources,reports,Financials,Asset Management & Custody Banks,"San Mateo, California",,0000038777,1947 +FCX,Freeport-McMoRan Inc.,reports,Materials,Copper,"Phoenix, Arizona",,0000831259,1912 +GPS,Gap Inc.,reports,Consumer Discretionary,Apparel Retail,"San Francisco, California",1986-08-31,0000039911,1969 +GRMN,Garmin Ltd.,reports,Consumer Discretionary,Consumer Electronics,"Schaffhausen, Switzerland",2012-12-12,0001121788,1989 +IT,Gartner Inc,reports,Information Technology,IT Consulting & Other Services,"Stamford, Connecticut",2017-04-05,0000749251,1979 +GD,General Dynamics,reports,Industrials,Aerospace & Defense,"Falls Church, Virginia",1957-03-04,0000040533,1899 +GE,General Electric,reports,Industrials,Industrial Conglomerates,"Boston, Massachusetts",,0000040545,1892 +GIS,General Mills,reports,Consumer Staples,Packaged Foods & Meats,"Golden Valley, Minnesota",1969-03-31,0000040704,1856 +GM,General Motors,reports,Consumer Discretionary,Automobile Manufacturers,"Detroit, Michigan",2013-06-06,0001467858,1908 +GPC,Genuine Parts,reports,Consumer Discretionary,Specialty Stores,"Atlanta, Georgia",1973-12-31,0000040987,1925 +GILD,Gilead Sciences,reports,Health Care,Biotechnology,"Foster City, California",2004-07-01,0000882095,1987 +GL,Globe Life Inc.,reports,Financials,Life & Health Insurance,"McKinney, Texas",1989-04-30,0000320335,1900 +GPN,Global Payments Inc.,reports,Information Technology,Data Processing & Outsourced Services,"Atlanta, Georgia",2016-04-25,0001123360,2000 +GS,Goldman Sachs Group,reports,Financials,Investment Banking & Brokerage,"New York, New York",2002-07-22,0000886982,1869 +GWW,Grainger (W.W.) Inc.,reports,Industrials,Industrial Machinery,"Lake Forest, Illinois",1981-06-30,0000277135,1927 +HAL,Halliburton Co.,reports,Energy,Oil & Gas Equipment & Services,"Houston, Texas",1957-03-04,0000045012,1919 +HBI,Hanesbrands Inc,reports,Consumer Discretionary,"Apparel, Accessories & Luxury Goods","Winston-Salem, North Carolina",2015-03-20,0001359841,2000 +HIG,Hartford Financial Svc.Gp.,reports,Financials,Property & Casualty Insurance,"Hartford, Connecticut",1957-03-04,0000874766,1810 +HAS,Hasbro Inc.,reports,Consumer Discretionary,Leisure Products,"Pawtucket, Rhode Island",1984-09-30,0000046080,1923 +HCA,HCA Healthcare,reports,Health Care,Health Care Facilities,"Nashville, Tennessee",2015-01-27,0000860730,1968 +PEAK,Healthpeak Properties,reports,Real Estate,Health Care REITs,"Long Beach, California",2008-03-31,0000765880,1985 +HSIC,Henry Schein,reports,Health Care,Health Care Distributors,"Melville, New York",2015-03-17,0001000228,1932 +HSY,The Hershey Company,reports,Consumer Staples,Packaged Foods & Meats,"Hershey, Pennsylvania",1957-03-04,0000047111,1894 +HES,Hess Corporation,reports,Energy,Integrated Oil & Gas,"New York, New York",1984-05-31,0000004447,1919 +HPE,Hewlett Packard Enterprise,reports,Information Technology,"Technology Hardware, Storage & Peripherals","Houston, Texas",2015-11-02,0001645590,2015 +HLT,Hilton Worldwide Holdings Inc,reports,Consumer Discretionary,"Hotels, Resorts & Cruise Lines","Tysons Corner, Virginia",2017-06-19,0001585689,1919 +HFC,HollyFrontier Corp,reports,Energy,Oil & Gas Refining & Marketing,"Dallas, Texas",2018-06-18,0000048039,1947 +HOLX,Hologic,reports,Health Care,Health Care Equipment,"Marlborough, Massachusetts",2016-03-30,0000859737,1985 +HD,Home Depot,reports,Consumer Discretionary,Home Improvement Retail,"Atlanta, Georgia",1988-03-31,0000354950,1978 +HON,Honeywell Int'l Inc.,reports,Industrials,Industrial Conglomerates,"Morristown, New Jersey",1964-03-31,0000773840,1906 +HRL,Hormel Foods Corp.,reports,Consumer Staples,Packaged Foods & Meats,"Austin, Minnesota",2009-03-04,0000048465,1891 +HST,Host Hotels & Resorts,reports,Real Estate,Hotel & Resort REITs,"Bethesda, Maryland",2007-03-20,0001070750,1993 +HWM,Howmet Aerospace,reports,Industrials,Aerospace & Defense,"Pittsburgh, Pennsylvania",1964-03-31,0000004281,2016 +HPQ,HP Inc.,reports,Information Technology,"Technology Hardware, Storage & Peripherals","Palo Alto, California",1974-12-31,0000047217,1939 (2015) +HUM,Humana Inc.,reports,Health Care,Managed Health Care,"Louisville, Kentucky",,0000049071,1961 +HBAN,Huntington Bancshares,reports,Financials,Regional Banks,"Columbus, Ohio",,0000049196,1866 +HII,Huntington Ingalls Industries,reports,Industrials,Aerospace & Defense,"Newport News, Virginia",2018-01-03,0001501585,2011 +IEX,IDEX Corporation,reports,Industrials,Industrial Machinery,"Lake Forest, Illinois",2019-08-09,0000832101,1988 +IDXX,IDEXX Laboratories,reports,Health Care,Health Care Equipment,"Westbrook, Maine",2017-01-05,0000874716,1983 +INFO,IHS Markit Ltd.,reports,Industrials,Research & Consulting Services,"London, United Kingdom",2017-06-02,0001598014,1959 +ITW,Illinois Tool Works,reports,Industrials,Industrial Machinery,"Glenview, Illinois",1986-02-28,0000049826,1912 +ILMN,Illumina Inc,reports,Health Care,Life Sciences Tools & Services,"San Diego, California",2015-11-19,0001110803,1998 +INCY,Incyte,reports,Health Care,Biotechnology,"Wilmington, Delaware",2017-02-28,0000879169,1991 +IR,Ingersoll Rand,reports,Industrials,Industrial Machinery,"Milwaukee, Wisconsin",2020-03-03,0001699150,1859 +INTC,Intel Corp.,reports,Information Technology,Semiconductors,"Santa Clara, California",1976-12-31,0000050863,1968 +ICE,Intercontinental Exchange,reports,Financials,Financial Exchanges & Data,"Atlanta, Georgia",2007-09-26,0001571949,2000 +IBM,International Business Machines,reports,Information Technology,IT Consulting & Other Services,"Armonk, New York",1957-03-04,0000051143,1911 +IP,International Paper,reports,Materials,Paper Packaging,"Memphis, Tennessee",1957-03-04,0000051434,1898 +IPG,Interpublic Group,reports,Communication Services,Advertising,"New York, New York",1992-10-01,0000051644,1961 (1930) +IFF,International Flavors & Fragrances,reports,Materials,Specialty Chemicals,"New York, New York",1976-03-31,0000051253,1958 (1889) +INTU,Intuit Inc.,reports,Information Technology,Application Software,"Mountain View, California",2000-12-05,0000896878,1983 +ISRG,Intuitive Surgical Inc.,reports,Health Care,Health Care Equipment,"Sunnyvale, California",2008-06-02,0001035267,1995 +IVZ,Invesco Ltd.,reports,Financials,Asset Management & Custody Banks,"Atlanta, Georgia",2008-08-21,0000914208,1935 +IPGP,IPG Photonics Corp.,reports,Information Technology,Electronic Manufacturing Services,"Oxford, Massachusetts",2018-03-07,0001111928,1990 +IQV,IQVIA Holdings Inc.,reports,Health Care,Life Sciences Tools & Services,"Durham, North Carolina",2017-08-29,0001478242,1982 +IRM,Iron Mountain Incorporated,reports,Real Estate,Specialized REITs,"Boston, Massachusetts",2009-01-06,0001020569,1951 +JKHY,Jack Henry & Associates,reports,Information Technology,Data Processing & Outsourced Services,"Monett, Missouri",2018-11-13,0000779152,1976 +J,Jacobs Engineering Group,reports,Industrials,Construction & Engineering,"Dallas, Texas",2007-10-26,0000052988,1947 +JBHT,J. B. Hunt Transport Services,reports,Industrials,Trucking,"Lowell, Arkansas",2015-07-01,0000728535,1961 +SJM,JM Smucker,reports,Consumer Staples,Packaged Foods & Meats,"Orrville, Ohio",2008-11-06,0000091419,1897 +JNJ,Johnson & Johnson,reports,Health Care,Pharmaceuticals,"New Brunswick, New Jersey",1973-06-30,0000200406,1886 +JCI,Johnson Controls International,reports,Industrials,Building Products,"Cork, Ireland",2010-08-27,0000833444,1885 +JPM,JPMorgan Chase & Co.,reports,Financials,Diversified Banks,"New York, New York",1975-06-30,0000019617,2000 (1799 / 1871) +JNPR,Juniper Networks,reports,Information Technology,Communications Equipment,"Sunnyvale, California",2006-06-02,0001043604,1996 +KSU,Kansas City Southern,reports,Industrials,Railroads,"Kansas City, Missouri",2013-05-24,0000054480,1887 +K,Kellogg Co.,reports,Consumer Staples,Packaged Foods & Meats,"Battle Creek, Michigan",,0000055067,1906 +KEY,KeyCorp,reports,Financials,Regional Banks,"Cleveland, Ohio",1994-03-01,0000091576,1825 +KEYS,Keysight Technologies,reports,Information Technology,Electronic Equipment & Instruments,"Santa Rosa, California",2018-11-06,0001601046,2014 +KMB,Kimberly-Clark,reports,Consumer Staples,Household Products,"Irving, Texas",1957-03-04,0000055785,1872 +KIM,Kimco Realty,reports,Real Estate,Retail REITs,"New Hyde Park, New York",2006-04-04,0000879101,1958 +KMI,Kinder Morgan,reports,Energy,Oil & Gas Storage & Transportation,"Houston, Texas",2012-05-25,0001506307,1997 +KLAC,KLA Corporation,reports,Information Technology,Semiconductor Equipment,"Milpitas, California",,0000319201,1975/1977 (1997) +KHC,Kraft Heinz Co,reports,Consumer Staples,Packaged Foods & Meats,"Chicago, Illinois; Pittsburgh, Pennsylvania",2015-07-06,0001637459,2015 (1869) +KR,Kroger Co.,reports,Consumer Staples,Food Retail,"Cincinnati, Ohio",1957-03-04,0000056873,1883 +LB,L Brands Inc.,reports,Consumer Discretionary,Apparel Retail,"Columbus, Ohio",1983-09-30,0000701985,1963 +LHX,L3Harris Technologies,reports,Industrials,Aerospace & Defense,"Melbourne, Florida",,0000202058,2019 (1895) +LH,Laboratory Corp. of America Holding,reports,Health Care,Health Care Services,"Burlington, North Carolina",2004-11-01,0000920148,1978 +LRCX,Lam Research,reports,Information Technology,Semiconductor Equipment,"Fremont, California",2012-06-29,0000707549,1980 +LW,Lamb Weston Holdings Inc,reports,Consumer Staples,Packaged Foods & Meats,"Eagle, Idaho",2018-12-03,0001679273,2016 (1950) +LVS,Las Vegas Sands,reports,Consumer Discretionary,Casinos & Gaming,"Las Vegas, Nevada",2019-10-03,0001300514,1988 +LEG,Leggett & Platt,reports,Consumer Discretionary,Home Furnishings,"Carthage, Missouri",,0000058492,1883 +LDOS,Leidos Holdings,reports,Information Technology,IT Consulting & Other Services,"Reston, Virginia",2019-08-09,0001336920,1969 +LEN,Lennar Corp.,reports,Consumer Discretionary,Homebuilding,"Miami, Florida",2005-10-04,0000920760,1954 +LLY,Lilly (Eli) & Co.,reports,Health Care,Pharmaceuticals,"Indianapolis, Indiana",1970-12-31,0000059478,1876 +LNC,Lincoln National,reports,Financials,Multi-line Insurance,"Radnor, Pennsylvania",1976-06-30,0000059558,1905 +LIN,Linde plc,reports,Materials,Industrial Gases,"Guildford, Surrey, United Kingdom",1992-07-01,0001707925,1879 +LYV,Live Nation Entertainment,reports,Communication Services,Movies & Entertainment,"Beverly Hills, California",2019-12-23,0001335258,2010 +LKQ,LKQ Corporation,reports,Consumer Discretionary,Distributors,"Chicago, Illinois",2016-05-23,0001065696,1998 +LMT,Lockheed Martin Corp.,reports,Industrials,Aerospace & Defense,"Bethesda, Maryland",1984-07-31,0000936468,1995 +L,Loews Corp.,reports,Financials,Multi-line Insurance,"New York, New York",,0000060086,1959 +LOW,Lowe's Cos.,reports,Consumer Discretionary,Home Improvement Retail,"Mooresville, North Carolina",1984-02-29,0000060667,1904/1946/1959 +LUMN,Lumen Technologies,reports,Communication Services,Alternative Carriers,"Monroe, Louisiana",1999-03-25,0000018926,1983 (1877) +LYB,LyondellBasell,reports,Materials,Specialty Chemicals,"Rotterdam, Netherlands",2012-09-05,0001489393,2007 +MTB,M&T Bank Corp.,reports,Financials,Regional Banks,"Buffalo, New York",2004-02-23,0000036270,1856 +MRO,Marathon Oil Corp.,reports,Energy,Oil & Gas Exploration & Production,"Houston, Texas",1991-05-01,0000101778,1887 +MPC,Marathon Petroleum,reports,Energy,Oil & Gas Refining & Marketing,"Findlay, Ohio",2011-07-01,0001510295,2009 (1887) +MKTX,MarketAxess,reports,Financials,Financial Exchanges & Data,"New York, New York",2019-07-01,0001278021,2000 +MAR,Marriott Int'l.,reports,Consumer Discretionary,"Hotels, Resorts & Cruise Lines","Bethesda, Maryland",,0001048286,1927 +MMC,Marsh & McLennan,reports,Financials,Insurance Brokers,"New York, New York",1987-08-31,0000062709,1905 +MLM,Martin Marietta Materials,reports,Materials,Construction Materials,"Raleigh, North Carolina",2014-07-02,0000916076,1993 +MAS,Masco Corp.,reports,Industrials,Building Products,"Livonia, Michigan",1981-06-30,0000062996,1929 +MA,Mastercard Inc.,reports,Information Technology,Data Processing & Outsourced Services,"Harrison, New York",2008-07-18,0001141391,1966 +MKC,McCormick & Co.,reports,Consumer Staples,Packaged Foods & Meats,"Hunt Valley, Maryland",,0000063754,1889 +MXIM,Maxim Integrated Products Inc,reports,Information Technology,Semiconductors,"San Jose, California",2018-12-03,0000743316,1983 +MCD,McDonald's Corp.,reports,Consumer Discretionary,Restaurants,"Chicago, Illinois",1970-06-30,0000063908,1940 +MCK,McKesson Corp.,reports,Health Care,Health Care Distributors,"Irving, Texas",,0000927653,1833 +MDT,Medtronic plc,reports,Health Care,Health Care Equipment,"Dublin, Ireland",1986-10-31,0001613103,1949 +MRK,Merck & Co.,reports,Health Care,Pharmaceuticals,"Kenilworth, New Jersey",1957-03-04,0000310158,1891 +MET,MetLife Inc.,reports,Financials,Life & Health Insurance,"New York, New York",,0001099219,1868 +MTD,Mettler Toledo,reports,Health Care,Life Sciences Tools & Services,"Columbus, Ohio",2016-09-06,0001037646,1945 +MGM,MGM Resorts International,reports,Consumer Discretionary,Casinos & Gaming,"Paradise, Nevada",2017-07-26,0000789570,1986 +MCHP,Microchip Technology,reports,Information Technology,Semiconductors,"Chandler, Arizona",2007-09-07,0000827054,1989 +MU,Micron Technology,reports,Information Technology,Semiconductors,"Boise, Idaho",1994-09-27,0000723125,1978 +MSFT,Microsoft Corp.,reports,Information Technology,Systems Software,"Redmond, Washington",1994-06-01,0000789019,1975 +MAA,Mid-America Apartments,reports,Real Estate,Residential REITs,"Memphis, Tennessee",2016-12-02,0000912595,1977 +MHK,Mohawk Industries,reports,Consumer Discretionary,Home Furnishings,"Calhoun, Georgia",2013-12-23,0000851968,1878 +TAP,Molson Coors Beverage Company,reports,Consumer Staples,Brewers,"Denver, Colorado",1976-06-30,0000024545,"2005 (Molson 1786, Coors 1873)" +MDLZ,Mondelez International,reports,Consumer Staples,Packaged Foods & Meats,"Chicago, Illinois",2012-10-02,0001103982,2012 +MNST,Monster Beverage,reports,Consumer Staples,Soft Drinks,"Corona, California",2012-06-28,0000865752,2012 (1935) +MCO,Moody's Corp,reports,Financials,Financial Exchanges & Data,"New York, New York",,0001059556,1909 +MS,Morgan Stanley,reports,Financials,Investment Banking & Brokerage,"New York, New York",,0000895421,1935 +MOS,The Mosaic Company,reports,Materials,Fertilizers & Agricultural Chemicals,"Tampa, Florida",2011-09-26,0001285785,2004 (1865 / 1909) +MSI,Motorola Solutions Inc.,reports,Information Technology,Communications Equipment,"Chicago, Illinois",,0000068505,1928 (2011) +MSCI,MSCI Inc,reports,Financials,Financial Exchanges & Data,"New York, New York",2018-04-04,0001408198,1969 +NDAQ,"Nasdaq, Inc.",reports,Financials,Financial Exchanges & Data,"New York, New York",2008-10-22,0001120193,1971 +NTAP,NetApp,reports,Information Technology,"Technology Hardware, Storage & Peripherals","Sunnyvale, California",1999-06-25,0001002047,1992 +NFLX,Netflix Inc.,reports,Communication Services,Movies & Entertainment,"Los Gatos, California",2010-12-20,0001065280,1997 +NWL,Newell Brands,reports,Consumer Discretionary,Housewares & Specialties,"Atlanta, Georgia",1989-04-30,0000814453,1903 +NEM,Newmont Corporation,reports,Materials,Gold,"Denver, Colorado",1969-06-30,0001164727,1921 +NWSA,News Corp (Class A),reports,Communication Services,Publishing,"New York, New York",2013-08-01,0001564708,2013 (1980) +NWS,News Corp (Class B),reports,Communication Services,Publishing,"New York, New York",2015-09-18,0001564708,2013 (1980) +NEE,NextEra Energy,reports,Utilities,Multi-Utilities,"Juno Beach, Florida",1976-06-30,0000753308,1984 (1925) +NLSN,Nielsen Holdings,reports,Industrials,Research & Consulting Services,"New York, New York",2013-07-09,0001492633,1923 +NKE,"Nike, Inc.",reports,Consumer Discretionary,"Apparel, Accessories & Luxury Goods","Washington County, Oregon",1988-11-30,0000320187,1964 +NI,NiSource Inc.,reports,Utilities,Multi-Utilities,"Merrillville, Indiana",,0001111711,1912 +NSC,Norfolk Southern Corp.,reports,Industrials,Railroads,"Norfolk, Virginia",1957-03-04,0000702165,1881/1894 (1980) +NTRS,Northern Trust Corp.,reports,Financials,Asset Management & Custody Banks,"Chicago, Illinois",,0000073124,1889 +NOC,Northrop Grumman,reports,Industrials,Aerospace & Defense,"West Falls Church, Virginia",1985-06-30,0001133421,"1994 (Northrop 1939, Grumman 1930)" +NLOK,NortonLifeLock,reports,Information Technology,Application Software,"Tempe, Arizona",2003-03-25,0000849399,1982 +NCLH,Norwegian Cruise Line Holdings,reports,Consumer Discretionary,"Hotels, Resorts & Cruise Lines","Miami, Florida",2017-10-13,0001513761,2011 (1966) +NOV,NOV Inc.,reports,Energy,Oil & Gas Equipment & Services,"Houston, Texas",2005-03-14,0001021860,1841 +NRG,NRG Energy,reports,Utilities,Independent Power Producers & Energy Traders,"Princeton, New Jersey",2010-01-29,0001013871,1992 +NUE,Nucor Corp.,reports,Materials,Steel,"Charlotte, North Carolina",1985-04-30,0000073309,1940 +NVDA,Nvidia Corporation,reports,Information Technology,Semiconductors,"Santa Clara, California",2001-11-30,0001045810,1993 +NVR,"NVR, Inc.",reports,Consumer Discretionary,Homebuilding,"Reston, Virginia",2019-09-26,0000906163,1980 +ORLY,O'Reilly Automotive,reports,Consumer Discretionary,Specialty Stores,"Springfield, Missouri",2009-03-27,0000898173,1957 +OXY,Occidental Petroleum,reports,Energy,Oil & Gas Exploration & Production,"Houston, Texas",1982-12-31,0000797468,1920 +ODFL,Old Dominion Freight Line,reports,Industrials,Trucking,"Thomasville, North Carolina",2019-12-09,0000878927,1934 +OMC,Omnicom Group,reports,Communication Services,Advertising,"New York, New York",,0000029989,1986 +OKE,ONEOK,reports,Energy,Oil & Gas Storage & Transportation,"Tulsa, Oklahoma",2010-03-15,0001039684,1906 +ORCL,Oracle Corp.,reports,Information Technology,Application Software,"Austin, Texas",1989-08-31,0001341439,1977 +OTIS,Otis Worldwide,reports,Industrials,Industrial Machinery,"Farmington, Connecticut",2020-04-03,0001781335,2020 (1853) +PCAR,PACCAR Inc.,reports,Industrials,Construction Machinery & Heavy Trucks,"Bellevue, Washington",1980-12-31,0000075362,1905 +PKG,Packaging Corporation of America,reports,Materials,Paper Packaging,"Lake Forest, Illinois",2017-07-26,0000075677,1959 +PH,Parker-Hannifin,reports,Industrials,Industrial Machinery,"Cleveland, Ohio",1985-11-30,0000076334,1917 +PAYX,Paychex Inc.,reports,Information Technology,Data Processing & Outsourced Services,"Penfield, New York",,0000723531,1971 +PAYC,Paycom,reports,Information Technology,Application Software,"Oklahoma City, Oklahoma",2020-01-28,0001590955,1998 +PYPL,PayPal,reports,Information Technology,Data Processing & Outsourced Services,"San Jose, California",2015-07-20,0001633917,1998 +PNR,Pentair plc,reports,Industrials,Industrial Machinery,"Worsley, UK",2012-10-01,0000077360,1966 +PBCT,People's United Financial,reports,Financials,Thrifts & Mortgage Finance,"Bridgeport, Connecticut",2008-11-13,0001378946,1842 +PEP,PepsiCo Inc.,reports,Consumer Staples,Soft Drinks,"Purchase, New York",1957-03-04,0000077476,1898 +PKI,PerkinElmer,reports,Health Care,Health Care Equipment,"Waltham, Massachusetts",1985-05-31,0000031791,1937 +PRGO,Perrigo,reports,Health Care,Pharmaceuticals,"Dublin, Ireland",2011-12-19,0001585364,2013 (1887) +PFE,Pfizer Inc.,reports,Health Care,Pharmaceuticals,"New York, New York",1957-03-04,0000078003,1849 +PM,Philip Morris International,reports,Consumer Staples,Tobacco,"New York, New York",2008-03-31,0001413329,2008 (1847) +PSX,Phillips 66,reports,Energy,Oil & Gas Refining & Marketing,"Houston, Texas",2012-05-01,0001534701,2012 (1917) +PNW,Pinnacle West Capital,reports,Utilities,Multi-Utilities,"Phoenix, Arizona",,0000764622,1985 +PXD,Pioneer Natural Resources,reports,Energy,Oil & Gas Exploration & Production,"Irving, Texas",2008-09-24,0001038357,1997 +PNC,PNC Financial Services,reports,Financials,Regional Banks,"Pittsburgh, Pennsylvania",1988-04-30,0000713676,1845 +POOL,Pool Corporation,reports,Consumer Discretionary,Distributors,"Covington, Louisiana",2020-10-07,0000945841,1993 +PPG,PPG Industries,reports,Materials,Specialty Chemicals,"Pittsburgh, Pennsylvania",1957-03-04,0000079879,1883 +PPL,PPL Corp.,reports,Utilities,Electric Utilities,"Allentown, Pennsylvania",,0000922224,1920 +PFG,Principal Financial Group,reports,Financials,Life & Health Insurance,"Des Moines, Iowa",2002-07-22,0001126328,1879 +PG,Procter & Gamble,reports,Consumer Staples,Personal Products,"Cincinnati, Ohio",1957-03-04,0000080424,1837 +PGR,Progressive Corp.,reports,Financials,Property & Casualty Insurance,"Mayfield Village, Ohio",1997-08-04,0000080661,1937 +PLD,Prologis,reports,Real Estate,Industrial REITs,"San Francisco, California",2003-07-17,0001045609,1983 +PRU,Prudential Financial,reports,Financials,Life & Health Insurance,"Newark, New Jersey",2002-07-22,0001137774,1875 +PEG,Public Service Enterprise Group (PSEG),reports,Utilities,Electric Utilities,"Newark, New Jersey",1957-03-04,0000788784,1903 +PSA,Public Storage,reports,Real Estate,Specialized REITs,"Glendale, California",2005-08-19,0001393311,1972 +PHM,PulteGroup,reports,Consumer Discretionary,Homebuilding,"Atlanta, Georgia",1984-04-30,0000822416,1956 +PVH,PVH Corp.,reports,Consumer Discretionary,"Apparel, Accessories & Luxury Goods","New York, New York",2013-02-15,0000078239,1881 +QRVO,Qorvo,reports,Information Technology,Semiconductors,"Greensboro, North Carolina",2015-06-11,0001604778,2015 +PWR,Quanta Services Inc.,reports,Industrials,Construction & Engineering,"Houston, Texas",2009-07-01,0001050915,1997 +QCOM,QUALCOMM Inc.,reports,Information Technology,Semiconductors,"San Diego, California",,0000804328,1985 +DGX,Quest Diagnostics,reports,Health Care,Health Care Services,"Secaucus, New Jersey",2002-12-12,0001022079,1967 +RL,Ralph Lauren Corporation,reports,Consumer Discretionary,"Apparel, Accessories & Luxury Goods","New York, New York",2007-02-02,0001037038,1967 +RJF,"Raymond James Financial, Inc.",reports,Financials,Investment Banking & Brokerage,"St. Petersburg, Florida",2017-03-20,0000720005,1962 +RTX,Raytheon Technologies,reports,Industrials,Aerospace & Defense,"Waltham, Massachusetts",,0000101829,1922 +O,Realty Income Corporation,reports,Real Estate,Retail REITs,"San Diego, California",2015-04-07,0000726728,1969 +REG,Regency Centers Corporation,reports,Real Estate,Retail REITs,"Jacksonville, Florida",2017-03-02,0000910606,1963 +REGN,Regeneron Pharmaceuticals,reports,Health Care,Biotechnology,"Tarrytown, New York",2013-05-01,0000872589,1988 +RF,Regions Financial Corp.,reports,Financials,Regional Banks,"Birmingham, Alabama",1998-08-28,0001281761,1971 +RSG,Republic Services Inc,reports,Industrials,Environmental & Facilities Services,"Phoenix, Arizona",2008-12-05,0001060391,1998 (1981) +RMD,ResMed,reports,Health Care,Health Care Equipment,"San Diego, California",2017-07-26,0000943819,1989 +RHI,Robert Half International,reports,Industrials,Human Resource & Employment Services,"Menlo Park, California",2000-12-05,0000315213,1948 +ROK,Rockwell Automation Inc.,reports,Industrials,Electrical Components & Equipment,"Milwaukee, Wisconsin",,0001024478,1903 +ROL,"Rollins, Inc.",reports,Industrials,Environmental & Facilities Services,"Atlanta, Georgia",2018-10-01,0000084839,1948 +ROP,Roper Technologies,reports,Industrials,Industrial Conglomerates,"Sarasota, Florida",2009-12-23,0000882835,1981 +ROST,Ross Stores,reports,Consumer Discretionary,Apparel Retail,"Dublin, California",2009-12-21,0000745732,1982 +RCL,Royal Caribbean Group,reports,Consumer Discretionary,"Hotels, Resorts & Cruise Lines","Miami, Florida",2014-12-05,0000884887,1997 +SPGI,S&P Global Inc.,reports,Financials,Financial Exchanges & Data,"New York, New York",,0000064040,1917 +CRM,Salesforce.com,reports,Information Technology,Application Software,"San Francisco, California",2008-09-15,0001108524,1999 +SBAC,SBA Communications,reports,Real Estate,Specialized REITs,"Boca Raton, Florida",2017-09-01,0001034054,1989 +SLB,Schlumberger Ltd.,reports,Energy,Oil & Gas Equipment & Services,"Curaçao, Kingdom of the Netherlands",1965-03-31,0000087347,1926 +STX,Seagate Technology,reports,Information Technology,"Technology Hardware, Storage & Peripherals","Dublin, Ireland",2012-07-02,0001137789,1979 +SEE,Sealed Air,reports,Materials,Paper Packaging,"Charlotte, North Carolina",1957-03-04,0001012100,1960 +SRE,Sempra Energy,reports,Utilities,Multi-Utilities,"San Diego, California",,0001032208,1998 +NOW,ServiceNow,reports,Information Technology,Systems Software,"Santa Clara, California",2019-11-21,0001373715,2003 +SHW,Sherwin-Williams,reports,Materials,Specialty Chemicals,"Cleveland, Ohio",1964-06-30,0000089800,1866 +SPG,Simon Property Group Inc,reports,Real Estate,Retail REITs,"Indianapolis, Indiana",2002-06-26,0001063761,2003 +SWKS,Skyworks Solutions,reports,Information Technology,Semiconductors,"Woburn, Massachusetts",2015-03-12,0000004127,2002 +SLG,SL Green Realty,reports,Real Estate,Office REITs,"New York, New York",2015-03-20,0001040971,1997 +SNA,Snap-on,reports,Industrials,Industrial Machinery,"Kenosha, Wisconsin",1982-09-30,0000091440,1920 +SO,Southern Company,reports,Utilities,Electric Utilities,"Atlanta, Georgia",1957-03-04,0000092122,1945 +LUV,Southwest Airlines,reports,Industrials,Airlines,"Dallas, Texas",1994-07-01,0000092380,1967 +SWK,Stanley Black & Decker,reports,Industrials,Industrial Machinery,"New Britain, Connecticut",1982-09-30,0000093556,1843 +SBUX,Starbucks Corp.,reports,Consumer Discretionary,Restaurants,"Seattle, Washington",,0000829224,1971 +STT,State Street Corp.,reports,Financials,Asset Management & Custody Banks,"Boston, Massachusetts",,0000093751,1792 +STE,STERIS plc,reports,Health Care,Health Care Equipment,"Dublin, Ireland",2019-12-23,0001757898,1985 +SYK,Stryker Corp.,reports,Health Care,Health Care Equipment,"Kalamazoo, Michigan",2000-12-12,0000310764,1941 +SIVB,SVB Financial,reports,Financials,Regional Banks,"Santa Clara, California",2018-03-19,0000719739,1983 +SYF,Synchrony Financial,reports,Financials,Consumer Finance,"Stamford, Connecticut",2015-11-18,0001601712,2003 +SNPS,Synopsys Inc.,reports,Information Technology,Application Software,"Mountain View, California",2017-03-16,0000883241,1986 +SYY,Sysco Corp.,reports,Consumer Staples,Food Distributors,"Houston, Texas",1986-12-31,0000096021,1969 +TMUS,T-Mobile US,reports,Communication Services,Wireless Telecommunication Services,"Bellevue, Washington",2019-07-15,0001283699,1994 +TROW,T. Rowe Price Group,reports,Financials,Asset Management & Custody Banks,"Baltimore, Maryland",,0001113169,1937 +TTWO,Take-Two Interactive,reports,Communication Services,Interactive Home Entertainment,"New York, New York",2018-03-19,0000946581,1993 +TPR,"Tapestry, Inc.",reports,Consumer Discretionary,"Apparel, Accessories & Luxury Goods","New York, New York",,0001116132,2017 +TGT,Target Corp.,reports,Consumer Discretionary,General Merchandise Stores,"Minneapolis, Minnesota",1976-12-31,0000027419,1902 +TEL,TE Connectivity Ltd.,reports,Information Technology,Electronic Manufacturing Services,"Schaffhausen, Switzerland",2011-10-17,0001385157,2007 +FTI,TechnipFMC,reports,Energy,Oil & Gas Equipment & Services,"London, United Kingdom",2009-06-05,0001681459,2017 (1958) +TDY,Teledyne Technologies,reports,Industrials,Aerospace & Defense,"Thousand Oaks, California",2020-06-22,0001094285,1960 +TFX,Teleflex,reports,Health Care,Health Care Equipment,"Wayne, Pennsylvania",2019-01-18,0000096943,1943 +TER,Teradyne,reports,Information Technology,Semiconductor Equipment,"North Reading, Massachusetts",2020-09-21,0000097210,1960 +TSLA,"Tesla, Inc.",reports,Consumer Discretionary,Automobile Manufacturers,"Palo Alto, California",2020-12-21,0001318605,2003 +TXN,Texas Instruments,reports,Information Technology,Semiconductors,"Dallas, Texas",,0000097476,1930 +TXT,Textron Inc.,reports,Industrials,Aerospace & Defense,"Providence, Rhode Island",1978-12-31,0000217346,1923 +TMO,Thermo Fisher Scientific,reports,Health Care,Life Sciences Tools & Services,"Waltham, Massachusetts",,0000097745,2006 (1902) +TJX,TJX Companies Inc.,reports,Consumer Discretionary,Apparel Retail,"Framingham, Massachusetts",1985-09-30,0000109198,1987 +TSCO,Tractor Supply Company,reports,Consumer Discretionary,Specialty Stores,"Brentwood, Tennessee",2014-01-24,0000916365,1938 +TT,Trane Technologies plc,reports,Industrials,Building Products,"Dublin, Ireland",2010-11-17,0001466258,1871 +TDG,TransDigm Group,reports,Industrials,Aerospace & Defense,"Cleveland, Ohio",2016-06-03,0001260221,1993 +TRV,The Travelers Companies Inc.,reports,Financials,Property & Casualty Insurance,"New York, New York",2002-08-21,0000086312,1853 +TRMB,Trimble Inc.,reports,Information Technology,Electronic Equipment & Instruments,"Sunnyvale, California",2021-01-21,0000864749,1978 +TFC,Truist Financial,reports,Financials,Regional Banks,"Charlotte, North Carolina",1997-12-04,0000092230,1872 +TWTR,"Twitter, Inc.",reports,Communication Services,Interactive Media & Services,"San Francisco, California",2018-06-07,0001418091,2006 +TYL,Tyler Technologies,reports,Information Technology,Application Software,"Plano, Texas",2020-06-22,0000860731,1966 +TSN,Tyson Foods,reports,Consumer Staples,Packaged Foods & Meats,"Springdale, Arkansas",,0000100493,1935 +UDR,"UDR, Inc.",reports,Real Estate,Residential REITs,"Highlands Ranch, Colorado",2016-03-07,0000074208,1972 +ULTA,Ulta Beauty,reports,Consumer Discretionary,Specialty Stores,"Bolingbrook, Illinois",2016-04-18,0001403568,1990 +USB,U.S. Bancorp,reports,Financials,Diversified Banks,"Minneapolis, Minnesota",,0000036104,1968 +UAA,Under Armour (Class A),reports,Consumer Discretionary,"Apparel, Accessories & Luxury Goods","Baltimore, Maryland",2014-05-01,0001336917,1996 +UA,Under Armour (Class C),reports,Consumer Discretionary,"Apparel, Accessories & Luxury Goods","Baltimore, Maryland",2016-04-08,0001336917,1996 +UNP,Union Pacific Corp,reports,Industrials,Railroads,"Omaha, Nebraska",1957-03-04,0000100885,1862 +UAL,United Airlines Holdings,reports,Industrials,Airlines,"Chicago, Illinois",2015-09-03,0000100517,1967 +UNH,UnitedHealth Group Inc.,reports,Health Care,Managed Health Care,"Minnetonka, Minnesota",1994-07-01,0000731766,1977 +UPS,United Parcel Service,reports,Industrials,Air Freight & Logistics,"Atlanta, Georgia",2002-07-22,0001090727,1907 +URI,"United Rentals, Inc.",reports,Industrials,Trading Companies & Distributors,"Stamford, Connecticut",2014-09-20,0001067701,1997 +UHS,Universal Health Services,reports,Health Care,Health Care Facilities,"King of Prussia, Pennsylvania",2014-09-20,0000352915,1979 +UNM,Unum Group,reports,Financials,Life & Health Insurance,"Chattanooga, Tennessee",1994-03-01,0000005513,1999 +VLO,Valero Energy,reports,Energy,Oil & Gas Refining & Marketing,"San Antonio, Texas",,0001035002,1980 +VAR,Varian Medical Systems,reports,Health Care,Health Care Equipment,"Palo Alto, California",2007-02-12,0000203527,1948 +VTR,Ventas Inc,reports,Real Estate,Health Care REITs,"Chicago, Illinois",2009-03-04,0000740260,1998 +VRSN,Verisign Inc.,reports,Information Technology,Internet Services & Infrastructure,"Dulles, Virginia",2006-02-01,0001014473,1995 +VRSK,Verisk Analytics,reports,Industrials,Research & Consulting Services,"Jersey City, New Jersey",2015-10-08,0001442145,1971 +VZ,Verizon Communications,reports,Communication Services,Integrated Telecommunication Services,"New York, New York",1983-11-30,0000732712,1983 (1877) +VRTX,Vertex Pharmaceuticals Inc,reports,Health Care,Biotechnology,"Cambridge, Massachusetts",2013-09-23,0000875320,1989 +VFC,VF Corporation,reports,Consumer Discretionary,"Apparel, Accessories & Luxury Goods","Denver, Colorado",1979-06-30,0000103379,1899 +VIAC,ViacomCBS,reports,Communication Services,Movies & Entertainment,"New York, New York",,0000813828,2019 (1952) +VTRS,Viatris,reports,Health Care,Pharmaceuticals,"Pittsburgh, Pennsylvania",2004-04-23,0001792044,1961 +V,Visa Inc.,reports,Information Technology,Data Processing & Outsourced Services,"San Francisco, California",2009-12-21,0001403161,1958 +VNT,Vontier,reports,Information Technology,Electronic Equipment & Instruments,"Raleigh, North Carolina",2020-10-09,0001786842,2019 +VNO,Vornado Realty Trust,reports,Real Estate,Office REITs,"New York, New York",,0000899689,1982 +VMC,Vulcan Materials,reports,Materials,Construction Materials,"Birmingham, Alabama",1999-06-30,0001396009,1909 +WRB,W. R. Berkley Corporation,reports,Financials,Property & Casualty Insurance,"Greenwich, Connecticut",2019-12-05,0000011544,1967 +WAB,Westinghouse Air Brake Technologies Corp,reports,Industrials,Construction Machinery & Heavy Trucks,"Wilmerding, Pennsylvania",2019-02-27,0000943452,1999 (1869) +WMT,Walmart,reports,Consumer Staples,Hypermarkets & Super Centers,"Bentonville, Arkansas",1982-08-31,0000104169,1962 +WBA,Walgreens Boots Alliance,reports,Consumer Staples,Drug Retail,"Deerfield, Illinois",1979-12-31,0001618921,2014 +DIS,The Walt Disney Company,reports,Communication Services,Movies & Entertainment,"Burbank, California",1976-06-30,0001744489,1923 +WM,Waste Management Inc.,reports,Industrials,Environmental & Facilities Services,"Houston, Texas",,0000823768,1968 +WAT,Waters Corporation,reports,Health Care,Health Care Distributors,"Milford, Massachusetts",,0001000697,1958 +WEC,WEC Energy Group,reports,Utilities,Electric Utilities,"Milwaukee, Wisconsin",2008-10-31,0000783325,1896 +WFC,Wells Fargo,reports,Financials,Diversified Banks,"San Francisco, California",1976-06-30,0000072971,1852 +WELL,Welltower Inc.,reports,Real Estate,Health Care REITs,"Toledo, Ohio",2009-01-30,0000766704,1970 +WST,West Pharmaceutical Services,reports,Health Care,Health Care Supplies,"Exton, Pennsylvania",2020-05-22,0000105770,1923 +WDC,Western Digital,reports,Information Technology,"Technology Hardware, Storage & Peripherals","San Jose, California",2009-07-01,0000106040,1970 +WU,Western Union Co,reports,Information Technology,Data Processing & Outsourced Services,"Englewood, Colorado",2006-09-29,0001365135,1851 +WRK,WestRock,reports,Materials,Paper Packaging,"Atlanta, Georgia",,0001732845,2015 +WY,Weyerhaeuser,reports,Real Estate,Specialized REITs,"Federal Way, Washington",,0000106535,1900 +WHR,Whirlpool Corp.,reports,Consumer Discretionary,Household Appliances,"Benton Harbor, Michigan",,0000106640,1911 +WMB,Williams Companies,reports,Energy,Oil & Gas Storage & Transportation,"Tulsa, Oklahoma",1975-03-31,0000107263,1908 +WLTW,Willis Towers Watson,reports,Financials,Insurance Brokers,"London, United Kingdom",2016-01-05,0001140536,2016 +WYNN,Wynn Resorts Ltd,reports,Consumer Discretionary,Casinos & Gaming,"Paradise, Nevada",2008-11-14,0001174922,2002 +XEL,Xcel Energy Inc,reports,Utilities,Multi-Utilities,"Minneapolis, Minnesota",1957-03-04,0000072903,1909 +XRX,Xerox,reports,Information Technology,"Technology Hardware, Storage & Peripherals","Norwalk, Connecticut",,0001770450,2017 (1906) +XLNX,Xilinx,reports,Information Technology,Semiconductors,"San Jose, California",1999-11-08,0000743988,1984 +XYL,Xylem Inc.,reports,Industrials,Industrial Machinery,"White Plains, New York",2011-11-01,0001524472,2011 +YUM,Yum! Brands Inc,reports,Consumer Discretionary,Restaurants,"Louisville, Kentucky",1997-10-06,0001041061,1997 +ZBRA,Zebra Technologies,reports,Information Technology,Electronic Equipment & Instruments,"Lincolnshire, Illinois",2019-12-23,0000877212,1969 +ZBH,Zimmer Biomet,reports,Health Care,Health Care Equipment,"Warsaw, Indiana",2001-08-07,0001136869,1927 +ZION,Zions Bancorp,reports,Financials,Regional Banks,"Salt Lake City, Utah",2001-06-22,0000109380,1873 +ZTS,Zoetis,reports,Health Care,Pharmaceuticals,"Florham Park, New Jersey",2013-06-21,0001555280,1952 diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py index 42dc01df..a70360b1 100644 --- a/tests/test_partner_selection.py +++ b/tests/test_partner_selection.py @@ -5,10 +5,11 @@ import unittest import pandas as pd +from matplotlib import axes from statsmodels.distributions.empirical_distribution import ECDF from arbitragelab.copula_approach.vine_copula_partner_selection import PartnerSelection from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, multivariate_rho, \ - diagonal_measure, extremal_measure, get_co_variance_matrix + diagonal_measure, extremal_measure, get_co_variance_matrix, get_sector_data class PartnerSelectionTests(unittest.TestCase): @@ -35,6 +36,8 @@ def setUpClass(cls) -> None: cls.co_variance_matrix = get_co_variance_matrix() + cls.constituents = pd.read_csv(project_path + '/test_data/sp500_constituents-detailed.csv', index_col='Symbol') + def test_sum_correlations(self): """ Tests Traditional Approach. @@ -59,5 +62,24 @@ def test_extremal_measure(self): """ self.assertEqual(round(extremal_measure(self.ps.ranked_returns[self.quadruple], self.co_variance_matrix), 4), 108.5128) + def test_get_sector_data(self): + """ + Tests Util method which returns sector data. + """ + self.assertIsInstance(get_sector_data(self.quadruple, self.constituents), pd.DataFrame) + + def test_plot_all_target_measures(self): + """ + Tests plot_all_target_measures plotting method. + """ + self.assertIsInstance(self.ps.plot_all_target_measures('A', 'traditional'), axes.Axes) + + def test_plot_selected_pairs(self): + """ + Tests plot_selected_pairs plotting method. + """ + self.assertIsInstance(self.ps.plot_selected_pairs([self.quadruple]), axes.Axes) + + if __name__ == '__main__': unittest.main() From 82aa1b173556ef8037e1634c972d54fe66946f83 Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Fri, 5 Mar 2021 01:06:59 +0900 Subject: [PATCH 008/103] first commit of distance approach revision first commit --- .../basic_distance_approach.py | 94 +++++++++++++++++-- 1 file changed, 85 insertions(+), 9 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index 014dfad3..b45bf3bb 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -22,6 +22,7 @@ class DistanceStrategy: in "Pairs trading: Performance of a relative-value arbitrage rule." (2006) https://papers.ssrn.com/sol3/papers.cfm?abstract_id=141615. """ + def __init__(self): """ Initialize Distance strategy. @@ -35,10 +36,11 @@ def __init__(self): self.normalized_data = None # Normalized test dataset self.portfolios = None # Pair portfolios composed from test dataset self.trading_signals = None # Final trading signals + self.num_crossing = None # Number of zero crossings from train dataset devadarsh.track('DistanceStrategy') - def form_pairs(self, train_data, num_top=5, skip_top=0, list_names=None): + def form_pairs(self, train_data, by_industry=False, industry_dict=None, num_top=50, skip_top=0, list_names=None): """ Forms pairs based on input training data. @@ -71,6 +73,8 @@ def form_pairs(self, train_data, num_top=5, skip_top=0, list_names=None): :param skip_top: (int) Number of first top pairs to skip. For example, use skip_top=10 if you'd like to take num_top pairs starting from the 10th one. :param list_names: (list) List containing names of elements if Numpy array is used as input. + :param by_industry: (boolean) Whether to use pair selection based on industry group or not. + :param industry_dict: (dictionary) Dictionary matching ticker to industry group. """ # If np.array given as an input @@ -83,8 +87,16 @@ def form_pairs(self, train_data, num_top=5, skip_top=0, list_names=None): # Dropping observations with missing values (for distance calculation) normalized = normalized.dropna(axis=0) - # Finding closest pairs for each element, excluding duplicates - all_pairs = self.find_pair(normalized) + # If sector is set to True, pairs are matched within the same industry group + if by_industry: + # Check whether the input of industry group dictionary is well given + if industry_dict is None: + raise Exception("Industry group dictionary is not given. Please provide the input") + all_pairs = self.find_pair(normalized, industry_dict) + + else: + # Finding closest pairs for each element, excluding duplicates + all_pairs = self.find_pair(normalized) # Choosing needed pairs to construct a portfolio self.pairs = self.sort_pairs(all_pairs, num_top, skip_top) @@ -92,6 +104,12 @@ def form_pairs(self, train_data, num_top=5, skip_top=0, list_names=None): # Calculating historical volatility of pair portfolios (diffs of normalized prices) self.train_std = self.find_volatility(normalized, self.pairs) + # Creating portfolios for pairs chosen in the pairs formation stage with train dataset + train_portfolio = self.find_portfolios(normalized, self.pairs) + + # Calculating the number of zero crossings from the dataset + self.num_crossing = self.get_number_crossing(train_portfolio) + def trade_pairs(self, test_data, divergence=2): """ Generates trading signals for formed pairs based on new testing(trading) data. @@ -189,6 +207,27 @@ def get_pairs(self): return self.pairs + def get_pairs_crossing(self, num_top=20, skip_top=0): + """ + Outputs pairs sorted by the number of zero crossings. + + :param num_top: (int) Number of top pairs to use for portfolio formation. + :param skip_top: (int) Number of first top pairs to skip. For example, use skip_top=10 + if you'd like to take num_top pairs starting from the 10th one. + :return: (list) List containing tuples of two strings, for names of elements in a pair. + """ + + # Sorting pairs from the dictionary by the number of zero crossings in an descending order + sorted_pairs = sorted(self.num_crossing.items(), key=lambda x: x[1], reverse=True) + + # Picking top pairs + top_pairs = sorted_pairs[skip_top:(skip_top + num_top)] + + # Removing the number of crossings, so we have only tuples with elements + top_pairs = [x[0] for x in top_pairs] + + return top_pairs + def plot_portfolio(self, num_pair): """ Plots a pair portfolio (difference between element prices) and trading signals @@ -262,7 +301,7 @@ def normalize_prices(data, min_values=None, max_values=None): return normalized, min_values, max_values @staticmethod - def find_pair(data): + def find_pair(data, industry_dict=None): """ Finds the pairs with smallest distances in a given dataframe. @@ -271,6 +310,7 @@ def find_pair(data): order. So pairs ('AA', 'BC') and ('BC', 'AA') are treated as one pair ('AA', 'BC'). :param data: (pd.DataFrame) Dataframe with normalized price series. + :param industry_dict: (dictionary) Dictionary matching ticker to industry group. :return: (dict) Dictionary with keys as closest pairs and values as their distances. """ @@ -283,6 +323,16 @@ def find_pair(data): # Removing the chosen element from the dataframe data_excluded = data.drop([ticker], axis=1) + # Removing tickers in different industry group if the industry dictionary is given + if industry_dict is not None: + # Getting the industry group for the ticker + industry_group = industry_dict[ticker] + # Getting the tickers within the same industry group + tickers_same_industry = [ticker for ticker, industry in industry_dict.items() + if industry == industry_group] + # Removing other tickers in different industry group + data_excluded = data_excluded.loc[:, data_excluded.columns.isin(tickers_same_industry)] + # Calculating differences between prices data_diff = data_excluded.sub(data[ticker], axis=0) @@ -291,7 +341,6 @@ def find_pair(data): # Iterating through second elements for second_element in sum_sq_diff.index: - # Adding all new pairs to the dictionary pairs[tuple(sorted((ticker, second_element)))] = sum_sq_diff[second_element] @@ -343,7 +392,6 @@ def find_volatility(data, pairs): # Iterating through pairs of elements for pair in pairs: - # Getting two price series for elements in a pair par = data[list(pair)] @@ -378,7 +426,6 @@ def find_portfolios(data, pairs): # Iterating through pairs for pair in pairs: - # Getting two price series for elements in a pair par = data[list(pair)] @@ -410,7 +457,7 @@ def signals(portfolios, variation, divergence): :param portfolios: (pd.DataFrame) Dataframe with portfolio price series for pairs. :param variation: (dict) Dictionary with keys as pairs and values as the - historical standard variation of their pair portfolio. + historical standard deviations of their pair portfolio. :param divergence: (float) Number of standard deviations used to open a position. :return: (pd.DataFrame) Dataframe with target quantity to hold for each portfolio. """ @@ -420,7 +467,6 @@ def signals(portfolios, variation, divergence): # Iterating through pairs for pair in portfolios: - # Getting names of individual elements from dataframe column names pair_val = pair.strip('\')(\'').split('\', \'') pair_val = tuple(pair_val) @@ -462,3 +508,33 @@ def signals(portfolios, variation, divergence): signals.columns = portfolios.columns return signals + + @staticmethod + def get_number_crossing(train_portfolio): + """ + Get number of crossings + :param train_portfolio: (pd.DataFrame) Dataframe with portfolio price series for pairs. + :return: (dictionary) Dictionary with keys as pairs and values as the number of zero + crossings for pairs. + """ + + # Creating a dictionary for number of zero crossings + num_zero_crossings = {} + + # Iterating through pairs + for pair in train_portfolio: + # Getting names of individual elements from dataframe column names + pair_val = pair.strip('\')(\'').split('\', \'') + pair_val = tuple(pair_val) + + # Check if portfolio price crossed zero + portfolio = train_portfolio[pair].to_frame() + pair_mult = portfolio * portfolio.shift(1) + + # Get the number of zero crossings for the portfolio + num_zero_crossings = len(portfolio[pair_mult.iloc[:, 0] <= 0].index) + + # Adding the pair's number of zero crossings to the dictionary + num_zero_crossings[pair_val] = num_zero_crossings + + return num_zero_crossings From c066072f3e847dc1b13824c203ec222fca78560e Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 4 Mar 2021 23:07:08 +0530 Subject: [PATCH 009/103] Added vectorized implementations for 3/4 approaches. Added additional test cases for coverage. Removed plotting method which is incompatible with vectorized code. Made some minor changes to sphinx docs. --- .../vine_copula_partner_selection.py | 154 ++++-------------- .../vine_copula_partner_selection_utils.py | 97 ++++++----- .../copula_approach/partner_selection.rst | 41 +++-- tests/test_partner_selection.py | 63 ++++--- 4 files changed, 162 insertions(+), 193 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 447b9d72..2bd428c2 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -1,3 +1,6 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html """ Module for implementing partner selection approaches for vine copulas. """ @@ -9,8 +12,8 @@ import seaborn as sns from statsmodels.distributions.empirical_distribution import ECDF -from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, \ - multivariate_rho, diagonal_measure, extremal_measure, get_co_variance_matrix +from arbitragelab.copula_approach.vine_copula_partner_selection_utils import extremal_measure, \ + get_co_variance_matrix, get_sum_correlations_vectorized, diagonal_measure_vectorized, multivariate_rho_vectorized class PartnerSelection: @@ -18,8 +21,10 @@ class PartnerSelection: Implementation of the Partner Selection procedures proposed in Section 3.1.1 in the following paper. 3 partner stocks are selected for a target stock based on four different approaches namely, Traditional approach, - Extended approach,Geometric approach and Extremal approach. - https://www.econstor.eu/bitstream/10419/147450/1/870932616.pdf + Extended approach, Geometric approach and Extremal approach. + + `Stübinger, J., Mangold, B. and Krauss, C., 2018. Statistical arbitrage with vine copulas. Quantitative Finance, 18(11), pp.1831-1849. + `__ """ def __init__(self, prices: pd.DataFrame): @@ -114,6 +119,20 @@ def _generate_all_quadruples_helper(row: pd.Series) -> list: quadruples.append([target] + list(triple)) return quadruples + @staticmethod + def _prepare_combinations_of_partners(stock_selection: list) -> np.array: + """Helper function to calculate all combinations for a target stock and it's potential partners + :param: stock_selection (pd.DataFrame): the target stock has to be the first element of the array + :return: the possible combinations for the quadruples.Shape (19600,4) or + if the target stock is left out (19600,3) + """ + # We will convert the stock names into integers and then get a list of all combinations with a length of 3 + num_of_stocks = len(stock_selection) + # We turn our partner stocks into numerical indices so we can use them directly for indexing + partner_stocks_idx = np.arange(1, num_of_stocks) # basically exclude the target stock + partner_stocks_idx_combs = itertools.combinations(partner_stocks_idx, 3) + return np.array(list((0,) + comb for comb in partner_stocks_idx_combs)) + # Method 1 def traditional(self, n_targets=5) -> list: """ @@ -128,17 +147,12 @@ def traditional(self, n_targets=5) -> list: output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: - max_sum_correlations = 0 # Variable used to extract the desired maximum value - final_quadruple = None # Stores the final desired quadruple - # Iterating on all unique quadruples generated for a target - for quadruple in self.all_quadruples[target]: - sum_correlations = get_sum_correlations(self.correlation_matrix, quadruple) - if sum_correlations > max_sum_correlations: - max_sum_correlations = sum_correlations - final_quadruple = quadruple + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() + data_subset = self.correlation_matrix.loc[stock_selection, stock_selection] + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) - print(final_quadruple) + final_quadruple = get_sum_correlations_vectorized(data_subset, all_possible_combinations)[0] # Appending the final quadruple for each target to the output matrix output_matrix.append(final_quadruple) @@ -156,25 +170,16 @@ def extended(self, n_targets=5) -> list: :return output_matrix: list: List of all selected quadruples """ - u = self.returns.copy() # Generating ranked returns from quantiles using statsmodels ECDF - for column in self.returns.columns: - ecdf = ECDF(self.returns.loc[:, column]) - u[column] = ecdf(self.returns.loc[:, column]) + ecdf_df = self.returns.apply(lambda x: ECDF(x)(x), axis=0) output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: - max_correlation = -np.inf # Variable used to extract the desired maximum value - final_quadruple = None # Stores the final desired quadruple + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() + data_subset = ecdf_df[stock_selection] + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) - # Iterating on all unique quadruples generated for a target - for quadruple in self.all_quadruples[target]: - correlation = multivariate_rho(u[quadruple]) - if correlation > max_correlation: - max_correlation = correlation - final_quadruple = quadruple - - print(final_quadruple) + final_quadruple = multivariate_rho_vectorized(data_subset, all_possible_combinations)[0] # Appending the final quadruple for each target to the output matrix output_matrix.append(final_quadruple) @@ -194,16 +199,11 @@ def geometric(self, n_targets=5) -> list: output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: - min_measure = np.inf # Variable used to extract the desired minimum value - final_quadruple = None # Stores the final desired quadruple + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() + data_subset = self.ranked_returns[stock_selection] + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) - # Iterating on all unique quadruples generated for a target - for quadruple in self.all_quadruples[target]: - measure = diagonal_measure(self.ranked_returns[quadruple]) - if measure < min_measure: - min_measure = measure - final_quadruple = quadruple - print(final_quadruple) + final_quadruple = diagonal_measure_vectorized(data_subset, all_possible_combinations)[0] # Appending the final quadruple for each target to the output matrix output_matrix.append(final_quadruple) @@ -233,7 +233,6 @@ def extremal(self, n_targets=5) -> list: if measure > max_measure: max_measure = measure final_quadruple = quadruple - print(final_quadruple) # Appending the final quadruple for each target to the output matrix output_matrix.append(final_quadruple) @@ -267,84 +266,3 @@ def plot_selected_pairs(self, quadruples: list): axs[i].set_ylabel('Cumulative Daily Returns') return axs - - def plot_all_target_measures(self, target: str, procedure: str): - """ - Plots a scatterplot showing measures calculated for all possible quadruples of a given target stock. - :param target: (str) : target stock ticker - :param procedure: (str) : name of procedure for calculating measure - """ - - if procedure not in ('traditional', 'extended', 'geometric', 'extremal'): - raise Exception("Please enter a valid procedure name, i.e ('traditional', 'extended', 'geometric', " - "'extremal') ") - - measures_list = [] - quadruples = self.all_quadruples[target] # List of all quadruples - final_quadruple = None - final_measure = -np.inf - - co_variance_matrix = None - u = None - - # Preprocessing steps for some approaches - if procedure == 'extremal': - co_variance_matrix = get_co_variance_matrix() - elif procedure == 'extended': - u = self.returns.copy() # Generating ranked returns from quantiles using statsmodels ECDF - for column in self.returns.columns: - ecdf = ECDF(self.returns.loc[:, column]) - u[column] = ecdf(self.returns.loc[:, column]) - elif procedure == 'geometric': - final_measure = np.inf - - for quadruple in quadruples: - # Separate functionality for geometric approach because here the minimum measure is required. - if procedure == 'geometric': - measure = diagonal_measure(self.ranked_returns[quadruple]) - measures_list.append(measure) - if measure < final_measure: - final_measure = measure - final_quadruple = quadruple - continue - - measure = 0 - if procedure == 'traditional': - measure = get_sum_correlations(self.correlation_matrix, quadruple) - elif procedure == 'extended': - measure = multivariate_rho(u[quadruple]) - elif procedure == 'extremal': - measure = extremal_measure(self.ranked_returns[quadruple], co_variance_matrix) - - measures_list.append(measure) # Storing all calculated measures - if measure > final_measure: - final_measure = measure - final_quadruple = quadruple - - print(final_quadruple) - - return self._plot_all_target_measures_helper(measures_list, target, procedure) - - @staticmethod - def _plot_all_target_measures_helper(measures_list: list, target:str, procedure: str): - """ - Helper Method for self.plot_all_target_measures. - :measures_list: (list) : List of calculated measures for all quadruples of a target - :param target: (str) : target stock ticker - :param procedure: (str) : name of procedure for calculating measure - """ - - # Code for plotting the final list of calculated measures - plt.figure(figsize=(20, 6)) - data = pd.DataFrame(measures_list, columns=['measure']) - data['indices'] = range(len(measures_list)) - data['hue'] = [0] * len(data) - if procedure == 'geometric': - data.loc[data['measure'].idxmin(), 'hue'] = 1 - else: - data.loc[data['measure'].idxmax(), 'hue'] = 1 - ax = sns.scatterplot(x='indices', y='measure', data=data, alpha=0.5, hue='hue', size='hue', - sizes={0: 5, 1: 40}, legend=False) - plt.title(f"Measures calculated from {procedure} approach for all quadruples of target {target}") - - return ax diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index b2232216..50f79382 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -1,3 +1,6 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html """ Utils for implementing partner selection approaches for vine copulas. """ @@ -18,63 +21,73 @@ def get_sector_data(quadruple, constituents): return pd.DataFrame() -def get_sum_correlations(corr_matrix, quadruple: list) -> float: +def get_sum_correlations_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: """ Helper function for traditional approach to partner selection. Calculates sum of pairwise correlations between all stocks in the quadruple. - :param corr_matrix: Correlation Matrix - :param quadruple: (list) : list of 4 stock tickers - :return: (float) : sum of correlations + :param data_subset: (pd.DataFrame) : + :param all_possible_combinations: (np.array) : + :return: """ - return (corr_matrix.loc[quadruple, quadruple].sum().sum() - len(quadruple)) / 2 + # Here the magic happens: + # We use the combinations as an index + corr_matrix_a = data_subset.values[:, all_possible_combinations] + # corr_matrix_a has now the shape of (51, 19600, 4) + # We now use take along axis to get the shape (4,19600,4), then we can sum the first and the last dimension + corr_sums = np.sum(np.take_along_axis(corr_matrix_a, all_possible_combinations.T[..., np.newaxis], axis=0), + axis=(0, 2)) + + d = all_possible_combinations.shape[-1] + corr_sums = (corr_sums - d) / 2 + # this returns the shape of + # (19600,1) + # Afterwards we return the maximum index for the sums + max_index = np.argmax( + corr_sums) + final_quadruple = data_subset.columns[list(all_possible_combinations[max_index])].tolist() + + return final_quadruple, corr_sums[max_index] -def multivariate_rho(u: pd.DataFrame) -> float: +def multivariate_rho_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: """ Helper function for extended approach to partner selection. Calculates 3 proposed estimators for high dimensional generalization for Spearman's rho. These implementations are present in Schmid, F., Schmidt, R., 2007. Multivariate extensions of Spearman’s rho and related statis-tics. - :param u: (pd.DataFrame) : ranked returns of quadruple - :return: (float) : mean of the three estimators of multivariate rho """ + quadruples_combinations_data = data_subset.values[:, all_possible_combinations] - n, d = u.shape # n : Number of samples, d : Number of stocks - h_d = (d + 1) / ((2 ** d) - d - 1) + n, _, d = quadruples_combinations_data.shape # n : Number of samples, d : Number of stocks + h_d = (d + 1) / (2 ** d - d - 1) - # # Calculating the first estimator of multivariate rho - sum_1 = np.prod(1 - u, axis=1).sum() - rho_1 = h_d * (-1 + (((2 ** d) / n) * sum_1)) + # Calculating the first estimator of multivariate rho + sum_1 = np.product(1 - quadruples_combinations_data, axis=-1).sum(axis=0) + rho_1 = h_d * (-1 + (2 ** d / n) * sum_1) - # # Calculating the second estimator of multivariate rho - sum_2 = np.prod(u, axis=1).sum() - rho_2 = h_d * (-1 + (((2 ** d) / n) * sum_2)) + # Calculating the second estimator of multivariate rho + sum_2 = np.product(quadruples_combinations_data, axis=-1).sum(axis=0) + rho_2 = h_d * (-1 + (2 ** d / n) * sum_2) # Calculating the third estimator of multivariate rho - pairs = itertools.combinations(range(u.shape[-1]), 2) - sum_3 = np.sum([(1 - u.iloc[:, k]) * (1 - u.iloc[:, l]) for (k, l) in pairs]) + pairs = np.array(list(itertools.combinations(range(d), 2))) + k, l = pairs[:, 0], pairs[:, 1] + sum_3 = ((1 - quadruples_combinations_data[:, :, k]) * (1 - quadruples_combinations_data[:, :, l])).sum(axis=(0, 2)) dc2 = scipy.special.comb(d, 2, exact=True) rho_3 = -3 + (12 / (n * dc2)) * sum_3 - return (rho_1 + rho_2 + rho_3) / 3 + quadruples_scores = (rho_1 + rho_2 + rho_3) / 3 + # The quadruple scores have the shape of (19600,1) now + max_index = np.argmax(quadruples_scores) + final_quadruple = data_subset.columns[list(all_possible_combinations[max_index])].tolist() -def distance_calc(a, ba, x): - """ - Helper function to calculate Euclidean distance between Point and diagonal used to calculate diagonal measure. - :param a: Origin (0,0,0,0) - :param ba: d-dimensional Diagonal - :param x: list of points on d-dimensions - :return: - """ - pa = x - a # Shape : (n,d), pa represents vector from point p to point a - t = np.dot(pa, ba) / np.dot(ba.T, ba) - return np.linalg.norm(pa - np.dot(t, ba.T), ord=2, axis=1) + return final_quadruple, quadruples_scores[max_index] -def diagonal_measure(points) -> float: +def diagonal_measure_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: """ Helper function for geometric approach to partner selection. Calculates the sum of Euclidean distances from the relative ranks to the (hyper-)diagonal in four dimensional space for a given target stock. @@ -82,15 +95,21 @@ def diagonal_measure(points) -> float: Reference for calculating the euclidean distance from a point to diagonal https://in.mathworks.com/matlabcentral/answers/76727-how-can-i-calculate-distance-between-a-point-and-a-line-in-4d-or-space-higer-than-3d - :param points: (pd.DataFrame) : ranked returns of 4 stock tickers - :return total_distance: (float) : total euclidean distance + """ - d = points.shape[-1] # d : Number of stocks - a = np.zeros((1, d)) # Point a denotes origin which is present on hyper-diagonal - b = np.ones((1, d)) # Point b denotes point (1,1,1,1) on hyper-diagonal - ba = (b - a).T # ba represents the hyper-diagonal - total_distance = distance_calc(a, ba, points).sum() - return total_distance + + quadruples_combinations_data = data_subset.values[:, all_possible_combinations] + d = quadruples_combinations_data.shape[-1] # Shape : (n, 19600, d) where n : Number of samples, d : Number of stocks + + line = np.ones(d) + # Einsum is great for specifying which dimension to multiply together + # this extends the distance method for all 19600 combinations + pp = (np.einsum("ijk,k->ji", quadruples_combinations_data, line) / np.linalg.norm(line)) + pn = np.sqrt(np.einsum('ijk,ijk->ji', quadruples_combinations_data, quadruples_combinations_data)) + distance_scores = np.sqrt(pn ** 2 - pp ** 2).sum(axis=1) + min_index = np.argmin(distance_scores) + final_quadruple = data_subset.columns[list(all_possible_combinations[min_index])].tolist() + return final_quadruple, distance_scores[min_index] def extremal_measure(u, co_variance_matrix): diff --git a/docs/source/copula_approach/partner_selection.rst b/docs/source/copula_approach/partner_selection.rst index 06efd7b4..6854a790 100644 --- a/docs/source/copula_approach/partner_selection.rst +++ b/docs/source/copula_approach/partner_selection.rst @@ -15,14 +15,22 @@ Vine Copula Partner Selection Approaches This module contains implementation of the four partner selection approaches mentioned in Section 3.1.1 of Statistical Arbitrage with Vine Copulas. -In this paper[1], Stubinger, Mangold and Krauss developed a multivariate statistical arbitrage strategy based on vine copulas - a highly flexible instrument for linear and nonlinear multivariate dependence modeling. Pairs trading is a relative-value arbitrage strategy, where an investor seeks to profit from mean-reversion properties of the price spread between two co-moving securities. Existing literature focused on using bivariate copulas to model the dependence structure between two stock return time series, and to identify mispricings that can potentially be exploited in a pairs trading application. +In this paper[1], Stubinger, Mangold and Krauss developed a multivariate statistical arbitrage strategy based on vine copulas - +a highly flexible instrument for linear and nonlinear multivariate dependence modeling. Pairs trading is a relative-value arbitrage strategy, +where an investor seeks to profit from mean-reversion properties of the price spread between two co-moving securities. +Existing literature focused on using bivariate copulas to model the dependence structure between two stock return time series, +and to identify mispricings that can potentially be exploited in a pairs trading application. -This paper proposes a multivariate copula-based statistical arbitrage framework, where specifically, for each stock in the S&P 500 data base, the three most suitable partners are selected by leveraging different selection criteria. Then, the multivariate copula models are benchmarked to capture the dependence structure of the selected quadruples. Later on, the paper focusses on the generation of trading signals and backtesting. +This paper proposes a multivariate copula-based statistical arbitrage framework, where specifically, +for each stock in the S&P 500 data base, the three most suitable partners are selected by leveraging different selection criteria. +Then, the multivariate copula models are benchmarked to capture the dependence structure of the selected quadruples. +Later on, the paper focusses on the generation of trading signals and backtesting. Introduction ############ -This module will focus on the various Partner Selection procedures and their implementations, as described in the paper. For every stock in the S&P 500, a partner triple is identified based on adequate measures of association. The following four partner selection approaches are implemented : +This module will focus on the various Partner Selection procedures and their implementations, as described in the paper. +For every stock in the S&P 500, a partner triple is identified based on adequate measures of association. The following four partner selection approaches are implemented : - Traditional Approach - baseline approach where the high dimensional relation between the four stocks is approximated by their pairwise bivariate correlations via Spearman’s :math:`\rho`; @@ -32,26 +40,33 @@ This module will focus on the various Partner Selection procedures and their imp - Extremal Approach - involves calculating a non-parametric :math:`\chi^2` test statistic based on Mangold (2015)[3] to measure the degree of deviation from independence. -Firstly, all measures of association are calculated using the ranks of the daily discrete returns of our samples. Ranked transformation provides robustness against outliers. Secondly, only the top 50 most highly correlated stocks are taken into consideration for each target stock, to reduce the computational burden. +Firstly, all measures of association are calculated using the ranks of the daily discrete returns of our samples. +Ranked transformation provides robustness against outliers. +Secondly, only the top 50 most highly correlated stocks are taken into consideration for each target stock, to reduce the computational burden. Traditional Approach -******************** +#################### -Extended Approach -******************** +Implementation +************** -Geometric Approach -******************** +Extended Approach +################# -Extremal Approach -******************** +Implementation +************** +Geometric Approach +################## Implementation -############## - +************** +Extremal Approach +################# +Implementation +************** Research Notebooks ################## diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py index a70360b1..6227c147 100644 --- a/tests/test_partner_selection.py +++ b/tests/test_partner_selection.py @@ -1,15 +1,19 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html """ Tests for the partner selection approaches from the Copula module. """ import os import unittest +import numpy as np import pandas as pd from matplotlib import axes from statsmodels.distributions.empirical_distribution import ECDF from arbitragelab.copula_approach.vine_copula_partner_selection import PartnerSelection -from arbitragelab.copula_approach.vine_copula_partner_selection_utils import get_sum_correlations, multivariate_rho, \ - diagonal_measure, extremal_measure, get_co_variance_matrix, get_sector_data +from arbitragelab.copula_approach.vine_copula_partner_selection_utils import multivariate_rho_vectorized, \ + extremal_measure, get_co_variance_matrix, get_sector_data, get_sum_correlations_vectorized, diagonal_measure_vectorized class PartnerSelectionTests(unittest.TestCase): @@ -29,37 +33,60 @@ def setUpClass(cls) -> None: prices = pd.read_csv(data_path, parse_dates=True, index_col='Date').dropna() cls.ps = PartnerSelection(prices) - cls.u = cls.ps.returns.copy() - for column in cls.ps.returns.columns: - ecdf = ECDF(cls.ps.returns.loc[:, column]) - cls.u[column] = ecdf(cls.ps.returns.loc[:, column]) + cls.u = cls.ps.returns.apply(lambda x: ECDF(x)(x), axis=0) cls.co_variance_matrix = get_co_variance_matrix() cls.constituents = pd.read_csv(project_path + '/test_data/sp500_constituents-detailed.csv', index_col='Symbol') - def test_sum_correlations(self): + def test_traditional(self): """ Tests Traditional Approach. """ - self.assertEqual(round(get_sum_correlations(self.ps.correlation_matrix, self.quadruple), 4), 1.9678) + self.assertEqual(self.ps.traditional(1),[['A', 'AAL', 'AAPL', 'AAP']]) - def test_multivariate_rho(self): + def test_extended(self): """ Tests Extended Approach. """ - self.assertEqual(round(multivariate_rho(self.u[self.quadruple]), 4), 0.3114) + self.assertEqual(self.ps.extended(1), [['A', 'AAL', 'AAPL', 'AAP']]) - def test_diagonal_measure(self): + def test_geometric(self): """ Tests Geometric Approach. """ - self.assertEqual(round(diagonal_measure(self.ps.ranked_returns[self.quadruple]), 4), 91.9374) + self.assertEqual(self.ps.geometric(1),[['A', 'AAL', 'AAPL', 'AAP']]) - def test_extremal_measure(self): + def test_extremal(self): """ Tests Extremal Approach. """ + self.assertEqual(self.ps.extremal(1), [['A', 'AAL', 'AAPL', 'AAP']]) + + def test_sum_correlations(self): + """ + Tests helper function of Traditional Approach. + """ + self.assertEqual(round( + get_sum_correlations_vectorized(self.ps.correlation_matrix.loc[self.quadruple, self.quadruple], + np.array([[0, 1, 2, 3]]))[1], 4), 1.9678) + + def test_multivariate_rho(self): + """ + Tests helper function of Extended Approach. + """ + self.assertEqual(round(multivariate_rho_vectorized(self.u[self.quadruple], np.array([[0,1,2,3]]))[1], 4), 0.3114) + + def test_diagonal_measure(self): + """ + Tests helper function of Geometric Approach. + """ + self.assertEqual(round(diagonal_measure_vectorized(self.ps.ranked_returns[self.quadruple], np.array([[0,1,2,3]]))[1], 4), 91.9374) + + def test_extremal_measure(self): + """ + Tests helper function of Extremal Approach. + """ self.assertEqual(round(extremal_measure(self.ps.ranked_returns[self.quadruple], self.co_variance_matrix), 4), 108.5128) def test_get_sector_data(self): @@ -68,18 +95,8 @@ def test_get_sector_data(self): """ self.assertIsInstance(get_sector_data(self.quadruple, self.constituents), pd.DataFrame) - def test_plot_all_target_measures(self): - """ - Tests plot_all_target_measures plotting method. - """ - self.assertIsInstance(self.ps.plot_all_target_measures('A', 'traditional'), axes.Axes) - def test_plot_selected_pairs(self): """ Tests plot_selected_pairs plotting method. """ self.assertIsInstance(self.ps.plot_selected_pairs([self.quadruple]), axes.Axes) - - -if __name__ == '__main__': - unittest.main() From 7fbe65e30b7db00a8fffd57baa70172a3caa47a5 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 5 Mar 2021 12:25:03 +0530 Subject: [PATCH 010/103] Making changes to docstrings and comments based on PR review. --- .../vine_copula_partner_selection.py | 79 ++++++++-------- .../vine_copula_partner_selection_utils.py | 89 ++++++++++--------- tests/test_partner_selection.py | 1 + 3 files changed, 90 insertions(+), 79 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 2bd428c2..8ff92e7d 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -34,7 +34,7 @@ def __init__(self, prices: pd.DataFrame): These steps include, finding the returns and ranked returns of the stocks, and calculating the top 50 correlated stocks for each stock in the universe. - :param prices: (pd.DataFrame): Contains price series of all stocks in universe + :param prices: (pd.DataFrame) Contains price series of all stocks in universe. """ if len(prices) == 0: @@ -57,7 +57,7 @@ def _correlation(self) -> pd.DataFrame: """ Calculates correlation between all stocks in universe. - :return: (pd.DataFrame) : Correlation Matrix + :return: (pd.DataFrame) Correlation Matrix. """ return self.ranked_returns.corr(method='pearson') # Pearson or spearman,we get same results as input is ranked @@ -67,8 +67,8 @@ def _get_returns(self) -> (pd.DataFrame, pd.DataFrame): Calculating daily returns and ranked daily returns of the stocks. :return (tuple): - returns_df : (pd.DataFrame) : Dataframe consists of daily returns - returns_df_ranked : (pd.DataFrame) : Dataframe consists of ranked daily returns between [0,1] + returns_df : (pd.DataFrame) Dataframe consists of daily returns. + returns_df_ranked : (pd.DataFrame) Dataframe consists of ranked daily returns between [0,1]. """ returns_df = self.universe.pct_change() @@ -82,7 +82,7 @@ def _top_50_tickers(self) -> pd.DataFrame: """ Calculates the top 50 correlated stocks for each target stock. - :return: (pd.DataFrame) : Dataframe consisting of 50 columns for each stock in the universe + :return: (pd.DataFrame) Dataframe consisting of 50 columns for each stock in the universe. """ def tickers_list(col): @@ -99,7 +99,7 @@ def _generate_all_quadruples(self) -> pd.DataFrame: """ Method generates unique quadruples for all target stocks in universe. - :return: (pd.DataFrame) : consists of all quadruples for every target stock + :return: (pd.DataFrame) consists of all quadruples for every target stock. """ return self.top_50_correlations.apply(self._generate_all_quadruples_helper, axis=1) @@ -109,8 +109,8 @@ def _generate_all_quadruples_helper(row: pd.Series) -> list: """ Helper function which generates unique quadruples for each target stock. - :param row: (pd.Series) : list of 50 partner stocks - :return: (list) : quadruples + :param row: (pd.Series) list of 50 partner stocks. + :return: (list) quadruples. """ target = row.name @@ -121,15 +121,17 @@ def _generate_all_quadruples_helper(row: pd.Series) -> list: @staticmethod def _prepare_combinations_of_partners(stock_selection: list) -> np.array: - """Helper function to calculate all combinations for a target stock and it's potential partners - :param: stock_selection (pd.DataFrame): the target stock has to be the first element of the array - :return: the possible combinations for the quadruples.Shape (19600,4) or - if the target stock is left out (19600,3) + """Helper function to calculate all combinations for a target stock and it's potential partners. + Stocks are treated as integers for vectorization purposes. + + :param stock_selection: (pd.DataFrame) the target stock has to be the first element of the array. + :return: the possible combinations for the quadruples. Shape (19600,4) . """ - # We will convert the stock names into integers and then get a list of all combinations with a length of 3 + + # We will convert the stock names into integers and then get a list of all combinations with a length of 3. num_of_stocks = len(stock_selection) - # We turn our partner stocks into numerical indices so we can use them directly for indexing - partner_stocks_idx = np.arange(1, num_of_stocks) # basically exclude the target stock + # We turn our partner stocks into numerical indices so we can use them directly for indexing. + partner_stocks_idx = np.arange(1, num_of_stocks) # basically exclude the target stock. partner_stocks_idx_combs = itertools.combinations(partner_stocks_idx, 3) return np.array(list((0,) + comb for comb in partner_stocks_idx_combs)) @@ -140,20 +142,20 @@ def traditional(self, n_targets=5) -> list: For all possible quadruples of a given stock, we calculate the sum of all pairwise correlations. For every target stock the quadruple with the highest sum is returned. - :param n_targets: (int) : number of target stocks to select - :return output_matrix: list: List of all selected quadruples + :param n_targets: (int) number of target stocks to select. + :return output_matrix: (list) List of all selected quadruples. """ output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target. data_subset = self.correlation_matrix.loc[stock_selection, stock_selection] - all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4). final_quadruple = get_sum_correlations_vectorized(data_subset, all_possible_combinations)[0] - # Appending the final quadruple for each target to the output matrix + # Appending the final quadruple for each target to the output matrix. output_matrix.append(final_quadruple) return output_matrix @@ -166,21 +168,21 @@ def extended(self, n_targets=5) -> list: for all possible quadruples of a given stock. For every target stock the quadruple with the highest correlation is returned. - :param n_targets: (int) : number of target stocks to select - :return output_matrix: list: List of all selected quadruples + :param n_targets: (int) number of target stocks to select. + :return output_matrix: (list) List of all selected quadruples. """ - ecdf_df = self.returns.apply(lambda x: ECDF(x)(x), axis=0) + ecdf_df = self.returns.apply(lambda x: ECDF(x)(x), axis=0) # Calculating ranks of returns using quantiles data. output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target. data_subset = ecdf_df[stock_selection] - all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4). final_quadruple = multivariate_rho_vectorized(data_subset, all_possible_combinations)[0] - # Appending the final quadruple for each target to the output matrix + # Appending the final quadruple for each target to the output matrix. output_matrix.append(final_quadruple) return output_matrix @@ -192,19 +194,19 @@ def geometric(self, n_targets=5) -> list: It involves calculating the four dimensional diagonal measure for all possible quadruples of a given stock. For every target stock the quadruple with the lowest diagonal measure is returned. - :param n_targets: (int) : number of target stocks to select - :return output_matrix: list: List of all selected quadruples + :param n_targets: (int) number of target stocks to select. + :return output_matrix: (list) List of all selected quadruples. """ output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target. data_subset = self.ranked_returns[stock_selection] - all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4). final_quadruple = diagonal_measure_vectorized(data_subset, all_possible_combinations)[0] - # Appending the final quadruple for each target to the output matrix + # Appending the final quadruple for each target to the output matrix. output_matrix.append(final_quadruple) return output_matrix @@ -216,24 +218,24 @@ def extremal(self, n_targets=5) -> list: It involves calculating a non-parametric test statistic based on Mangold (2015) to measure the degree of deviation from independence. Main focus of this measure is the occurrence of joint extreme events. - :param n_targets: (int) : number of target stocks to select - :return output_matrix: list: List of all selected quadruples + :param n_targets: (int) number of target stocks to select. + :return output_matrix: (list) List of all selected quadruples. """ co_variance_matrix = get_co_variance_matrix() output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: - max_measure = -np.inf # Variable used to extract the desired maximum value - final_quadruple = None # Stores the final desired quadruple + max_measure = -np.inf # Variable used to extract the desired maximum value. + final_quadruple = None # Stores the final desired quadruple. - # Iterating on all unique quadruples generated for a target + # Iterating on all unique quadruples generated for a target. for quadruple in self.all_quadruples[target]: measure = extremal_measure(self.ranked_returns[quadruple], co_variance_matrix) if measure > max_measure: max_measure = measure final_quadruple = quadruple - # Appending the final quadruple for each target to the output matrix + # Appending the final quadruple for each target to the output matrix. output_matrix.append(final_quadruple) return output_matrix @@ -241,7 +243,8 @@ def extremal(self, n_targets=5) -> list: def plot_selected_pairs(self, quadruples: list): """ Plots the final selection of quadruples. - :param quadruples: List of quadruples + + :param quadruples: (list) List of quadruples. """ if quadruples is None: diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index 50f79382..a55c01d7 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -13,7 +13,7 @@ def get_sector_data(quadruple, constituents): """ - Function returns Sector and Sub sector information from tickers. + Function returns Sector and Sub sector information for all tickers in quadruple. """ try: return constituents.loc[quadruple, ['Security', 'GICS Sector', 'GICS Sub-Industry']] @@ -24,26 +24,26 @@ def get_sector_data(quadruple, constituents): def get_sum_correlations_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: """ Helper function for traditional approach to partner selection. - Calculates sum of pairwise correlations between all stocks in the quadruple. + Calculates sum of pairwise correlations between all stocks in each quadruple. + Returns the quadruple with the largest sum. - :param data_subset: (pd.DataFrame) : - :param all_possible_combinations: (np.array) : - :return: + :param data_subset: (pd.DataFrame) Dataset storing correlations data. + :param all_possible_combinations: (np.array) Array of indices of 19600 quadruples. + + :return: (tuple) final quadruple, corresponding measure """ - # Here the magic happens: - # We use the combinations as an index - corr_matrix_a = data_subset.values[:, all_possible_combinations] - # corr_matrix_a has now the shape of (51, 19600, 4) - # We now use take along axis to get the shape (4,19600,4), then we can sum the first and the last dimension - corr_sums = np.sum(np.take_along_axis(corr_matrix_a, all_possible_combinations.T[..., np.newaxis], axis=0), - axis=(0, 2)) + # We use the combinations as an index. + corr_matrix = data_subset.values[:, all_possible_combinations] + # corr_matrix has shape of (51, 19600, 4). + # We now use np.take_along_axis to get the shape (4,19600,4), then we can sum the first and the last dimension. + corr_sums = np.sum(np.take_along_axis(corr_matrix, all_possible_combinations.T[..., np.newaxis], axis=0), + axis=(0, 2)) #Shape: (19600,1). d = all_possible_combinations.shape[-1] corr_sums = (corr_sums - d) / 2 - # this returns the shape of - # (19600,1) - # Afterwards we return the maximum index for the sums + + # Return the maximum index for the sums. max_index = np.argmax( corr_sums) final_quadruple = data_subset.columns[list(all_possible_combinations[max_index])].tolist() @@ -56,22 +56,26 @@ def multivariate_rho_vectorized(data_subset: pd.DataFrame, all_possible_combinat Helper function for extended approach to partner selection. Calculates 3 proposed estimators for high dimensional generalization for Spearman's rho. These implementations are present in Schmid, F., Schmidt, R., 2007. Multivariate extensions of Spearman’s rho and related statis-tics. + Returns the quadruple with the largest measure. + :param data_subset: (pd.DataFrame) Dataset storing ranked returns data. + :param all_possible_combinations: (np.array) Array of indices of 19600 quadruples. + :return: (tuple) final quadruple, corresponding measure """ - quadruples_combinations_data = data_subset.values[:, all_possible_combinations] + quadruples_combinations_data = data_subset.values[:, all_possible_combinations] #Shape: (n, 19600, d). - n, _, d = quadruples_combinations_data.shape # n : Number of samples, d : Number of stocks + n, _, d = quadruples_combinations_data.shape # n : Number of samples, d : Number of stocks. h_d = (d + 1) / (2 ** d - d - 1) - # Calculating the first estimator of multivariate rho + # Calculating the first estimator of multivariate rho. sum_1 = np.product(1 - quadruples_combinations_data, axis=-1).sum(axis=0) rho_1 = h_d * (-1 + (2 ** d / n) * sum_1) - # Calculating the second estimator of multivariate rho + # Calculating the second estimator of multivariate rho. sum_2 = np.product(quadruples_combinations_data, axis=-1).sum(axis=0) rho_2 = h_d * (-1 + (2 ** d / n) * sum_2) - # Calculating the third estimator of multivariate rho + # Calculating the third estimator of multivariate rho. pairs = np.array(list(itertools.combinations(range(d), 2))) k, l = pairs[:, 0], pairs[:, 1] sum_3 = ((1 - quadruples_combinations_data[:, :, k]) * (1 - quadruples_combinations_data[:, :, l])).sum(axis=(0, 2)) @@ -79,7 +83,7 @@ def multivariate_rho_vectorized(data_subset: pd.DataFrame, all_possible_combinat rho_3 = -3 + (12 / (n * dc2)) * sum_3 quadruples_scores = (rho_1 + rho_2 + rho_3) / 3 - # The quadruple scores have the shape of (19600,1) now + # The quadruple scores have the shape of (19600,1) now. max_index = np.argmax(quadruples_scores) final_quadruple = data_subset.columns[list(all_possible_combinations[max_index])].tolist() @@ -90,20 +94,20 @@ def multivariate_rho_vectorized(data_subset: pd.DataFrame, all_possible_combinat def diagonal_measure_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: """ Helper function for geometric approach to partner selection. Calculates the sum of Euclidean distances - from the relative ranks to the (hyper-)diagonal in four dimensional space for a given target stock. - - Reference for calculating the euclidean distance from a point to diagonal - https://in.mathworks.com/matlabcentral/answers/76727-how-can-i-calculate-distance-between-a-point-and-a-line-in-4d-or-space-higer-than-3d - + from the relative ranks to the (hyper-)diagonal in four dimensional space for each quadruple of a target stock. + Returns the quadruple with the smallest measure. + :param data_subset: (pd.DataFrame) Dataset storing ranked returns data. + :param all_possible_combinations: (np.array) Array of indices of 19600 quadruples. + :return: (tuple) final quadruple, corresponding measure """ quadruples_combinations_data = data_subset.values[:, all_possible_combinations] - d = quadruples_combinations_data.shape[-1] # Shape : (n, 19600, d) where n : Number of samples, d : Number of stocks + d = quadruples_combinations_data.shape[-1] # Shape : (n, 19600, d) where n : Number of samples, d : Number of stocks. line = np.ones(d) - # Einsum is great for specifying which dimension to multiply together - # this extends the distance method for all 19600 combinations + # Einsum is great for specifying which dimension to multiply together. + # this extends the distance method for all 19600 combinations. pp = (np.einsum("ijk,k->ji", quadruples_combinations_data, line) / np.linalg.norm(line)) pn = np.sqrt(np.einsum('ijk,ijk->ji', quadruples_combinations_data, quadruples_combinations_data)) distance_scores = np.sqrt(pn ** 2 - pp ** 2).sum(axis=1) @@ -116,16 +120,17 @@ def extremal_measure(u, co_variance_matrix): """ Helper function to calculate chi-squared test statistic based on p-dimensional Nelsen copulas. Specifically, proposition 3.3 from Mangold (2015) is implemented for 4 dimensions. - :param u: (pd.DataFrame) : ranked returns of stocks in quadruple. - :param co_variance_matrix: (np.array) : Covariance matrix - :return: test statistic + + :param u: (pd.DataFrame) ranked returns of stocks in quadruple. + :param co_variance_matrix: (np.array) Covariance matrix. + :return: test statistic. """ u = u.to_numpy() n = u.shape[0] - # Calculating array T_(4,n) from proposition 3.3 - t = t_calc(u).mean(axis=1).reshape(-1, 1) # Shape : (16, 1), Taking the mean w.r.t n - # Calculating the final test statistic + # Calculating array T_(4,n) from proposition 3.3. + t = t_calc(u).mean(axis=1).reshape(-1, 1) # Shape : (16, 1), Taking the mean w.r.t n. + # Calculating the final test statistic. t_test_statistic = n * np.matmul(t.T, np.matmul(co_variance_matrix, t)) return t_test_statistic[0, 0] @@ -142,7 +147,7 @@ def get_co_variance_matrix(): # Integrals in lower triangle are skipped. continue - # Numerical Integration of 4 dimensions + # Numerical Integration of 4 dimensions. co_variance_matrix[i, j] = scipy.integrate.nquad(variance_integral_func, [(0, 1)] * 4, args=(l1, l2))[0] inds = np.tri(16, k=-1, dtype=bool) # Storing the indices of elements in lower triangle. @@ -154,8 +159,9 @@ def t_calc(u): """ Calculates T_(4,n) as seen in proposition 3.3. Each of the 16 rows in the array are appended to output and returned as numpy array. - :param u: - :return: (np.array) of Shape (16, n) + + :param u: (pd.DataFrame) ranked returns of stocks in quadruple. + :return: (np.array) of Shape (16, n). """ output = [] for l in itertools.product([1, 2], [1, 2], [1, 2], [1, 2]): @@ -164,15 +170,16 @@ def t_calc(u): res = func(u[:, 0], l[0]) * func(u[:, 1], l[1]) * func(u[:, 2], l[2]) * func(u[:, 3], l[3]) output.append(res) - return np.array(output) # Shape (16, n) + return np.array(output) # Shape (16, n). def func(t, value): """ Function returns equation form of respective variable after partial differentiation. All variables in the differential equations are in one of two forms. - :param t: (np.array) Variable - :param value: (int) Flag denoting equation form of variable + + :param t: (np.array) Variable. + :param value: (int) Flag denoting equation form of variable. :return: """ diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py index 6227c147..b1002a01 100644 --- a/tests/test_partner_selection.py +++ b/tests/test_partner_selection.py @@ -25,6 +25,7 @@ class PartnerSelectionTests(unittest.TestCase): def setUpClass(cls) -> None: """ Creates dataframes with returns and quantile data to work with corresponding test cases. + Using setUpClass instead of setUp for performance reasons as setUpClass is executed just once for all test cases. """ project_path = os.path.dirname(__file__) From 22dd2672e65914e791dee4dbdfec1b2573260a6f Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Fri, 5 Mar 2021 18:55:03 +0900 Subject: [PATCH 011/103] add documentations add documentations and fixed some minor issues --- .../basic_distance_approach.py | 82 +++++++++++-------- 1 file changed, 50 insertions(+), 32 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index b45bf3bb..dab8b1a7 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -35,6 +35,7 @@ def __init__(self): self.train_std = None # Historical volatility for each chosen pair portfolio self.normalized_data = None # Normalized test dataset self.portfolios = None # Pair portfolios composed from test dataset + self.train_portfolio = None # Pair portfolios composed from train dataset self.trading_signals = None # Final trading signals self.num_crossing = None # Number of zero crossings from train dataset @@ -53,6 +54,9 @@ def form_pairs(self, train_data, by_industry=False, industry_dict=None, num_top= prices that would have a minimum sum of square differences between normalized prices. Only unique pairs are picked in this step (pairs ('AA', 'BD') and ('BD', 'AA') are assumed to be one pair ('AA', 'BD')). + During this step, if one decides to match pairs within the same industry group, with the + industry dictionary given, the sum of square differences is calculated only for the pairs + of prices within the same industry group. Third, based on the desired number of top pairs to chose and the pairs to skip, they are taken from the list of created pairs in the previous step. Pairs are sorted so that ones @@ -89,9 +93,12 @@ def form_pairs(self, train_data, by_industry=False, industry_dict=None, num_top= # If sector is set to True, pairs are matched within the same industry group if by_industry: + # Check whether the input of industry group dictionary is well given if industry_dict is None: raise Exception("Industry group dictionary is not given. Please provide the input") + + # Finding closest pairs for each element, excluding duplicates all_pairs = self.find_pair(normalized, industry_dict) else: @@ -105,10 +112,10 @@ def form_pairs(self, train_data, by_industry=False, industry_dict=None, num_top= self.train_std = self.find_volatility(normalized, self.pairs) # Creating portfolios for pairs chosen in the pairs formation stage with train dataset - train_portfolio = self.find_portfolios(normalized, self.pairs) + self.train_portfolio = self.find_portfolios(normalized, self.pairs) # Calculating the number of zero crossings from the dataset - self.num_crossing = self.get_number_crossing(train_portfolio) + self.num_crossing = self.count_number_crossing() def trade_pairs(self, test_data, divergence=2): """ @@ -228,6 +235,47 @@ def get_pairs_crossing(self, num_top=20, skip_top=0): return top_pairs + def get_num_crossing(self): + """ + Outputs pairs that were created in the pairs formation step with its number of zero crossing + :return: (dictionary) Dictionary with keys as pairs and values as the number of zero + crossings for pairs. + """ + return self.num_crossing + + def count_number_crossing(self): + """ + Calculate the number of zero crossings for the portfolio dataframe generated with train dataset. + + As the number of zero crossings in the formation period does have some usefulness in predicting + future convergence, this method calculates the number of times the normalized spread crosses the + value zero which measures the frequency of divergence and convergence between two securities. + + :return: (dictionary) Dictionary with keys as pairs and values as the number of zero + crossings for pairs. + """ + + # Creating a dictionary for number of zero crossings + num_zeros_dict = {} + + # Iterating through pairs + for pair in self.train_portfolio: + # Getting names of individual elements from dataframe column names + pair_val = pair.strip('\')(\'').split('\', \'') + pair_val = tuple(pair_val) + + # Check if portfolio price crossed zero + portfolio = self.train_portfolio[pair].to_frame() + pair_mult = portfolio * portfolio.shift(1) + + # Get the number of zero crossings for the portfolio + num_zero_crossings = len(portfolio[pair_mult.iloc[:, 0] <= 0].index) + + # Adding the pair's number of zero crossings to the dictionary + num_zeros_dict[pair_val] = num_zero_crossings + + return num_zeros_dict + def plot_portfolio(self, num_pair): """ Plots a pair portfolio (difference between element prices) and trading signals @@ -508,33 +556,3 @@ def signals(portfolios, variation, divergence): signals.columns = portfolios.columns return signals - - @staticmethod - def get_number_crossing(train_portfolio): - """ - Get number of crossings - :param train_portfolio: (pd.DataFrame) Dataframe with portfolio price series for pairs. - :return: (dictionary) Dictionary with keys as pairs and values as the number of zero - crossings for pairs. - """ - - # Creating a dictionary for number of zero crossings - num_zero_crossings = {} - - # Iterating through pairs - for pair in train_portfolio: - # Getting names of individual elements from dataframe column names - pair_val = pair.strip('\')(\'').split('\', \'') - pair_val = tuple(pair_val) - - # Check if portfolio price crossed zero - portfolio = train_portfolio[pair].to_frame() - pair_mult = portfolio * portfolio.shift(1) - - # Get the number of zero crossings for the portfolio - num_zero_crossings = len(portfolio[pair_mult.iloc[:, 0] <= 0].index) - - # Adding the pair's number of zero crossings to the dictionary - num_zero_crossings[pair_val] = num_zero_crossings - - return num_zero_crossings From dd8a0c3649541b58bbbd55e678b69ffb801a1aa0 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 5 Mar 2021 16:24:04 +0530 Subject: [PATCH 012/103] Added support for dynamic number of partner stocks for extremal approach instead of 4. Cleaned up some functions and test cases. --- .../vine_copula_partner_selection.py | 48 +++++++++------- .../vine_copula_partner_selection_utils.py | 57 +++++++++++++------ tests/test_partner_selection.py | 19 +++++-- 3 files changed, 81 insertions(+), 43 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 8ff92e7d..88a9e919 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -5,14 +5,14 @@ Module for implementing partner selection approaches for vine copulas. """ # pylint: disable = invalid-name +import functools import itertools import matplotlib.pyplot as plt import numpy as np import pandas as pd import seaborn as sns -from statsmodels.distributions.empirical_distribution import ECDF -from arbitragelab.copula_approach.vine_copula_partner_selection_utils import extremal_measure, \ +from arbitragelab.copula_approach.vine_copula_partner_selection_utils import extremal_measure, get_quantiles_data ,\ get_co_variance_matrix, get_sum_correlations_vectorized, diagonal_measure_vectorized, multivariate_rho_vectorized @@ -51,7 +51,7 @@ def __init__(self, prices: pd.DataFrame): # For each stock in universe, tickers of top 50 most correlated stocks are stored self.top_50_correlations = self._top_50_tickers() # Quadruple combinations for all stocks in universe - self.all_quadruples = self._generate_all_quadruples() + self.all_quadruples = self._generate_all_combinations() def _correlation(self) -> pd.DataFrame: """ @@ -95,33 +95,36 @@ def tickers_list(col): # Returns DataFrame with all stocks as indices and their respective top 50 correlated stocks as columns. return self.correlation_matrix.apply(tickers_list, axis=0).T - def _generate_all_quadruples(self) -> pd.DataFrame: + def _generate_all_combinations(self, d = 4) -> pd.DataFrame: """ - Method generates unique quadruples for all target stocks in universe. + Method generates unique combinations for all target stocks in universe. - :return: (pd.DataFrame) consists of all quadruples for every target stock. + :param d: (int) number of partner stocks. + :return: (pd.DataFrame) consists of all combinations for every target stock. """ - - return self.top_50_correlations.apply(self._generate_all_quadruples_helper, axis=1) + generate_all_combinations_helper_wrapper = functools.partial(self._generate_all_combinations_helper, d=d) + return self.top_50_correlations.apply(generate_all_combinations_helper_wrapper, axis=1) @staticmethod - def _generate_all_quadruples_helper(row: pd.Series) -> list: + def _generate_all_combinations_helper(row: pd.Series, d) -> list: """ - Helper function which generates unique quadruples for each target stock. + Helper function which generates unique combinations for each target stock. :param row: (pd.Series) list of 50 partner stocks. - :return: (list) quadruples. + :param d: (int) number of partner stocks. + :return: (list) combinations. """ target = row.name - quadruples = [] - for triple in itertools.combinations(row, 3): - quadruples.append([target] + list(triple)) - return quadruples + combinations = [] + for comb in itertools.combinations(row, d - 1): + combinations.append([target] + list(comb)) + return combinations @staticmethod def _prepare_combinations_of_partners(stock_selection: list) -> np.array: - """Helper function to calculate all combinations for a target stock and it's potential partners. + """ + Helper function to calculate all combinations for a target stock and it's potential partners. Stocks are treated as integers for vectorization purposes. :param stock_selection: (pd.DataFrame) the target stock has to be the first element of the array. @@ -172,7 +175,7 @@ def extended(self, n_targets=5) -> list: :return output_matrix: (list) List of all selected quadruples. """ - ecdf_df = self.returns.apply(lambda x: ECDF(x)(x), axis=0) # Calculating ranks of returns using quantiles data. + ecdf_df = self.returns.apply(get_quantiles_data, axis=0) # Calculating ranks of returns using quantiles data. output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. @@ -212,17 +215,22 @@ def geometric(self, n_targets=5) -> list: return output_matrix # Method 4 - def extremal(self, n_targets=5) -> list: + def extremal(self, n_targets = 5, d = 4) -> list: """ This method implements the fourth procedure described in Section 3.1.1. It involves calculating a non-parametric test statistic based on Mangold (2015) to measure the degree of deviation from independence. Main focus of this measure is the occurrence of joint extreme events. :param n_targets: (int) number of target stocks to select. + :param d: (int) number of partner stocks. :return output_matrix: (list) List of all selected quadruples. """ - co_variance_matrix = get_co_variance_matrix() + if d > 50: + raise Exception("Please make sure number of partner stocks is <= 50") + + co_variance_matrix = get_co_variance_matrix(d) + all_combinations = self._generate_all_combinations(d) output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: @@ -230,7 +238,7 @@ def extremal(self, n_targets=5) -> list: final_quadruple = None # Stores the final desired quadruple. # Iterating on all unique quadruples generated for a target. - for quadruple in self.all_quadruples[target]: + for quadruple in all_combinations[target]: measure = extremal_measure(self.ranked_returns[quadruple], co_variance_matrix) if measure > max_measure: max_measure = measure diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index a55c01d7..14a63db6 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -10,6 +10,13 @@ import pandas as pd import scipy +from statsmodels.distributions.empirical_distribution import ECDF + +def get_quantiles_data(col): + """ + Returns ranked quantiles from returns. + """ + return ECDF(col)(col) def get_sector_data(quadruple, constituents): """ @@ -135,42 +142,51 @@ def extremal_measure(u, co_variance_matrix): return t_test_statistic[0, 0] -def get_co_variance_matrix(): +def get_co_variance_matrix(d): """ - Calculates 16x16 dimensional covariance matrix. Since the matrix is symmetric, only the integrals + Calculates d**2 x d**2 dimensional covariance matrix. Since the matrix is symmetric, only the integrals in the upper triangle are calculated. The remaining values are filled from the transpose. + + :param d: (int) Number of stocks """ - co_variance_matrix = np.zeros((16, 16)) - for i, l1 in enumerate(itertools.product([1, 2], [1, 2], [1, 2], [1, 2])): - for j, l2 in enumerate(itertools.product([1, 2], [1, 2], [1, 2], [1, 2])): + args = [[1,2]] * d + + co_variance_matrix = np.zeros((d**2, d**2)) + for i, l1 in enumerate(itertools.product(*args)): + for j, l2 in enumerate(itertools.product(*args)): if j < i: # Integrals in lower triangle are skipped. continue - # Numerical Integration of 4 dimensions. - co_variance_matrix[i, j] = scipy.integrate.nquad(variance_integral_func, [(0, 1)] * 4, args=(l1, l2))[0] + # Numerical Integration of d dimensions. + co_variance_matrix[i, j] = scipy.integrate.nquad(variance_integral_func, [(0, 1)] * d, args=(l1, l2))[0] - inds = np.tri(16, k=-1, dtype=bool) # Storing the indices of elements in lower triangle. + inds = np.tri(d**2, k=-1, dtype=bool) # Storing the indices of elements in lower triangle. co_variance_matrix[inds] = co_variance_matrix.T[inds] return np.linalg.inv(co_variance_matrix) def t_calc(u): """ - Calculates T_(4,n) as seen in proposition 3.3. Each of the 16 rows in the array are appended to output and + Calculates T_(d,n) as seen in proposition 3.3. Each of the d**2 rows in the array are appended to output and returned as numpy array. :param u: (pd.DataFrame) ranked returns of stocks in quadruple. - :return: (np.array) of Shape (16, n). + :return: (np.array) of Shape (d**2, n). """ + + d = u.shape[1] + args = [[1,2]] * d output = [] - for l in itertools.product([1, 2], [1, 2], [1, 2], [1, 2]): - # Equation form for each one of u1,u2,u3,u4 after partial differentials are calculated and multiplied + for l in itertools.product(*args): + # Equation form for each one of u1,u2,u3,u4,... after partial differentials are calculated and multiplied # together. - res = func(u[:, 0], l[0]) * func(u[:, 1], l[1]) * func(u[:, 2], l[2]) * func(u[:, 3], l[3]) + res = 1 + for ind in range(d): + res *= func(u[:, ind], l[ind]) output.append(res) - return np.array(output) # Shape (16, n). + return np.array(output) # Shape (d**2, n). def func(t, value): @@ -192,9 +208,16 @@ def func(t, value): return res -def variance_integral_func(u1, u2, u3, u4, l1, l2): +def variance_integral_func(*args): """ Calculates Integrand for covariance matrix calculation. """ - return func(u1, l1[0]) * func(u2, l1[1]) * func(u3, l1[2]) * func(u4, l1[3]) * \ - func(u1, l2[0]) * func(u2, l2[1]) * func(u3, l2[2]) * func(u4, l2[3]) + + l1 = args[-2] + l2 = args[-1] + + res = 1 + for ind in range(len(args[:-2])): + res *= func(args[ind], l1[ind]) * func(args[ind], l2[ind]) + + return res diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py index b1002a01..61b7cf1a 100644 --- a/tests/test_partner_selection.py +++ b/tests/test_partner_selection.py @@ -10,9 +10,8 @@ import pandas as pd from matplotlib import axes -from statsmodels.distributions.empirical_distribution import ECDF from arbitragelab.copula_approach.vine_copula_partner_selection import PartnerSelection -from arbitragelab.copula_approach.vine_copula_partner_selection_utils import multivariate_rho_vectorized, \ +from arbitragelab.copula_approach.vine_copula_partner_selection_utils import multivariate_rho_vectorized, get_quantiles_data, \ extremal_measure, get_co_variance_matrix, get_sector_data, get_sum_correlations_vectorized, diagonal_measure_vectorized @@ -34,9 +33,7 @@ def setUpClass(cls) -> None: prices = pd.read_csv(data_path, parse_dates=True, index_col='Date').dropna() cls.ps = PartnerSelection(prices) - cls.u = cls.ps.returns.apply(lambda x: ECDF(x)(x), axis=0) - - cls.co_variance_matrix = get_co_variance_matrix() + cls.u = cls.ps.returns.apply(get_quantiles_data, axis=0) cls.constituents = pd.read_csv(project_path + '/test_data/sp500_constituents-detailed.csv', index_col='Symbol') @@ -84,11 +81,21 @@ def test_diagonal_measure(self): """ self.assertEqual(round(diagonal_measure_vectorized(self.ps.ranked_returns[self.quadruple], np.array([[0,1,2,3]]))[1], 4), 91.9374) + def test_extremal_covariance_matrix(self): + """ + Tests helper function for extremal approach which calculates the covariance matrix. + """ + self.assertIsNone(np.testing.assert_almost_equal(get_co_variance_matrix(2), [[ 64., -16., -16., 4.], + [-16., 64., 4., -16.], + [-16., 4., 64., -16.], + [ 4., -16., -16., 64.]] ,7)) + def test_extremal_measure(self): """ Tests helper function of Extremal Approach. """ - self.assertEqual(round(extremal_measure(self.ps.ranked_returns[self.quadruple], self.co_variance_matrix), 4), 108.5128) + co_variance_matrix = get_co_variance_matrix(4) + self.assertEqual(round(extremal_measure(self.ps.ranked_returns[self.quadruple], co_variance_matrix), 4), 108.5128) def test_get_sector_data(self): """ From a758b16336102ae051886a1dfe5694986587c77c Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Sat, 6 Mar 2021 00:14:57 +0530 Subject: [PATCH 013/103] Added additional test cases for code coverage. --- .../vine_copula_partner_selection.py | 6 ++--- .../vine_copula_partner_selection_utils.py | 10 ++++--- tests/test_partner_selection.py | 27 ++++++++++++++++++- 3 files changed, 35 insertions(+), 8 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 88a9e919..63f3edd6 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -226,8 +226,8 @@ def extremal(self, n_targets = 5, d = 4) -> list: :return output_matrix: (list) List of all selected quadruples. """ - if d > 50: - raise Exception("Please make sure number of partner stocks is <= 50") + if d > 50 or d < 2: + raise Exception("Please make sure number of partner stocks d is 2<=d<=50") co_variance_matrix = get_co_variance_matrix(d) all_combinations = self._generate_all_combinations(d) @@ -255,7 +255,7 @@ def plot_selected_pairs(self, quadruples: list): :param quadruples: (list) List of quadruples. """ - if quadruples is None: + if len(quadruples) == 0: raise Exception("Input list is empty") _, axs = plt.subplots(len(quadruples), diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index 14a63db6..d415a942 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -5,6 +5,7 @@ Utils for implementing partner selection approaches for vine copulas. """ # pylint: disable = invalid-name +from contextlib import suppress import itertools import numpy as np import pandas as pd @@ -22,10 +23,8 @@ def get_sector_data(quadruple, constituents): """ Function returns Sector and Sub sector information for all tickers in quadruple. """ - try: + with suppress(KeyError): return constituents.loc[quadruple, ['Security', 'GICS Sector', 'GICS Sub-Industry']] - except KeyError: - return pd.DataFrame() def get_sum_correlations_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: @@ -163,8 +162,11 @@ def get_co_variance_matrix(d): inds = np.tri(d**2, k=-1, dtype=bool) # Storing the indices of elements in lower triangle. co_variance_matrix[inds] = co_variance_matrix.T[inds] - return np.linalg.inv(co_variance_matrix) + try: + return np.linalg.inv(co_variance_matrix) + except np.linalg.LinAlgError as err: + raise Exception("Singular Matrix found. Cannot proceed further.") if 'Singular matrix' in str(err) else err def t_calc(u): """ diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py index 61b7cf1a..8aadc9f4 100644 --- a/tests/test_partner_selection.py +++ b/tests/test_partner_selection.py @@ -37,6 +37,18 @@ def setUpClass(cls) -> None: cls.constituents = pd.read_csv(project_path + '/test_data/sp500_constituents-detailed.csv', index_col='Symbol') + def test_partner_selection_exceptions(self): + """ + Tests exceptions in partner selection __init__. + """ + with self.assertRaises(Exception): + # Testing empty DataFrame exception. + PartnerSelection(pd.DataFrame()) + + with self.assertRaises(Exception): + # Testing input type exception. + PartnerSelection(np.array([0])) + def test_traditional(self): """ Tests Traditional Approach. @@ -59,7 +71,11 @@ def test_extremal(self): """ Tests Extremal Approach. """ - self.assertEqual(self.ps.extremal(1), [['A', 'AAL', 'AAPL', 'AAP']]) + with self.assertRaises(Exception): + # Testing number of partner stocks exception. + self.ps.extremal(1, 100) + + self.assertEqual(self.ps.extremal(1, 2), [['A', 'AAL']]) def test_sum_correlations(self): """ @@ -85,6 +101,10 @@ def test_extremal_covariance_matrix(self): """ Tests helper function for extremal approach which calculates the covariance matrix. """ + with self.assertRaises(Exception): + # Testing Singular Matrix exception. + get_co_variance_matrix(3) + self.assertIsNone(np.testing.assert_almost_equal(get_co_variance_matrix(2), [[ 64., -16., -16., 4.], [-16., 64., 4., -16.], [-16., 4., 64., -16.], @@ -107,4 +127,9 @@ def test_plot_selected_pairs(self): """ Tests plot_selected_pairs plotting method. """ + with self.assertRaises(Exception): + # Testing empty list of quadruples exception. + self.ps.plot_selected_pairs([]) + self.assertIsInstance(self.ps.plot_selected_pairs([self.quadruple]), axes.Axes) + self.assertIsInstance(self.ps.plot_selected_pairs([self.quadruple, self.quadruple])[0], axes.Axes) From b13d46cb59a1abe1bf0132ffaa4b626d677ca2fa Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 8 Mar 2021 16:48:12 +0530 Subject: [PATCH 014/103] Added descriptions and equations to documentation. --- arbitragelab/copula_approach/__init__.py | 1 + .../copula_approach/partner_selection.rst | 226 +++++++++++++++++- 2 files changed, 220 insertions(+), 7 deletions(-) diff --git a/arbitragelab/copula_approach/__init__.py b/arbitragelab/copula_approach/__init__.py index b01fd79c..66d5d1ef 100644 --- a/arbitragelab/copula_approach/__init__.py +++ b/arbitragelab/copula_approach/__init__.py @@ -11,3 +11,4 @@ from arbitragelab.copula_approach.copula_strategy_basic import BasicCopulaStrategy from arbitragelab.copula_approach.copula_strategy_mpi import CopulaStrategyMPI from arbitragelab.copula_approach.copula_generate_mixedcopula import (MixedCopula, CFGMixCop, CTGMixCop) +from arbitragelab.copula_approach.vine_copula_partner_selection import PartnerSelection diff --git a/docs/source/copula_approach/partner_selection.rst b/docs/source/copula_approach/partner_selection.rst index 6854a790..2f40db1d 100644 --- a/docs/source/copula_approach/partner_selection.rst +++ b/docs/source/copula_approach/partner_selection.rst @@ -13,9 +13,10 @@ Vine Copula Partner Selection Approaches ======================================== -This module contains implementation of the four partner selection approaches mentioned in Section 3.1.1 of Statistical Arbitrage with Vine Copulas. +This module contains implementation of the four partner selection approaches +mentioned in Section 3.1.1 of Statistical Arbitrage with Vine Copulas. -In this paper[1], Stubinger, Mangold and Krauss developed a multivariate statistical arbitrage strategy based on vine copulas - +In this paper, Stubinger, Mangold and Krauss developed a multivariate statistical arbitrage strategy based on vine copulas - a highly flexible instrument for linear and nonlinear multivariate dependence modeling. Pairs trading is a relative-value arbitrage strategy, where an investor seeks to profit from mean-reversion properties of the price spread between two co-moving securities. Existing literature focused on using bivariate copulas to model the dependence structure between two stock return time series, @@ -30,44 +31,257 @@ Introduction ############ This module will focus on the various Partner Selection procedures and their implementations, as described in the paper. -For every stock in the S&P 500, a partner triple is identified based on adequate measures of association. The following four partner selection approaches are implemented : +For every stock in the S&P 500, a partner triple is identified based on adequate measures of association. +The following four partner selection approaches are implemented : - Traditional Approach - baseline approach where the high dimensional relation between the four stocks is approximated by their pairwise bivariate correlations via Spearman’s :math:`\rho`; -- Extended Approach - calculating the multivariate version of Spearman’s :math:`\rho` based on Schmid and Schmidt (2007)[2]; +- Extended Approach - calculating the multivariate version of Spearman’s :math:`\rho` based on Schmid and Schmidt (2007); - Geometric Approach - involves calculating the sum of euclidean distances from the 4-dimensional hyper-diagonal; -- Extremal Approach - involves calculating a non-parametric :math:`\chi^2` test statistic based on Mangold (2015)[3] to measure the degree of deviation from independence. +- Extremal Approach - involves calculating a non-parametric :math:`\chi^2` test statistic based on Mangold (2015) to measure the degree of deviation from independence. Firstly, all measures of association are calculated using the ranks of the daily discrete returns of our samples. Ranked transformation provides robustness against outliers. + Secondly, only the top 50 most highly correlated stocks are taken into consideration for each target stock, to reduce the computational burden. +The traditional, the extended, and the geometric approach share a common feature - they measure the deviation from linearity in ranks. +All three aim at finding the quadruple that behaves as linearly as possible to ensure that there is an actual relation between its components to model. +While it is true that this aspiration for linearity excludes quadruples with components that are not connected (say, independent), +it also rules out nonlinear dependencies in ranks. +On the other hand, the extremal approach tries to maximize the distance to independence with focus on the joint extreme observations. + Traditional Approach #################### +As baseline approach, the high dimensional relation between the four stocks is approximated +by their pairwise bi-variate correlations via Spearman’s :math:`\rho`. +We used ranked returns data for this approach. In addition to the robustness obtained by rank transformation, +it allows to capture non-linearities in the data to a certain degree. + +The procedure is as follows: + +- Calculate the sum of all pairwise correlations for all possible quadruples, consisting of a fixed target stock. + +- Quadruple with the largest sum of pairwise correlations is considered as the final quadruple and saved to the output matrix. + Implementation ************** +.. automodule:: arbitragelab.copula_approach + +.. autoclass:: PartnerSelection + :members: __init__ + +.. automethod:: PartnerSelection.traditional + Extended Approach ################# +Schmid and Schmidt (2007) introduce multivariate rank based measures of association. +This paper generalizes Spearman’s :math:`\rho` to arbitrary dimensions - a natural extension of the traditional approach. + +In contrast to the strictly bi-variate case, this extended approach – and the two following approaches – +directly reflect multivariate dependence instead of approximating it by pairwise measures only. +This approach provides a more precise modeling of high dimensional association and thus a better performance in trading strategies. + +The procedure is as follows: + +- Calculate the multivariate version of Spearman’s :math:`\rho` for all possible quadruples, consisting of a fixed target stock. + +- Quadruple with the largest value is considered as the final quadruple and saved to the output matrix. + + +:math:`d` denotes the number of stocks daily returns observed from day :math:`1` to day :math:`n`. :math:`X_i` denotes the :math:`i`-th stock's return. + +1. We calculate the empirical cumulative density function (ECDF) :math:`\hat{F}_i` for stock :math:`i`. + +2. Calculate quantile data for each :math:`X_{i}`, by + +.. math:: + + \hat{U}_i = \frac{1}{n} (\text{rank of} \ X_i) = \hat{F}_i(X_i) + +The formula for the three estimators are given below, as in the paper. + +.. math:: + + \hat{\rho}_1 = h(d) \times \Bigg\{-1 + \frac{2^d}{n} \sum_{j=1}^n \prod_{i=1}^d (1 - \hat{U}_{ij}) \Bigg\} + + \hat{\rho}_2 = h(d) \times \Bigg\{-1 + \frac{2^d}{n} \sum_{j=1}^n \prod_{i=1}^d \hat{U}_{ij} \Bigg\} + + \hat{\rho}_3 = -3 + \frac{12}{n {d \choose 2}} \times \sum_{k`__ * `Schmid, F., Schmidt, R., 2007. Multivariate extensions of Spearman’s rho and related statis-tics. Statistics & Probability Letters 77 (4), 407–416. `__ * `Mangold, B., 2015. A multivariate linear rank test of independence based on a multipara-metric copula with cubic sections. IWQW Discussion Paper Series, University of Erlangen-N ̈urnberg. `__ - - From 1a76f65a3fffe0b97e6daa8bba17b3e56377e885 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 8 Mar 2021 21:29:06 +0530 Subject: [PATCH 015/103] Added code example to documentation. --- .../copula_approach/partner_selection.rst | 34 ++++++++++++++++++- 1 file changed, 33 insertions(+), 1 deletion(-) diff --git a/docs/source/copula_approach/partner_selection.rst b/docs/source/copula_approach/partner_selection.rst index 2f40db1d..07154a2a 100644 --- a/docs/source/copula_approach/partner_selection.rst +++ b/docs/source/copula_approach/partner_selection.rst @@ -277,9 +277,41 @@ Implementation Code Example ############ +.. code-block:: + # Importing the module and other libraries + from arbitragelab.copula_approach.vine_copula_partner_selection import PartnerSelection + import pandas as pd + # Importing DataFrame of daily pricing data for all stocks in S&P 500.(atleast 12 months data) + df = pd.read_csv(DATA_PATH, parse_dates=True, index_col='Date').dropna() + # Instantiating the partner selection module. + ps = PartnerSelection(df) + + # Calculating final quadruples using traditional approach for first 20 target stocks. + Q = ps.traditional(20) + print(Q) + # Plotting the final quadruples. + ps.plot_selected_pairs(Q) + + # Calculating final quadruples using extended approach for first 20 target stocks. + Q = ps.extended(20) + print(Q) + # Plotting the final quadruples. + ps.plot_selected_pairs(Q) + + # Calculating final quadruples using geometric approach for first 20 target stocks. + Q = ps.geometric(20) + print(Q) + # Plotting the final quadruples. + ps.plot_selected_pairs(Q) + + # Calculating final quadruples using extremal approach for first 20 target stocks. + Q = ps.extremal(20) + print(Q) + # Plotting the final quadruples. + ps.plot_selected_pairs(Q) Research Notebooks @@ -289,7 +321,7 @@ The following research notebook can be used to better understand the partner sel * `Vine Copula Partner Selection Approaches`_ -.. _`Vine Copula Partner Selection Approaches`: +.. _`Vine Copula Partner Selection Approaches`: https://github.com/hudson-and-thames/arbitrage_research/blob/partner_selection_vine_copula/Copula%20Approach/vine_copula_partner_selection.ipynb References ########## From 77685e9142f7df297d3054e03effa16892151ec8 Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Tue, 9 Mar 2021 22:55:21 +0900 Subject: [PATCH 016/103] Add variance approach and unittest Add variance approach and unittest --- .../basic_distance_approach.py | 58 +++++++++++++------ tests/test_basic_distance_approach.py | 47 +++++++++++++-- 2 files changed, 82 insertions(+), 23 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index dab8b1a7..5e999c96 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -205,35 +205,57 @@ def get_scaling_parameters(self): return scale - def get_pairs(self): + def get_pairs(self, method='standard', num_top=20, skip_top=0): """ - Outputs pairs that were created in the pairs formation step. - - :return: (list) List containing tuples of two strings, for names of elements in a pair. - """ - - return self.pairs - - def get_pairs_crossing(self, num_top=20, skip_top=0): - """ - Outputs pairs sorted by the number of zero crossings. + Outputs pairs that were created in the pairs formation step and sorted by the method. + :param method: (str) Method for choosing ways of sorting pairs. By default, it uses + ‘standard’ and other available methods are: ‘industry’, ‘zero_crossing’ and ‘variance’. :param num_top: (int) Number of top pairs to use for portfolio formation. :param skip_top: (int) Number of first top pairs to skip. For example, use skip_top=10 if you'd like to take num_top pairs starting from the 10th one. :return: (list) List containing tuples of two strings, for names of elements in a pair. """ - # Sorting pairs from the dictionary by the number of zero crossings in an descending order - sorted_pairs = sorted(self.num_crossing.items(), key=lambda x: x[1], reverse=True) + if method == 'standard': - # Picking top pairs - top_pairs = sorted_pairs[skip_top:(skip_top + num_top)] + return self.pairs - # Removing the number of crossings, so we have only tuples with elements - top_pairs = [x[0] for x in top_pairs] + elif method == 'industry': - return top_pairs + return self.pairs + + elif method == 'zero_crossing': + + # Sorting pairs from the dictionary by the number of zero crossings in a descending order + sorted_pairs = sorted(self.num_crossing.items(), key=lambda x: x[1], reverse=True) + + # Picking top pairs + self.pairs = sorted_pairs[skip_top:(skip_top + num_top)] + + # Removing the number of crossings, so we have only tuples with elements + self.pairs = [x[0] for x in self.pairs] + + return self.pairs + + elif method == 'variance': + + # Sorting pairs from the dictionary by the size of variance in a descending order + sorted_pairs = sorted(self.train_std.items(), key=lambda x: x[1], reverse=True) + + # Picking top pairs + self.pairs = sorted_pairs[skip_top:(skip_top + num_top)] + + # Removing the variance, so we have only tuples with elements + self.pairs = [x[0] for x in self.pairs] + + return self.pairs + + else: + + # Raise an error if the given method is inappropriate. + raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, ‘zero_crossing’, " + "‘industry’, or ‘variance’.") def get_num_crossing(self): """ diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index 6a437a65..f33b9f41 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -26,23 +26,41 @@ def setUp(self): """ # Using saved ETF price series for testing and trading - project_path = os.path.dirname(__file__) + + # Change back the path to relative path + project_path = os.path.dirname(os.path.abspath(__file__)) data_path = project_path + "/test_data/stock_prices.csv" data = pd.read_csv(data_path, parse_dates=True, index_col="Date") + # Generate a random industry dictionary for testing + industry_dict = {} + for index, ticker in enumerate(data.columns): + if index < len(data.columns) * (1 / 3): + industry_dict[ticker] = 'Information Technology' + elif index < len(data.columns) * (2 / 3): + industry_dict[ticker] = 'Financials' + else: + industry_dict[ticker] = 'Industrials' + # Datasets for pairs formation and trading steps of the strategy self.train_data = data[:100] self.test_data = data[100:] + self.industry_dict = industry_dict def test_form_pairs(self): """ Tests the generation of pairs from the DistanceStrategy class. """ - + # Basic Strategy strategy = DistanceStrategy() + # Industry based Strategy + strategy_industry = DistanceStrategy() + # Performing the pairs formation step strategy.form_pairs(self.train_data, num_top=5, skip_top=0) + strategy_industry.form_pairs(self.train_data, by_industry=True, + industry_dict=self.industry_dict, num_top=5, skip_top=0) # Testing min and max values of series used for dataset normalization self.assertAlmostEqual(strategy.min_normalize.mean(), 63.502009, delta=1e-5) @@ -51,11 +69,19 @@ def test_form_pairs(self): # Testing values of historical volatility for portfolios self.assertAlmostEqual(np.mean(list(strategy.train_std.values())), 0.056361, delta=1e-5) - # Testing the list of created pairs + # Testing values of train portfolio which was created to get the number of zero crossings + self.assertAlmostEqual(strategy_industry.train_portfolio.mean().mean(), 0.011405, delta=1e-5) + + # Testing the number of zero crossings for the pairs + self.assertAlmostEqual(np.mean(list(strategy_industry.num_crossing.values())), 16.4, delta=1e-5) + + # Testing the list of created pairs for both of the cases expected_pairs = [('EFA', 'VGK'), ('EPP', 'VPL'), ('EWQ', 'VGK'), ('EFA', 'EWQ'), ('EPP', 'SPY')] - + expected_pairs_industry = [('EFA', 'EWQ'), ('EFA', 'EWU'), ('SPY', 'VPL'), + ('EEM', 'EWU'), ('DIA', 'SPY')] self.assertCountEqual(strategy.pairs, expected_pairs) + self.assertCountEqual(strategy_industry.pairs,expected_pairs_industry) def test_trade_pairs(self): """ @@ -182,7 +208,10 @@ def test_get_pairs(self): expected_pairs = [('EFA', 'VGK'), ('EPP', 'VPL'), ('EWQ', 'VGK'), ('EFA', 'EWQ'), ('EPP', 'SPY')] - self.assertCountEqual(strategy.get_pairs(), expected_pairs) + self.assertCountEqual(strategy.get_pairs(method='standard'), expected_pairs) + self.assertCountEqual(strategy.get_pairs(method='zero_crossing'), expected_pairs) + self.assertCountEqual(strategy.get_pairs(method='industry'), expected_pairs) + self.assertCountEqual(strategy.get_pairs(method='variance'), expected_pairs) def test_exceptions(self): """ @@ -194,3 +223,11 @@ def test_exceptions(self): # When trying to generate trading signals without creating pairs first with self.assertRaises(Exception): strategy.trade_pairs(self.test_data, divergence=2) + + # When trying to form pairs based on industry approach without giving an industry dictionary as an input + with self.assertRaises(Exception): + strategy.form_pairs(self.train_data, by_industry=True) + + # When trying to get pairs with inappropriate method + with self.assertRaises(Exception): + strategy.get_pairs(method='wrong input') From 320d4f519593885917bc5bce25cca662fdbf83d5 Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Tue, 9 Mar 2021 23:33:26 +0900 Subject: [PATCH 017/103] Fixed some issues regarding pylint Fixed some issues regarding pylint --- .../basic_distance_approach.py | 17 +++++++++-------- tests/test_basic_distance_approach.py | 2 +- 2 files changed, 10 insertions(+), 9 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index 5e999c96..fa8afd25 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -216,16 +216,21 @@ def get_pairs(self, method='standard', num_top=20, skip_top=0): if you'd like to take num_top pairs starting from the 10th one. :return: (list) List containing tuples of two strings, for names of elements in a pair. """ + if method not in ['standard', 'industry', 'zero_crossing', 'variance']: + + # Raise an error if the given method is inappropriate. + raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, ‘zero_crossing’, " + "‘industry’, or ‘variance’.") if method == 'standard': return self.pairs - elif method == 'industry': + if method == 'industry': return self.pairs - elif method == 'zero_crossing': + if method == 'zero_crossing': # Sorting pairs from the dictionary by the number of zero crossings in a descending order sorted_pairs = sorted(self.num_crossing.items(), key=lambda x: x[1], reverse=True) @@ -238,7 +243,7 @@ def get_pairs(self, method='standard', num_top=20, skip_top=0): return self.pairs - elif method == 'variance': + if method == 'variance': # Sorting pairs from the dictionary by the size of variance in a descending order sorted_pairs = sorted(self.train_std.items(), key=lambda x: x[1], reverse=True) @@ -251,11 +256,7 @@ def get_pairs(self, method='standard', num_top=20, skip_top=0): return self.pairs - else: - - # Raise an error if the given method is inappropriate. - raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, ‘zero_crossing’, " - "‘industry’, or ‘variance’.") + return None def get_num_crossing(self): """ diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index f33b9f41..6b1461fd 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -28,7 +28,7 @@ def setUp(self): # Using saved ETF price series for testing and trading # Change back the path to relative path - project_path = os.path.dirname(os.path.abspath(__file__)) + project_path = os.path.dirname(__file__) data_path = project_path + "/test_data/stock_prices.csv" data = pd.read_csv(data_path, parse_dates=True, index_col="Date") From 6418c6c33cd9a2bc59d765317666b77e966d4fbb Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 9 Mar 2021 18:07:30 +0100 Subject: [PATCH 018/103] Minor style adjustments to Partner Selection Module --- .../vine_copula_partner_selection.py | 134 ++++++++++-------- .../vine_copula_partner_selection_utils.py | 87 +++++++----- tests/test_partner_selection.py | 8 +- 3 files changed, 127 insertions(+), 102 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 63f3edd6..aa2d95f0 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -30,21 +30,22 @@ class PartnerSelection: def __init__(self, prices: pd.DataFrame): """ Inputs the price series required for further calculations. - Also includes preprocessing steps described in the paper, before starting the Partner Selection procedures. + + It also includes preprocessing steps described in the paper, before starting the Partner Selection procedures. These steps include, finding the returns and ranked returns of the stocks, and calculating the top 50 correlated stocks for each stock in the universe. - :param prices: (pd.DataFrame) Contains price series of all stocks in universe. + :param prices: (pd.DataFrame) Contains price series of all stocks in the universe. """ if len(prices) == 0: - raise Exception("Input does not contain any data") + raise Exception("Input does not contain any data.") if not isinstance(prices, pd.DataFrame): - raise Exception("Partner Selection Class requires a pandas DataFrame as input") + raise Exception("Partner Selection Class requires a pandas DataFrame as input.") - self.universe = prices # Contains daily prices for all stocks in universe. - self.returns, self.ranked_returns = self._get_returns() # Daily returns and corresponding ranked returns. + self.universe = prices # Contains daily prices for all stocks in universe + self.returns, self.ranked_returns = self._get_returns() # Daily returns and corresponding ranked returns # Correlation matrix containing all stocks in universe self.correlation_matrix = self._correlation() @@ -55,12 +56,12 @@ def __init__(self, prices: pd.DataFrame): def _correlation(self) -> pd.DataFrame: """ - Calculates correlation between all stocks in universe. + Calculates correlation between all stocks in the universe. :return: (pd.DataFrame) Correlation Matrix. """ - return self.ranked_returns.corr(method='pearson') # Pearson or spearman,we get same results as input is ranked + return self.ranked_returns.corr(method='pearson') # Pearson or spearman, we get same results as input is ranked def _get_returns(self) -> (pd.DataFrame, pd.DataFrame): """ @@ -89,36 +90,40 @@ def tickers_list(col): """ Returns list of tickers ordered according to correlations with target. """ - # Sort the column data in descending order and return the index of top 50 rows. + + # Sort the column data in descending order and return the index of top 50 rows return col.sort_values(ascending=False)[1:51].index.to_list() - # Returns DataFrame with all stocks as indices and their respective top 50 correlated stocks as columns. + # Returns DataFrame with all stocks as indices and their respective top 50 correlated stocks as columns return self.correlation_matrix.apply(tickers_list, axis=0).T - def _generate_all_combinations(self, d = 4) -> pd.DataFrame: + def _generate_all_combinations(self, d: int = 4) -> pd.DataFrame: + """ + Method generates unique combinations for all target stocks in universe. + + :param d: (int) Number of partner stocks. + :return: (pd.DataFrame) Consists of all combinations for every target stock. """ - Method generates unique combinations for all target stocks in universe. - :param d: (int) number of partner stocks. - :return: (pd.DataFrame) consists of all combinations for every target stock. - """ generate_all_combinations_helper_wrapper = functools.partial(self._generate_all_combinations_helper, d=d) + return self.top_50_correlations.apply(generate_all_combinations_helper_wrapper, axis=1) @staticmethod - def _generate_all_combinations_helper(row: pd.Series, d) -> list: + def _generate_all_combinations_helper(row: pd.Series, d: int) -> list: """ - Helper function which generates unique combinations for each target stock. + Helper function which generates unique combinations for each target stock. - :param row: (pd.Series) list of 50 partner stocks. - :param d: (int) number of partner stocks. - :return: (list) combinations. - """ + :param row: (pd.Series) List of 50 partner stocks. + :param d: (int) Number of partner stocks. + :return: (list) Combinations. + """ target = row.name combinations = [] for comb in itertools.combinations(row, d - 1): combinations.append([target] + list(comb)) + return combinations @staticmethod @@ -127,139 +132,144 @@ def _prepare_combinations_of_partners(stock_selection: list) -> np.array: Helper function to calculate all combinations for a target stock and it's potential partners. Stocks are treated as integers for vectorization purposes. - :param stock_selection: (pd.DataFrame) the target stock has to be the first element of the array. - :return: the possible combinations for the quadruples. Shape (19600,4) . + :param stock_selection: (pd.DataFrame) The target stock has to be the first element of the array. + :return: (np.array) The possible combinations for the quadruples. Shape (19600,4). """ - # We will convert the stock names into integers and then get a list of all combinations with a length of 3. + # We will convert the stock names into integers and then get a list of all combinations with a length of 3 num_of_stocks = len(stock_selection) - # We turn our partner stocks into numerical indices so we can use them directly for indexing. - partner_stocks_idx = np.arange(1, num_of_stocks) # basically exclude the target stock. + # We turn our partner stocks into numerical indices so we can use them directly for indexing + partner_stocks_idx = np.arange(1, num_of_stocks) # Basically exclude the target stock partner_stocks_idx_combs = itertools.combinations(partner_stocks_idx, 3) + return np.array(list((0,) + comb for comb in partner_stocks_idx_combs)) # Method 1 - def traditional(self, n_targets=5) -> list: + def traditional(self, n_targets: int = 5) -> list: """ This method implements the first procedure described in Section 3.1.1. + For all possible quadruples of a given stock, we calculate the sum of all pairwise correlations. For every target stock the quadruple with the highest sum is returned. - :param n_targets: (int) number of target stocks to select. - :return output_matrix: (list) List of all selected quadruples. + :param n_targets: (int) Number of target stocks to select. + :return: (list) List of all selected quadruples. """ output_matrix = [] # Stores the final set of quadruples. # Iterating on the top 50 indices for each target stock. for target in self.top_50_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target. + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target data_subset = self.correlation_matrix.loc[stock_selection, stock_selection] - all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4). + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4) final_quadruple = get_sum_correlations_vectorized(data_subset, all_possible_combinations)[0] - # Appending the final quadruple for each target to the output matrix. + # Appending the final quadruple for each target to the output matrix output_matrix.append(final_quadruple) return output_matrix # Method 2 - def extended(self, n_targets=5) -> list: + def extended(self, n_targets: int = 5) -> list: """ This method implements the second procedure described in Section 3.1.1. + It involves calculating the multivariate version of Spearman's correlation for all possible quadruples of a given stock. For every target stock the quadruple with the highest correlation is returned. - :param n_targets: (int) number of target stocks to select. - :return output_matrix: (list) List of all selected quadruples. + :param n_targets: (int) Number of target stocks to select. + :return: (list) List of all selected quadruples. """ - ecdf_df = self.returns.apply(get_quantiles_data, axis=0) # Calculating ranks of returns using quantiles data. + ecdf_df = self.returns.apply(get_quantiles_data, axis=0) # Calculating ranks of returns using quantiles data - output_matrix = [] # Stores the final set of quadruples. - # Iterating on the top 50 indices for each target stock. + output_matrix = [] # Stores the final set of quadruples + # Iterating on the top 50 indices for each target stock for target in self.top_50_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target. + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target data_subset = ecdf_df[stock_selection] - all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4). + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4) final_quadruple = multivariate_rho_vectorized(data_subset, all_possible_combinations)[0] - # Appending the final quadruple for each target to the output matrix. + # Appending the final quadruple for each target to the output matrix output_matrix.append(final_quadruple) return output_matrix # Method 3 - def geometric(self, n_targets=5) -> list: + def geometric(self, n_targets: int = 5) -> list: """ This method implements the third procedure described in Section 3.1.1. + It involves calculating the four dimensional diagonal measure for all possible quadruples of a given stock. For every target stock the quadruple with the lowest diagonal measure is returned. :param n_targets: (int) number of target stocks to select. - :return output_matrix: (list) List of all selected quadruples. + :return: (list) List of all selected quadruples. """ - output_matrix = [] # Stores the final set of quadruples. - # Iterating on the top 50 indices for each target stock. + output_matrix = [] # Stores the final set of quadruples + # Iterating on the top 50 indices for each target stock for target in self.top_50_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target. + stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target data_subset = self.ranked_returns[stock_selection] - all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4). + all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4) final_quadruple = diagonal_measure_vectorized(data_subset, all_possible_combinations)[0] - # Appending the final quadruple for each target to the output matrix. + # Appending the final quadruple for each target to the output matrix output_matrix.append(final_quadruple) return output_matrix # Method 4 - def extremal(self, n_targets = 5, d = 4) -> list: + def extremal(self, n_targets: int = 5, d: int = 4) -> list: """ This method implements the fourth procedure described in Section 3.1.1. + It involves calculating a non-parametric test statistic based on Mangold (2015) to measure the degree of deviation from independence. Main focus of this measure is the occurrence of joint extreme events. - :param n_targets: (int) number of target stocks to select. - :param d: (int) number of partner stocks. + :param n_targets: (int) Number of target stocks to select. + :param d: (int) Number of partner stocks. :return output_matrix: (list) List of all selected quadruples. """ if d > 50 or d < 2: - raise Exception("Please make sure number of partner stocks d is 2<=d<=50") + raise Exception("Please make sure number of partner stocks d is 2<=d<=50.") co_variance_matrix = get_co_variance_matrix(d) all_combinations = self._generate_all_combinations(d) - output_matrix = [] # Stores the final set of quadruples. - # Iterating on the top 50 indices for each target stock. + output_matrix = [] # Stores the final set of quadruples + # Iterating on the top 50 indices for each target stock for target in self.top_50_correlations.index[:n_targets]: - max_measure = -np.inf # Variable used to extract the desired maximum value. - final_quadruple = None # Stores the final desired quadruple. + max_measure = -np.inf # Variable used to extract the desired maximum value + final_quadruple = None # Stores the final desired quadruple - # Iterating on all unique quadruples generated for a target. + # Iterating on all unique quadruples generated for a target for quadruple in all_combinations[target]: measure = extremal_measure(self.ranked_returns[quadruple], co_variance_matrix) if measure > max_measure: max_measure = measure final_quadruple = quadruple - # Appending the final quadruple for each target to the output matrix. + # Appending the final quadruple for each target to the output matrix output_matrix.append(final_quadruple) return output_matrix - def plot_selected_pairs(self, quadruples: list): + def plot_selected_pairs(self, quadruples: list) -> list: """ Plots the final selection of quadruples. :param quadruples: (list) List of quadruples. + :return: (list) List of Axes objects. """ if len(quadruples) == 0: - raise Exception("Input list is empty") + raise Exception("Input list is empty.") - _, axs = plt.subplots(len(quadruples), - figsize=(15, 3 * len(quadruples))) + _, axs = plt.subplots(len(quadruples), figsize=(15, 3 * len(quadruples))) plt.subplots_adjust(hspace=0.6) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index d415a942..5abca7ea 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -17,12 +17,14 @@ def get_quantiles_data(col): """ Returns ranked quantiles from returns. """ + return ECDF(col)(col) def get_sector_data(quadruple, constituents): """ Function returns Sector and Sub sector information for all tickers in quadruple. """ + with suppress(KeyError): return constituents.loc[quadruple, ['Security', 'GICS Sector', 'GICS Sub-Industry']] @@ -30,28 +32,27 @@ def get_sector_data(quadruple, constituents): def get_sum_correlations_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: """ Helper function for traditional approach to partner selection. + Calculates sum of pairwise correlations between all stocks in each quadruple. Returns the quadruple with the largest sum. :param data_subset: (pd.DataFrame) Dataset storing correlations data. :param all_possible_combinations: (np.array) Array of indices of 19600 quadruples. - - :return: (tuple) final quadruple, corresponding measure + :return: (tuple) Final quadruple, corresponding measure. """ - # We use the combinations as an index. + # We use the combinations as an index corr_matrix = data_subset.values[:, all_possible_combinations] - # corr_matrix has shape of (51, 19600, 4). - # We now use np.take_along_axis to get the shape (4,19600,4), then we can sum the first and the last dimension. + # corr_matrix has shape of (51, 19600, 4) + # We now use np.take_along_axis to get the shape (4,19600,4), then we can sum the first and the last dimension corr_sums = np.sum(np.take_along_axis(corr_matrix, all_possible_combinations.T[..., np.newaxis], axis=0), - axis=(0, 2)) #Shape: (19600,1). + axis=(0, 2)) # Shape: (19600,1) d = all_possible_combinations.shape[-1] corr_sums = (corr_sums - d) / 2 # Return the maximum index for the sums. - max_index = np.argmax( - corr_sums) + max_index = np.argmax(corr_sums) final_quadruple = data_subset.columns[list(all_possible_combinations[max_index])].tolist() return final_quadruple, corr_sums[max_index] @@ -59,29 +60,32 @@ def get_sum_correlations_vectorized(data_subset: pd.DataFrame, all_possible_comb def multivariate_rho_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: """ - Helper function for extended approach to partner selection. Calculates 3 proposed estimators for - high dimensional generalization for Spearman's rho. These implementations are present in + Helper function for extended approach to partner selection. + + Calculates 3 proposed estimators for high dimensional generalization for Spearman's rho. + These implementations are present in Schmid, F., Schmidt, R., 2007. Multivariate extensions of Spearman’s rho and related statis-tics. Returns the quadruple with the largest measure. :param data_subset: (pd.DataFrame) Dataset storing ranked returns data. :param all_possible_combinations: (np.array) Array of indices of 19600 quadruples. - :return: (tuple) final quadruple, corresponding measure + :return: (tuple) Final quadruple, corresponding measure. """ - quadruples_combinations_data = data_subset.values[:, all_possible_combinations] #Shape: (n, 19600, d). - n, _, d = quadruples_combinations_data.shape # n : Number of samples, d : Number of stocks. + quadruples_combinations_data = data_subset.values[:, all_possible_combinations] # Shape: (n, 19600, d) + + n, _, d = quadruples_combinations_data.shape # n : Number of samples, d : Number of stocks h_d = (d + 1) / (2 ** d - d - 1) - # Calculating the first estimator of multivariate rho. + # Calculating the first estimator of multivariate rho sum_1 = np.product(1 - quadruples_combinations_data, axis=-1).sum(axis=0) rho_1 = h_d * (-1 + (2 ** d / n) * sum_1) - # Calculating the second estimator of multivariate rho. + # Calculating the second estimator of multivariate rho sum_2 = np.product(quadruples_combinations_data, axis=-1).sum(axis=0) rho_2 = h_d * (-1 + (2 ** d / n) * sum_2) - # Calculating the third estimator of multivariate rho. + # Calculating the third estimator of multivariate rho pairs = np.array(list(itertools.combinations(range(d), 2))) k, l = pairs[:, 0], pairs[:, 1] sum_3 = ((1 - quadruples_combinations_data[:, :, k]) * (1 - quadruples_combinations_data[:, :, l])).sum(axis=(0, 2)) @@ -89,7 +93,7 @@ def multivariate_rho_vectorized(data_subset: pd.DataFrame, all_possible_combinat rho_3 = -3 + (12 / (n * dc2)) * sum_3 quadruples_scores = (rho_1 + rho_2 + rho_3) / 3 - # The quadruple scores have the shape of (19600,1) now. + # The quadruple scores have the shape of (19600,1) now max_index = np.argmax(quadruples_scores) final_quadruple = data_subset.columns[list(all_possible_combinations[max_index])].tolist() @@ -99,55 +103,62 @@ def multivariate_rho_vectorized(data_subset: pd.DataFrame, all_possible_combinat def diagonal_measure_vectorized(data_subset: pd.DataFrame, all_possible_combinations: np.array) -> tuple: """ - Helper function for geometric approach to partner selection. Calculates the sum of Euclidean distances - from the relative ranks to the (hyper-)diagonal in four dimensional space for each quadruple of a target stock. + Helper function for geometric approach to partner selection. + + Calculates the sum of Euclidean distances from the relative ranks to the (hyper-)diagonal + in four dimensional space for each quadruple of a target stock. Returns the quadruple with the smallest measure. :param data_subset: (pd.DataFrame) Dataset storing ranked returns data. :param all_possible_combinations: (np.array) Array of indices of 19600 quadruples. - :return: (tuple) final quadruple, corresponding measure + :return: (tuple) Final quadruple, corresponding measure """ quadruples_combinations_data = data_subset.values[:, all_possible_combinations] - d = quadruples_combinations_data.shape[-1] # Shape : (n, 19600, d) where n : Number of samples, d : Number of stocks. + d = quadruples_combinations_data.shape[-1] # Shape: (n, 19600, d) where n: Number of samples, d: Number of stocks line = np.ones(d) - # Einsum is great for specifying which dimension to multiply together. - # this extends the distance method for all 19600 combinations. + # Einsum is great for specifying which dimension to multiply together + # this extends the distance method for all 19600 combinations pp = (np.einsum("ijk,k->ji", quadruples_combinations_data, line) / np.linalg.norm(line)) pn = np.sqrt(np.einsum('ijk,ijk->ji', quadruples_combinations_data, quadruples_combinations_data)) distance_scores = np.sqrt(pn ** 2 - pp ** 2).sum(axis=1) min_index = np.argmin(distance_scores) final_quadruple = data_subset.columns[list(all_possible_combinations[min_index])].tolist() + return final_quadruple, distance_scores[min_index] -def extremal_measure(u, co_variance_matrix): +def extremal_measure(u: pd.DataFrame, co_variance_matrix: np.array): """ Helper function to calculate chi-squared test statistic based on p-dimensional Nelsen copulas. + Specifically, proposition 3.3 from Mangold (2015) is implemented for 4 dimensions. - :param u: (pd.DataFrame) ranked returns of stocks in quadruple. + :param u: (pd.DataFrame) Ranked returns of stocks in quadruple. :param co_variance_matrix: (np.array) Covariance matrix. - :return: test statistic. + :return: (float) Test statistic. """ + u = u.to_numpy() n = u.shape[0] - # Calculating array T_(4,n) from proposition 3.3. - t = t_calc(u).mean(axis=1).reshape(-1, 1) # Shape : (16, 1), Taking the mean w.r.t n. + # Calculating array T_(4,n) from proposition 3.3 + t = t_calc(u).mean(axis=1).reshape(-1, 1) # Shape :(16, 1), Taking the mean w.r.t n. # Calculating the final test statistic. t_test_statistic = n * np.matmul(t.T, np.matmul(co_variance_matrix, t)) + return t_test_statistic[0, 0] -def get_co_variance_matrix(d): +def get_co_variance_matrix(d: int): """ Calculates d**2 x d**2 dimensional covariance matrix. Since the matrix is symmetric, only the integrals in the upper triangle are calculated. The remaining values are filled from the transpose. - :param d: (int) Number of stocks + :param d: (int) Number of stocks. """ + args = [[1,2]] * d co_variance_matrix = np.zeros((d**2, d**2)) @@ -168,13 +179,14 @@ def get_co_variance_matrix(d): except np.linalg.LinAlgError as err: raise Exception("Singular Matrix found. Cannot proceed further.") if 'Singular matrix' in str(err) else err + def t_calc(u): """ Calculates T_(d,n) as seen in proposition 3.3. Each of the d**2 rows in the array are appended to output and returned as numpy array. - :param u: (pd.DataFrame) ranked returns of stocks in quadruple. - :return: (np.array) of Shape (d**2, n). + :param u: (pd.DataFrame) Ranked returns of stocks in quadruple. + :return: (np.array) Array of Shape (d**2, n). """ d = u.shape[1] @@ -182,23 +194,23 @@ def t_calc(u): output = [] for l in itertools.product(*args): # Equation form for each one of u1,u2,u3,u4,... after partial differentials are calculated and multiplied - # together. + # together res = 1 for ind in range(d): res *= func(u[:, ind], l[ind]) output.append(res) - return np.array(output) # Shape (d**2, n). + return np.array(output) # Shape (d**2, n) -def func(t, value): +def func(t: np.array, value: int): """ Function returns equation form of respective variable after partial differentiation. All variables in the differential equations are in one of two forms. :param t: (np.array) Variable. :param value: (int) Flag denoting equation form of variable. - :return: + :return: (float) Differentiation result. """ res = None @@ -213,6 +225,9 @@ def func(t, value): def variance_integral_func(*args): """ Calculates Integrand for covariance matrix calculation. + + :param args: (list) Given parameters. + :return: (float) Integrand value. """ l1 = args[-2] diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py index 8aadc9f4..110d105a 100644 --- a/tests/test_partner_selection.py +++ b/tests/test_partner_selection.py @@ -53,7 +53,7 @@ def test_traditional(self): """ Tests Traditional Approach. """ - self.assertEqual(self.ps.traditional(1),[['A', 'AAL', 'AAPL', 'AAP']]) + self.assertEqual(self.ps.traditional(1), [['A', 'AAL', 'AAPL', 'AAP']]) def test_extended(self): """ @@ -65,7 +65,7 @@ def test_geometric(self): """ Tests Geometric Approach. """ - self.assertEqual(self.ps.geometric(1),[['A', 'AAL', 'AAPL', 'AAP']]) + self.assertEqual(self.ps.geometric(1), [['A', 'AAL', 'AAPL', 'AAP']]) def test_extremal(self): """ @@ -89,13 +89,13 @@ def test_multivariate_rho(self): """ Tests helper function of Extended Approach. """ - self.assertEqual(round(multivariate_rho_vectorized(self.u[self.quadruple], np.array([[0,1,2,3]]))[1], 4), 0.3114) + self.assertEqual(round(multivariate_rho_vectorized(self.u[self.quadruple], np.array([[0, 1, 2, 3]]))[1], 4), 0.3114) def test_diagonal_measure(self): """ Tests helper function of Geometric Approach. """ - self.assertEqual(round(diagonal_measure_vectorized(self.ps.ranked_returns[self.quadruple], np.array([[0,1,2,3]]))[1], 4), 91.9374) + self.assertEqual(round(diagonal_measure_vectorized(self.ps.ranked_returns[self.quadruple], np.array([[0, 1, 2, 3]]))[1], 4), 91.9374) def test_extremal_covariance_matrix(self): """ From 078cf308f725cd08e7cf7b6214a09d4d9fad5fc3 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 10 Mar 2021 14:11:04 +0530 Subject: [PATCH 019/103] Made changes according to PR review and corrected extremal approach code. --- .../vine_copula_partner_selection.py | 23 ++++++------ .../vine_copula_partner_selection_utils.py | 35 +++++++++++-------- docs/source/changelog.rst | 2 ++ tests/test_partner_selection.py | 3 -- 4 files changed, 35 insertions(+), 28 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index aa2d95f0..53708506 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -132,7 +132,7 @@ def _prepare_combinations_of_partners(stock_selection: list) -> np.array: Helper function to calculate all combinations for a target stock and it's potential partners. Stocks are treated as integers for vectorization purposes. - :param stock_selection: (pd.DataFrame) The target stock has to be the first element of the array. + :param stock_selection: (list) The target stock has to be the first element of the array. :return: (np.array) The possible combinations for the quadruples. Shape (19600,4). """ @@ -228,12 +228,13 @@ def extremal(self, n_targets: int = 5, d: int = 4) -> list: """ This method implements the fourth procedure described in Section 3.1.1. - It involves calculating a non-parametric test statistic based on Mangold (2015) to measure the + It involves calculating a non-parametric test statistic based on + `Mangold (2015) `__ to measure the degree of deviation from independence. Main focus of this measure is the occurrence of joint extreme events. :param n_targets: (int) Number of target stocks to select. :param d: (int) Number of partner stocks. - :return output_matrix: (list) List of all selected quadruples. + :return output_matrix: (list) List of all selected combinations. """ if d > 50 or d < 2: @@ -241,20 +242,20 @@ def extremal(self, n_targets: int = 5, d: int = 4) -> list: co_variance_matrix = get_co_variance_matrix(d) all_combinations = self._generate_all_combinations(d) - output_matrix = [] # Stores the final set of quadruples + output_matrix = [] # Stores the final set of combinations # Iterating on the top 50 indices for each target stock for target in self.top_50_correlations.index[:n_targets]: max_measure = -np.inf # Variable used to extract the desired maximum value - final_quadruple = None # Stores the final desired quadruple + final_combination = None # Stores the final desired combination - # Iterating on all unique quadruples generated for a target - for quadruple in all_combinations[target]: - measure = extremal_measure(self.ranked_returns[quadruple], co_variance_matrix) + # Iterating on all unique combinations generated for a target + for combination in all_combinations[target]: + measure = extremal_measure(self.ranked_returns[combination], co_variance_matrix) if measure > max_measure: max_measure = measure - final_quadruple = quadruple - # Appending the final quadruple for each target to the output matrix - output_matrix.append(final_quadruple) + final_combination = combination + # Appending the final combination for each target to the output matrix + output_matrix.append(final_combination) return output_matrix diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index 5abca7ea..19249068 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -13,16 +13,22 @@ from statsmodels.distributions.empirical_distribution import ECDF -def get_quantiles_data(col): +def get_quantiles_data(col: pd.Series): """ Returns ranked quantiles from returns. + :param col: (pd.Series) returns data for a single stock. + :return: ranked returns from quantiles. """ return ECDF(col)(col) -def get_sector_data(quadruple, constituents): + +def get_sector_data(quadruple: list, constituents: pd.DataFrame): """ Function returns Sector and Sub sector information for all tickers in quadruple. + :param quadruple: (list) List of four tickers. + :param constituents: (pd.DataFrame) Dataframe consisting of sector data for all tickers in universe. + :return: Data corresponding to the quadruple. """ with suppress(KeyError): @@ -64,7 +70,10 @@ def multivariate_rho_vectorized(data_subset: pd.DataFrame, all_possible_combinat Calculates 3 proposed estimators for high dimensional generalization for Spearman's rho. These implementations are present in - Schmid, F., Schmidt, R., 2007. Multivariate extensions of Spearman’s rho and related statis-tics. + `Multivariate extensions of Spearman’s rho and related statistics. (2007) + `__ + by Schmid, F., Schmidt, R. + Returns the quadruple with the largest measure. :param data_subset: (pd.DataFrame) Dataset storing ranked returns data. @@ -133,7 +142,8 @@ def extremal_measure(u: pd.DataFrame, co_variance_matrix: np.array): """ Helper function to calculate chi-squared test statistic based on p-dimensional Nelsen copulas. - Specifically, proposition 3.3 from Mangold (2015) is implemented for 4 dimensions. + Specifically, proposition 3.3 from `Mangold (2015) `__ + is implemented for 4 dimensions. :param u: (pd.DataFrame) Ranked returns of stocks in quadruple. :param co_variance_matrix: (np.array) Covariance matrix. @@ -153,7 +163,7 @@ def extremal_measure(u: pd.DataFrame, co_variance_matrix: np.array): def get_co_variance_matrix(d: int): """ - Calculates d**2 x d**2 dimensional covariance matrix. Since the matrix is symmetric, only the integrals + Calculates 2**d x 2**d dimensional covariance matrix. Since the matrix is symmetric, only the integrals in the upper triangle are calculated. The remaining values are filled from the transpose. :param d: (int) Number of stocks. @@ -161,7 +171,7 @@ def get_co_variance_matrix(d: int): args = [[1,2]] * d - co_variance_matrix = np.zeros((d**2, d**2)) + co_variance_matrix = np.zeros((2**d, 2**d)) for i, l1 in enumerate(itertools.product(*args)): for j, l2 in enumerate(itertools.product(*args)): if j < i: @@ -171,22 +181,19 @@ def get_co_variance_matrix(d: int): # Numerical Integration of d dimensions. co_variance_matrix[i, j] = scipy.integrate.nquad(variance_integral_func, [(0, 1)] * d, args=(l1, l2))[0] - inds = np.tri(d**2, k=-1, dtype=bool) # Storing the indices of elements in lower triangle. + inds = np.tri(2**d, k=-1, dtype=bool) # Storing the indices of elements in lower triangle. co_variance_matrix[inds] = co_variance_matrix.T[inds] - try: - return np.linalg.inv(co_variance_matrix) - except np.linalg.LinAlgError as err: - raise Exception("Singular Matrix found. Cannot proceed further.") if 'Singular matrix' in str(err) else err + return np.linalg.inv(co_variance_matrix) def t_calc(u): """ - Calculates T_(d,n) as seen in proposition 3.3. Each of the d**2 rows in the array are appended to output and + Calculates T_(d,n) as seen in proposition 3.3. Each of the 2**d rows in the array are appended to output and returned as numpy array. :param u: (pd.DataFrame) Ranked returns of stocks in quadruple. - :return: (np.array) Array of Shape (d**2, n). + :return: (np.array) Array of Shape (2**d, n). """ d = u.shape[1] @@ -200,7 +207,7 @@ def t_calc(u): res *= func(u[:, ind], l[ind]) output.append(res) - return np.array(output) # Shape (d**2, n) + return np.array(output) # Shape (2**d, n) def func(t: np.array, value: int): diff --git a/docs/source/changelog.rst b/docs/source/changelog.rst index fee37d21..1f1c402e 100644 --- a/docs/source/changelog.rst +++ b/docs/source/changelog.rst @@ -12,6 +12,8 @@ Changelog .. For Help: https://releases.readthedocs.io/en/latest/index.html +* :feature:`40` Vine Copula Partner Selection Approaches added to the Copula Approach Module. +* :support:`40` Vine Copula Partner Selection Approaches documentation. * :support:`38` Removed TensorFlow from requirements and adjusted installation guide. * :release:`0.3.0 <2021-02-16>` diff --git a/tests/test_partner_selection.py b/tests/test_partner_selection.py index 110d105a..e7a08cb7 100644 --- a/tests/test_partner_selection.py +++ b/tests/test_partner_selection.py @@ -101,9 +101,6 @@ def test_extremal_covariance_matrix(self): """ Tests helper function for extremal approach which calculates the covariance matrix. """ - with self.assertRaises(Exception): - # Testing Singular Matrix exception. - get_co_variance_matrix(3) self.assertIsNone(np.testing.assert_almost_equal(get_co_variance_matrix(2), [[ 64., -16., -16., 4.], [-16., 64., 4., -16.], From e69e7ada455a7d5e0a5ae94070561b100f50d134 Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Wed, 10 Mar 2021 19:20:24 +0900 Subject: [PATCH 020/103] Fix some codes for coverage test Fix some codes for coverage test --- .../basic_distance_approach.py | 24 +++++++------------ tests/test_basic_distance_approach.py | 11 +++++++++ 2 files changed, 19 insertions(+), 16 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index fa8afd25..cd538969 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -222,41 +222,33 @@ def get_pairs(self, method='standard', num_top=20, skip_top=0): raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, ‘zero_crossing’, " "‘industry’, or ‘variance’.") - if method == 'standard': - - return self.pairs - - if method == 'industry': - - return self.pairs - if method == 'zero_crossing': # Sorting pairs from the dictionary by the number of zero crossings in a descending order sorted_pairs = sorted(self.num_crossing.items(), key=lambda x: x[1], reverse=True) # Picking top pairs - self.pairs = sorted_pairs[skip_top:(skip_top + num_top)] + pairs_selected = sorted_pairs[skip_top:(skip_top + num_top)] # Removing the number of crossings, so we have only tuples with elements - self.pairs = [x[0] for x in self.pairs] + pairs_selected = [x[0] for x in pairs_selected] - return self.pairs + self.pairs = pairs_selected - if method == 'variance': + elif method == 'variance': # Sorting pairs from the dictionary by the size of variance in a descending order sorted_pairs = sorted(self.train_std.items(), key=lambda x: x[1], reverse=True) # Picking top pairs - self.pairs = sorted_pairs[skip_top:(skip_top + num_top)] + pairs_selected = sorted_pairs[skip_top:(skip_top + num_top)] # Removing the variance, so we have only tuples with elements - self.pairs = [x[0] for x in self.pairs] + pairs_selected = [x[0] for x in pairs_selected] - return self.pairs + self.pairs = pairs_selected - return None + return self.pairs def get_num_crossing(self): """ diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index 6b1461fd..bf981dc5 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -213,6 +213,17 @@ def test_get_pairs(self): self.assertCountEqual(strategy.get_pairs(method='industry'), expected_pairs) self.assertCountEqual(strategy.get_pairs(method='variance'), expected_pairs) + def test_get_num_crossing(self): + """ + Tests the number of crossings. + """ + + strategy = DistanceStrategy() + + strategy.form_pairs(self.train_data, num_top=5, skip_top=0) + + self.assertAlmostEqual(len(strategy.get_num_crossing()), 5, delta=1e-5) + def test_exceptions(self): """ Tests exceptions from methods of the class. From c6d180765c3072be545a2e62dc9081b6d01f77a5 Mon Sep 17 00:00:00 2001 From: PanPip Date: Wed, 10 Mar 2021 11:56:05 +0100 Subject: [PATCH 021/103] Minor docs adjustments for Partner Selection Module --- docs/source/copula_approach/partner_selection.rst | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/docs/source/copula_approach/partner_selection.rst b/docs/source/copula_approach/partner_selection.rst index 07154a2a..db47006d 100644 --- a/docs/source/copula_approach/partner_selection.rst +++ b/docs/source/copula_approach/partner_selection.rst @@ -32,7 +32,7 @@ Introduction This module will focus on the various Partner Selection procedures and their implementations, as described in the paper. For every stock in the S&P 500, a partner triple is identified based on adequate measures of association. -The following four partner selection approaches are implemented : +The following four partner selection approaches are implemented: - Traditional Approach - baseline approach where the high dimensional relation between the four stocks is approximated by their pairwise bivariate correlations via Spearman’s :math:`\rho`; @@ -56,7 +56,7 @@ On the other hand, the extremal approach tries to maximize the distance to indep Traditional Approach #################### -As baseline approach, the high dimensional relation between the four stocks is approximated +As a baseline approach, the high dimensional relation between the four stocks is approximated by their pairwise bi-variate correlations via Spearman’s :math:`\rho`. We used ranked returns data for this approach. In addition to the robustness obtained by rank transformation, it allows to capture non-linearities in the data to a certain degree. @@ -65,7 +65,7 @@ The procedure is as follows: - Calculate the sum of all pairwise correlations for all possible quadruples, consisting of a fixed target stock. -- Quadruple with the largest sum of pairwise correlations is considered as the final quadruple and saved to the output matrix. +- Quadruple with the largest sum of pairwise correlations is considered the final quadruple and saved to the output matrix. Implementation ************** @@ -91,7 +91,7 @@ The procedure is as follows: - Calculate the multivariate version of Spearman’s :math:`\rho` for all possible quadruples, consisting of a fixed target stock. -- Quadruple with the largest value is considered as the final quadruple and saved to the output matrix. +- Quadruple with the largest value is considered the final quadruple and saved to the output matrix. :math:`d` denotes the number of stocks daily returns observed from day :math:`1` to day :math:`n`. :math:`X_i` denotes the :math:`i`-th stock's return. @@ -144,7 +144,7 @@ The procedure is as follows: - Calculate the four dimensional diagonal measure for all possible quadruples, consisting of a fixed target stock. -- Quadruple with the smallest diagonal measure is considered as the final quadruple and saved to the output matrix. +- Quadruple with the smallest diagonal measure is considered the final quadruple and saved to the output matrix. The diagonal measure in four dimensional space is calculated using the following equation, @@ -186,7 +186,7 @@ The procedure is as follows: - Calculate the :math:`\chi^2` test statistic for all possible quadruples, consisting of a fixed target stock. -- Quadruple with the largest test statistic is considered as the final quadruple and saved to the output matrix. +- Quadruple with the largest test statistic is considered the final quadruple and saved to the output matrix. Given below are the steps to calculate the :math:`\chi^2` test statistic described in Proposition 3.3 of Mangold (2015): @@ -283,7 +283,7 @@ Code Example from arbitragelab.copula_approach.vine_copula_partner_selection import PartnerSelection import pandas as pd - # Importing DataFrame of daily pricing data for all stocks in S&P 500.(atleast 12 months data) + # Importing DataFrame of daily pricing data for all stocks in S&P 500.(at least 12 months data) df = pd.read_csv(DATA_PATH, parse_dates=True, index_col='Date').dropna() # Instantiating the partner selection module. From e653a1d9cee94e4583cfe91134c97187e0a8e6d7 Mon Sep 17 00:00:00 2001 From: PanPip Date: Wed, 10 Mar 2021 13:16:30 +0100 Subject: [PATCH 022/103] Minor code adjustments for Partner Selection Module --- .../copula_approach/vine_copula_partner_selection_utils.py | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index 19249068..75a2825c 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -16,8 +16,9 @@ def get_quantiles_data(col: pd.Series): """ Returns ranked quantiles from returns. - :param col: (pd.Series) returns data for a single stock. - :return: ranked returns from quantiles. + + :param col: (pd.Series) Returns data for a single stock. + :return: Ranked returns from quantiles. """ return ECDF(col)(col) @@ -26,6 +27,7 @@ def get_quantiles_data(col: pd.Series): def get_sector_data(quadruple: list, constituents: pd.DataFrame): """ Function returns Sector and Sub sector information for all tickers in quadruple. + :param quadruple: (list) List of four tickers. :param constituents: (pd.DataFrame) Dataframe consisting of sector data for all tickers in universe. :return: Data corresponding to the quadruple. From 3256656aeb7163f0b563118e77e02daadf1474f9 Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Wed, 10 Mar 2021 23:20:16 +0900 Subject: [PATCH 023/103] Change the form_pairs method and add docstring Change the form_pairs method and add docstring --- .../basic_distance_approach.py | 83 ++++++++++--------- .../distance_approach/distance_approach.rst | 46 ++++++++++ tests/test_basic_distance_approach.py | 28 +++++-- 3 files changed, 109 insertions(+), 48 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index cd538969..c7c085ce 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -41,7 +41,7 @@ def __init__(self): devadarsh.track('DistanceStrategy') - def form_pairs(self, train_data, by_industry=False, industry_dict=None, num_top=50, skip_top=0, list_names=None): + def form_pairs(self, train_data, method='standard', industry_dict=None, num_top=50, skip_top=0, list_names=None): """ Forms pairs based on input training data. @@ -77,7 +77,8 @@ def form_pairs(self, train_data, by_industry=False, industry_dict=None, num_top= :param skip_top: (int) Number of first top pairs to skip. For example, use skip_top=10 if you'd like to take num_top pairs starting from the 10th one. :param list_names: (list) List containing names of elements if Numpy array is used as input. - :param by_industry: (boolean) Whether to use pair selection based on industry group or not. + :param method: (str) Methods to use for sorting pairs [``standard`` by default, ``industry``, + ``zero_crossing``, ``variance``]. :param industry_dict: (dictionary) Dictionary matching ticker to industry group. """ @@ -92,7 +93,7 @@ def form_pairs(self, train_data, by_industry=False, industry_dict=None, num_top= normalized = normalized.dropna(axis=0) # If sector is set to True, pairs are matched within the same industry group - if by_industry: + if method == 'industry': # Check whether the input of industry group dictionary is well given if industry_dict is None: @@ -117,6 +118,44 @@ def form_pairs(self, train_data, by_industry=False, industry_dict=None, num_top= # Calculating the number of zero crossings from the dataset self.num_crossing = self.count_number_crossing() + self._selection_method(method, num_top, skip_top) + + def _selection_method(self, method, num_top, skip_top): + """ + Select pairs based on the method. + """ + + if method not in ['standard', 'industry', 'zero_crossing', 'variance']: + # Raise an error if the given method is inappropriate. + raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, ‘zero_crossing’, " + "‘industry’, or ‘variance’.") + + if method == 'zero_crossing': + + # Sorting pairs from the dictionary by the number of zero crossings in a descending order + sorted_pairs = sorted(self.num_crossing.items(), key=lambda x: x[1], reverse=True) + + # Picking top pairs + pairs_selected = sorted_pairs[skip_top:(skip_top + num_top)] + + # Removing the number of crossings, so we have only tuples with elements + pairs_selected = [x[0] for x in pairs_selected] + + self.pairs = pairs_selected + + elif method == 'variance': + + # Sorting pairs from the dictionary by the size of variance in a descending order + sorted_pairs = sorted(self.train_std.items(), key=lambda x: x[1], reverse=True) + + # Picking top pairs + pairs_selected = sorted_pairs[skip_top:(skip_top + num_top)] + + # Removing the variance, so we have only tuples with elements + pairs_selected = [x[0] for x in pairs_selected] + + self.pairs = pairs_selected + def trade_pairs(self, test_data, divergence=2): """ Generates trading signals for formed pairs based on new testing(trading) data. @@ -205,48 +244,12 @@ def get_scaling_parameters(self): return scale - def get_pairs(self, method='standard', num_top=20, skip_top=0): + def get_pairs(self): """ Outputs pairs that were created in the pairs formation step and sorted by the method. - :param method: (str) Method for choosing ways of sorting pairs. By default, it uses - ‘standard’ and other available methods are: ‘industry’, ‘zero_crossing’ and ‘variance’. - :param num_top: (int) Number of top pairs to use for portfolio formation. - :param skip_top: (int) Number of first top pairs to skip. For example, use skip_top=10 - if you'd like to take num_top pairs starting from the 10th one. :return: (list) List containing tuples of two strings, for names of elements in a pair. """ - if method not in ['standard', 'industry', 'zero_crossing', 'variance']: - - # Raise an error if the given method is inappropriate. - raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, ‘zero_crossing’, " - "‘industry’, or ‘variance’.") - - if method == 'zero_crossing': - - # Sorting pairs from the dictionary by the number of zero crossings in a descending order - sorted_pairs = sorted(self.num_crossing.items(), key=lambda x: x[1], reverse=True) - - # Picking top pairs - pairs_selected = sorted_pairs[skip_top:(skip_top + num_top)] - - # Removing the number of crossings, so we have only tuples with elements - pairs_selected = [x[0] for x in pairs_selected] - - self.pairs = pairs_selected - - elif method == 'variance': - - # Sorting pairs from the dictionary by the size of variance in a descending order - sorted_pairs = sorted(self.train_std.items(), key=lambda x: x[1], reverse=True) - - # Picking top pairs - pairs_selected = sorted_pairs[skip_top:(skip_top + num_top)] - - # Removing the variance, so we have only tuples with elements - pairs_selected = [x[0] for x in pairs_selected] - - self.pairs = pairs_selected return self.pairs diff --git a/docs/source/distance_approach/distance_approach.rst b/docs/source/distance_approach/distance_approach.rst index fe1072e0..dc53a2e6 100644 --- a/docs/source/distance_approach/distance_approach.rst +++ b/docs/source/distance_approach/distance_approach.rst @@ -88,6 +88,46 @@ will later be used to generate trading signals.\ Portfolio value (difference of normalized price series), constructed from a pair of elements from the previous example. + +Pair selection criteria +####################### + +As basic pairs formation confirms declining profitability in pairs trading, some other refined pair +selection criteria have emerged. Here, we describe three different methods from the basic approach in +selecting pairs for trading. + +First is only allowing for matching securities within the same industry group. The second is sorting +selected pairs based on the number of zero-crossings in the formation period and the third is sorting +selected pairs based on the historical standard deviation where pairs with high standard deviation are selected. + +1. **Pairs within the same industry group** + +In the pairs formation step above, one can add this method when finding pairs in order to match securities +within the same industry group. + +With a dictionary containing the name/ticker of the securities and each corresponding industry group, +the securities are first separated into different industry groups. Then, by calculating the Euclidean +square distance for each of the pair within the same group, the :math:`n` closest pairs are selected(in default, +our function also allows skipping a number of first pairs, so one can choose pairs 10-15 to study). + +2. **Pairs with a higher number of zero-crossings** + +The number of zero crossings in the formation period does have some usefulness in predicting the future +convergence according to the work of Do and Faff (2010). + +After pairs were matched either within the same industry group or every industry, the top :math:`n` pairs +that had the highest number of zero crossings during the 12-month formation period are admitted to the +portfolio we select. This method incorporates the time-series dimension of the historical data in the +form of the number of zero crossings. + +3. **Pairs with a higher historical standard deviation** + +The historical standard deviation calculated in the formation period can also be a criterion to sort +selected pairs. + +After pairs were matched, by sorting the pairs based on their historical standard deviation in the +formation period, we can select top :math:`n` pairs that have the highest standard deviation. + Implementation ************** @@ -207,6 +247,10 @@ Code Example strategy = DistanceStrategy() strategy.form_pairs(data_pairs_formation, num_top=20, skip_top=5) + # Using the number of zero-crossing for pair selection method + strategy_zero_crossing = DistanceStrategy() + strategy_zero_crossing.form_pairs(data_pairs_formation, method='zero_crossing', num_top=20, skip_top=5) + # Checking a list of pairs that were created pairs = strategy.get_pairs() @@ -236,5 +280,7 @@ References ########## * `Do, B. and Faff, R., 2010. Does simple pairs trading still work?. Financial Analysts Journal, 66(4), pp.83-95. `_ +* `Do, B., and Faff, R. (2012). Are pairs trading profits robust to trading costs? Journal of Financial Research, 35(2):261–287. `_ * `Gatev, E., Goetzmann, W.N. and Rouwenhorst, K.G., 2006. Pairs trading: Performance of a relative-value arbitrage rule. The Review of Financial Studies, 19(3), pp.797-827. `_ * `Krauss, C., 2017. Statistical arbitrage pairs trading strategies: Review and outlook. Journal of Economic Surveys, 31(2), pp.513-545. `_ + diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index bf981dc5..0e3ee76b 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -57,10 +57,18 @@ def test_form_pairs(self): # Industry based Strategy strategy_industry = DistanceStrategy() + # Zero-crossing based Strategy + strategy_zero_crossing = DistanceStrategy() + + # Variance based Strategy + strategy_variance = DistanceStrategy() + # Performing the pairs formation step strategy.form_pairs(self.train_data, num_top=5, skip_top=0) - strategy_industry.form_pairs(self.train_data, by_industry=True, + strategy_industry.form_pairs(self.train_data, method='industry', industry_dict=self.industry_dict, num_top=5, skip_top=0) + strategy_zero_crossing.form_pairs(self.train_data, method='zero_crossing', num_top=5, skip_top=0) + strategy_variance.form_pairs(self.train_data, method='variance', num_top=5, skip_top=0) # Testing min and max values of series used for dataset normalization self.assertAlmostEqual(strategy.min_normalize.mean(), 63.502009, delta=1e-5) @@ -80,8 +88,15 @@ def test_form_pairs(self): ('EFA', 'EWQ'), ('EPP', 'SPY')] expected_pairs_industry = [('EFA', 'EWQ'), ('EFA', 'EWU'), ('SPY', 'VPL'), ('EEM', 'EWU'), ('DIA', 'SPY')] + expected_pairs_zero_crossing = [('EPP', 'SPY'), ('EFA', 'VGK'), ('EPP', 'VPL'), + ('EWQ', 'VGK'), ('EFA', 'EWQ')] + expected_pairs_variance = [('EPP', 'SPY'), ('EPP', 'VPL'), ('EFA', 'EWQ'), + ('EWQ', 'VGK'), ('EFA', 'VGK')] + self.assertCountEqual(strategy.pairs, expected_pairs) - self.assertCountEqual(strategy_industry.pairs,expected_pairs_industry) + self.assertCountEqual(strategy_industry.pairs, expected_pairs_industry) + self.assertCountEqual(strategy_zero_crossing.pairs, expected_pairs_zero_crossing) + self.assertCountEqual(strategy_variance.pairs, expected_pairs_variance) def test_trade_pairs(self): """ @@ -208,10 +223,7 @@ def test_get_pairs(self): expected_pairs = [('EFA', 'VGK'), ('EPP', 'VPL'), ('EWQ', 'VGK'), ('EFA', 'EWQ'), ('EPP', 'SPY')] - self.assertCountEqual(strategy.get_pairs(method='standard'), expected_pairs) - self.assertCountEqual(strategy.get_pairs(method='zero_crossing'), expected_pairs) - self.assertCountEqual(strategy.get_pairs(method='industry'), expected_pairs) - self.assertCountEqual(strategy.get_pairs(method='variance'), expected_pairs) + self.assertCountEqual(strategy.get_pairs(), expected_pairs) def test_get_num_crossing(self): """ @@ -237,8 +249,8 @@ def test_exceptions(self): # When trying to form pairs based on industry approach without giving an industry dictionary as an input with self.assertRaises(Exception): - strategy.form_pairs(self.train_data, by_industry=True) + strategy.form_pairs(self.train_data, method='industry', industry_dict=None) # When trying to get pairs with inappropriate method with self.assertRaises(Exception): - strategy.get_pairs(method='wrong input') + strategy._selection_method(method='wrong input',num_top=5,skip_top=0) From eb7aec48eccc26508bc2e8a9a3175652446b39cb Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Wed, 10 Mar 2021 23:30:59 +0900 Subject: [PATCH 024/103] Fixed some issues and change test_get_num_crossing method Fixed some issues and change test_get_num_crossing method --- arbitragelab/distance_approach/basic_distance_approach.py | 7 +++++-- tests/test_basic_distance_approach.py | 5 +++-- 2 files changed, 8 insertions(+), 4 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index c7c085ce..7a1f3360 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -41,7 +41,7 @@ def __init__(self): devadarsh.track('DistanceStrategy') - def form_pairs(self, train_data, method='standard', industry_dict=None, num_top=50, skip_top=0, list_names=None): + def form_pairs(self, train_data, method='standard', industry_dict=None, num_top=5, skip_top=0, list_names=None): """ Forms pairs based on input training data. @@ -79,7 +79,7 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= :param list_names: (list) List containing names of elements if Numpy array is used as input. :param method: (str) Methods to use for sorting pairs [``standard`` by default, ``industry``, ``zero_crossing``, ``variance``]. - :param industry_dict: (dictionary) Dictionary matching ticker to industry group. + :param industry_dict: (dict) Dictionary matching ticker to industry group. """ # If np.array given as an input @@ -118,6 +118,8 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= # Calculating the number of zero crossings from the dataset self.num_crossing = self.count_number_crossing() + # In case of a selection method other than standard or industry is used, sorting paris + # based on the method self._selection_method(method, num_top, skip_top) def _selection_method(self, method, num_top, skip_top): @@ -256,6 +258,7 @@ def get_pairs(self): def get_num_crossing(self): """ Outputs pairs that were created in the pairs formation step with its number of zero crossing + :return: (dictionary) Dictionary with keys as pairs and values as the number of zero crossings for pairs. """ diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index 0e3ee76b..235bc62a 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -27,7 +27,6 @@ def setUp(self): # Using saved ETF price series for testing and trading - # Change back the path to relative path project_path = os.path.dirname(__file__) data_path = project_path + "/test_data/stock_prices.csv" data = pd.read_csv(data_path, parse_dates=True, index_col="Date") @@ -234,7 +233,9 @@ def test_get_num_crossing(self): strategy.form_pairs(self.train_data, num_top=5, skip_top=0) - self.assertAlmostEqual(len(strategy.get_num_crossing()), 5, delta=1e-5) + expected_number_crossings = [22, 20, 17, 16, 31] + + self.assertEqual(list(strategy.get_num_crossing().values()), expected_number_crossings) def test_exceptions(self): """ From ee3a6075ff4757f02f1eb7e7e71e3c2f10622fee Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 11 Mar 2021 16:30:08 +0530 Subject: [PATCH 025/103] Made changes to docs and inline comments according to review. Made changes to function and variable names to expand number of preselected stocks from 50. --- .../vine_copula_partner_selection.py | 82 +++++++++++-------- .../vine_copula_partner_selection_utils.py | 22 ++--- .../copula_approach/partner_selection.rst | 21 +++++ 3 files changed, 80 insertions(+), 45 deletions(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 53708506..6789c9a2 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -23,19 +23,24 @@ class PartnerSelection: 3 partner stocks are selected for a target stock based on four different approaches namely, Traditional approach, Extended approach, Geometric approach and Extremal approach. + In this module, target stock implies the ticker for which a unique combination of stocks is returned. + The stocks present in this unique combination are called partner stocks. + `Stübinger, J., Mangold, B. and Krauss, C., 2018. Statistical arbitrage with vine copulas. Quantitative Finance, 18(11), pp.1831-1849. `__ """ - def __init__(self, prices: pd.DataFrame): + def __init__(self, prices: pd.DataFrame, n: int = 50): """ Inputs the price series required for further calculations. It also includes preprocessing steps described in the paper, before starting the Partner Selection procedures. - These steps include, finding the returns and ranked returns of the stocks, and calculating the top 50 + These steps include, finding the returns and ranked returns of the stocks, and calculating the top n correlated stocks for each stock in the universe. :param prices: (pd.DataFrame) Contains price series of all stocks in the universe. + :param n: (int) For each target stock, the total number of stocks taken into consideration for partner stocks + in the final combination, from 500 stocks in the universe. """ if len(prices) == 0: @@ -45,12 +50,13 @@ def __init__(self, prices: pd.DataFrame): raise Exception("Partner Selection Class requires a pandas DataFrame as input.") self.universe = prices # Contains daily prices for all stocks in universe + self.num_stocks_per_target = n # Total number of stocks taken into consideration as partner stocks for each target self.returns, self.ranked_returns = self._get_returns() # Daily returns and corresponding ranked returns # Correlation matrix containing all stocks in universe self.correlation_matrix = self._correlation() - # For each stock in universe, tickers of top 50 most correlated stocks are stored - self.top_50_correlations = self._top_50_tickers() + # For each stock in universe, tickers of top n most correlated stocks are stored + self.top_n_correlations = self._top_n_tickers() # Quadruple combinations for all stocks in universe self.all_quadruples = self._generate_all_combinations() @@ -79,23 +85,26 @@ def _get_returns(self) -> (pd.DataFrame, pd.DataFrame): returns_df_ranked = returns_df.rank(axis=0, method='first', pct=True) return returns_df, returns_df_ranked - def _top_50_tickers(self) -> pd.DataFrame: + def _tickers_list(self, col: pd.Series) -> list: """ - Calculates the top 50 correlated stocks for each target stock. + Returns list of tickers ordered according to correlations with target. - :return: (pd.DataFrame) Dataframe consisting of 50 columns for each stock in the universe. + :param col: (pd.Series) Correlation data for a stock. + :return: (list) List of top n tickers. """ - def tickers_list(col): - """ - Returns list of tickers ordered according to correlations with target. - """ + # Sort the column data in descending order and return the index of top n rows + return col.sort_values(ascending=False)[1: self.num_stocks_per_target + 1].index.to_list() - # Sort the column data in descending order and return the index of top 50 rows - return col.sort_values(ascending=False)[1:51].index.to_list() + def _top_n_tickers(self) -> pd.DataFrame: + """ + Calculates the top n correlated stocks for each target stock. - # Returns DataFrame with all stocks as indices and their respective top 50 correlated stocks as columns - return self.correlation_matrix.apply(tickers_list, axis=0).T + :return: (pd.DataFrame) Dataframe consisting of n columns for each stock in the universe. + """ + + # Returns DataFrame with all stocks as indices and their respective top n correlated stocks as columns + return self.correlation_matrix.apply(self._tickers_list, axis=0).T def _generate_all_combinations(self, d: int = 4) -> pd.DataFrame: """ @@ -107,14 +116,14 @@ def _generate_all_combinations(self, d: int = 4) -> pd.DataFrame: generate_all_combinations_helper_wrapper = functools.partial(self._generate_all_combinations_helper, d=d) - return self.top_50_correlations.apply(generate_all_combinations_helper_wrapper, axis=1) + return self.top_n_correlations.apply(generate_all_combinations_helper_wrapper, axis=1) @staticmethod def _generate_all_combinations_helper(row: pd.Series, d: int) -> list: """ Helper function which generates unique combinations for each target stock. - :param row: (pd.Series) List of 50 partner stocks. + :param row: (pd.Series) List of n partner stocks. :param d: (int) Number of partner stocks. :return: (list) Combinations. """ @@ -157,10 +166,10 @@ def traditional(self, n_targets: int = 5) -> list: """ output_matrix = [] # Stores the final set of quadruples. - # Iterating on the top 50 indices for each target stock. - for target in self.top_50_correlations.index[:n_targets]: + # Iterating on the top n indices for each target stock. + for target in self.top_n_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target + stock_selection = [target] + self.top_n_correlations.loc[target].tolist() # List of n + 1 stocks including target data_subset = self.correlation_matrix.loc[stock_selection, stock_selection] all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4) @@ -175,9 +184,10 @@ def extended(self, n_targets: int = 5) -> list: """ This method implements the second procedure described in Section 3.1.1. - It involves calculating the multivariate version of Spearman's correlation - for all possible quadruples of a given stock. - For every target stock the quadruple with the highest correlation is returned. + It involves calculating the multivariate version of Spearman's correlation for all possible quadruples of a given stock. + The final measure taken into consideration is the mean of the three versions of Spearman's rho given in + `Schmid and Schmidt (2007) `__. + For every target stock the quadruple with the highest calculated measure is returned. :param n_targets: (int) Number of target stocks to select. :return: (list) List of all selected quadruples. @@ -186,9 +196,9 @@ def extended(self, n_targets: int = 5) -> list: ecdf_df = self.returns.apply(get_quantiles_data, axis=0) # Calculating ranks of returns using quantiles data output_matrix = [] # Stores the final set of quadruples - # Iterating on the top 50 indices for each target stock - for target in self.top_50_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target + # Iterating on the top n indices for each target stock + for target in self.top_n_correlations.index[:n_targets]: + stock_selection = [target] + self.top_n_correlations.loc[target].tolist() # List of n + 1 stocks including target data_subset = ecdf_df[stock_selection] all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4) @@ -204,6 +214,8 @@ def geometric(self, n_targets: int = 5) -> list: This method implements the third procedure described in Section 3.1.1. It involves calculating the four dimensional diagonal measure for all possible quadruples of a given stock. + For example, visually, say we are in 2D, we have a Quantile-Quantile plot for the data, + and this measure is just the sum of Euclidean distance for all data points to the y=x line (diagonal). For every target stock the quadruple with the lowest diagonal measure is returned. :param n_targets: (int) number of target stocks to select. @@ -211,9 +223,9 @@ def geometric(self, n_targets: int = 5) -> list: """ output_matrix = [] # Stores the final set of quadruples - # Iterating on the top 50 indices for each target stock - for target in self.top_50_correlations.index[:n_targets]: - stock_selection = [target] + self.top_50_correlations.loc[target].tolist() # List of 51 stocks including target + # Iterating on the top n indices for each target stock + for target in self.top_n_correlations.index[:n_targets]: + stock_selection = [target] + self.top_n_correlations.loc[target].tolist() # List of n + 1 stocks including target data_subset = self.ranked_returns[stock_selection] all_possible_combinations = self._prepare_combinations_of_partners(stock_selection) # Shape: (19600, 4) @@ -233,18 +245,18 @@ def extremal(self, n_targets: int = 5, d: int = 4) -> list: degree of deviation from independence. Main focus of this measure is the occurrence of joint extreme events. :param n_targets: (int) Number of target stocks to select. - :param d: (int) Number of partner stocks. + :param d: (int) Number of partner stocks(including target stock). :return output_matrix: (list) List of all selected combinations. """ - if d > 50 or d < 2: - raise Exception("Please make sure number of partner stocks d is 2<=d<=50.") + if d > self.num_stocks_per_target or d < 2: + raise Exception("Please make sure number of partner stocks d is 2<=d<=n.") co_variance_matrix = get_co_variance_matrix(d) all_combinations = self._generate_all_combinations(d) output_matrix = [] # Stores the final set of combinations - # Iterating on the top 50 indices for each target stock - for target in self.top_50_correlations.index[:n_targets]: + # Iterating on the top n indices for each target stock + for target in self.top_n_correlations.index[:n_targets]: max_measure = -np.inf # Variable used to extract the desired maximum value final_combination = None # Stores the final desired combination @@ -261,7 +273,7 @@ def extremal(self, n_targets: int = 5, d: int = 4) -> list: def plot_selected_pairs(self, quadruples: list) -> list: """ - Plots the final selection of quadruples. + For the list of quadruples, this method plots the line plots of the cumulative returns of all stocks in quadruple. :param quadruples: (list) List of quadruples. :return: (list) List of Axes objects. diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py index 75a2825c..ee4e40e4 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection_utils.py @@ -174,14 +174,14 @@ def get_co_variance_matrix(d: int): args = [[1,2]] * d co_variance_matrix = np.zeros((2**d, 2**d)) - for i, l1 in enumerate(itertools.product(*args)): - for j, l2 in enumerate(itertools.product(*args)): + for i, l_i in enumerate(itertools.product(*args)): + for j, l_j in enumerate(itertools.product(*args)): if j < i: # Integrals in lower triangle are skipped. continue # Numerical Integration of d dimensions. - co_variance_matrix[i, j] = scipy.integrate.nquad(variance_integral_func, [(0, 1)] * d, args=(l1, l2))[0] + co_variance_matrix[i, j] = scipy.integrate.nquad(variance_integral_func, [(0, 1)] * d, args=(l_i, l_j))[0] inds = np.tri(2**d, k=-1, dtype=bool) # Storing the indices of elements in lower triangle. co_variance_matrix[inds] = co_variance_matrix.T[inds] @@ -206,16 +206,16 @@ def t_calc(u): # together res = 1 for ind in range(d): - res *= func(u[:, ind], l[ind]) + res *= variable_form(u[:, ind], l[ind]) output.append(res) return np.array(output) # Shape (2**d, n) -def func(t: np.array, value: int): +def variable_form(t: np.array, value: int): """ - Function returns equation form of respective variable after partial differentiation. - All variables in the differential equations are in one of two forms. + Function returns form of respective variable after partial differentiation in the copula density function. + All variables in the density function are in one of two forms. :param t: (np.array) Variable. :param value: (int) Flag denoting equation form of variable. @@ -224,8 +224,10 @@ def func(t: np.array, value: int): res = None if value == 1: + # Value of 1 returns the differential of $t * (1 - t)^2$ res = (t - 1) * (3 * t - 1) if value == 2: + # Value of 2 returns the differential of $t^2 * (1 - t)$ res = t * (2 - 3 * t) return res @@ -239,11 +241,11 @@ def variance_integral_func(*args): :return: (float) Integrand value. """ - l1 = args[-2] - l2 = args[-1] + l_i = args[-2] # Tuple represents the variable forms of (u_1, u_2, ..., u_d) beside $\theta_i$ in the density function. + l_j = args[-1] # Tuple represents the variable forms of (u_1, u_2, ..., u_d) beside $\theta_j$ in the density function. res = 1 for ind in range(len(args[:-2])): - res *= func(args[ind], l1[ind]) * func(args[ind], l2[ind]) + res *= variable_form(args[ind], l_i[ind]) * variable_form(args[ind], l_j[ind]) return res diff --git a/docs/source/copula_approach/partner_selection.rst b/docs/source/copula_approach/partner_selection.rst index db47006d..91b094fc 100644 --- a/docs/source/copula_approach/partner_selection.rst +++ b/docs/source/copula_approach/partner_selection.rst @@ -53,6 +53,12 @@ While it is true that this aspiration for linearity excludes quadruples with com it also rules out nonlinear dependencies in ranks. On the other hand, the extremal approach tries to maximize the distance to independence with focus on the joint extreme observations. +.. Note:: + Out of the four approaches, only extremal approach takes into consideration both linear and non-linear dependencies. + This results in a better preselection and thus better results compared to the other routines. + + So, extremal approach is generally preferred and it should be considered as default for partner selection. + Traditional Approach #################### @@ -70,6 +76,9 @@ The procedure is as follows: Implementation ************** +.. Note:: + This approach takes around 25 ms to run for each target stock. + .. automodule:: arbitragelab.copula_approach .. autoclass:: PartnerSelection @@ -125,6 +134,9 @@ We use the mean of the above three estimators as the final measure used to retur Implementation ************** +.. Note:: + This approach takes around 500 ms to run for each target stock. + .. automethod:: PartnerSelection.extended Geometric Approach @@ -172,6 +184,9 @@ where :math:`u_i` represents the ranked returns of a stock :math:`i` in quadrupl Implementation ************** +.. Note:: + This approach takes around 180 ms to run for each target stock. + .. automethod:: PartnerSelection.geometric Extremal Approach @@ -272,6 +287,12 @@ where, Implementation ************** +.. Note:: + This approach is extremely heavy compared to other approaches and takes around 15 sec to run for each target stock. + + Please be aware that there is a big overhead at the start of this method which involves calculating the covariance matrix. + This should take around 1 to 2 minutes when d = 4 which is the default. Increasing the value of d will increase the processing time significantly. + .. automethod:: PartnerSelection.extremal Code Example From a3535ac4539c307b45cf2a263d7bf1ff08b96338 Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Thu, 11 Mar 2021 21:39:48 +0900 Subject: [PATCH 026/103] finalize documentation finalize documentation --- .../basic_distance_approach.py | 18 +++++++--------- .../distance_approach/distance_approach.rst | 21 ++++++++++++++++--- tests/test_basic_distance_approach.py | 6 +----- 3 files changed, 26 insertions(+), 19 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index 7a1f3360..17adf55a 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -77,8 +77,8 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= :param skip_top: (int) Number of first top pairs to skip. For example, use skip_top=10 if you'd like to take num_top pairs starting from the 10th one. :param list_names: (list) List containing names of elements if Numpy array is used as input. - :param method: (str) Methods to use for sorting pairs [``standard`` by default, ``industry``, - ``zero_crossing``, ``variance``]. + :param method: (str) Methods to use for sorting pairs [``standard`` by default, ``variance``, + ``zero_crossing``]. :param industry_dict: (dict) Dictionary matching ticker to industry group. """ @@ -92,12 +92,8 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= # Dropping observations with missing values (for distance calculation) normalized = normalized.dropna(axis=0) - # If sector is set to True, pairs are matched within the same industry group - if method == 'industry': - - # Check whether the input of industry group dictionary is well given - if industry_dict is None: - raise Exception("Industry group dictionary is not given. Please provide the input") + # If industry dictionary is given, pairs are matched within the same industry group + if industry_dict: # Finding closest pairs for each element, excluding duplicates all_pairs = self.find_pair(normalized, industry_dict) @@ -127,10 +123,10 @@ def _selection_method(self, method, num_top, skip_top): Select pairs based on the method. """ - if method not in ['standard', 'industry', 'zero_crossing', 'variance']: + if method not in ['standard', 'zero_crossing', 'variance']: # Raise an error if the given method is inappropriate. - raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, ‘zero_crossing’, " - "‘industry’, or ‘variance’.") + raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, " + "‘zero_crossing’, or 'variance'") if method == 'zero_crossing': diff --git a/docs/source/distance_approach/distance_approach.rst b/docs/source/distance_approach/distance_approach.rst index dc53a2e6..2cd872a6 100644 --- a/docs/source/distance_approach/distance_approach.rst +++ b/docs/source/distance_approach/distance_approach.rst @@ -108,7 +108,9 @@ within the same industry group. With a dictionary containing the name/ticker of the securities and each corresponding industry group, the securities are first separated into different industry groups. Then, by calculating the Euclidean square distance for each of the pair within the same group, the :math:`n` closest pairs are selected(in default, -our function also allows skipping a number of first pairs, so one can choose pairs 10-15 to study). +our function also allows skipping a number of first pairs, so one can choose pairs 10-15 to study). This pair +selection criterion can be used as default before adding other methods such as zero-crossings or variance if one +gives a dictionary of industry group as an input. 2. **Pairs with a higher number of zero-crossings** @@ -199,6 +201,8 @@ Functions that can be used to get data: - **get_pairs()** outputs a list of tuples, containing chosen top pairs in the pairs formation step. +- **get_num_crossing()** outputs a list of tuples, containing chosen top pairs with its number of zero-crossings. + Functions that can be used to plot data: - **plot_pair()** plots normalized price series for elements in a given pair and the corresponding @@ -217,6 +221,8 @@ Implementation .. automethod:: DistanceStrategy.get_pairs +.. automethod:: DistanceStrategy.get_num_crossing + .. automethod:: DistanceStrategy.plot_pair .. automethod:: DistanceStrategy.plot_portfolio @@ -247,13 +253,22 @@ Code Example strategy = DistanceStrategy() strategy.form_pairs(data_pairs_formation, num_top=20, skip_top=5) - # Using the number of zero-crossing for pair selection method + # Adding an industry-based selection criterion to The DistanceStrategy + strategy_industry = DistanceStrategy() + strategy_industry.form_pairs(data_pairs_formation, industry_dict=industry_dict, + num_top=20, skip_top=5) + + # Using the number of zero-crossing for pair selection after industry-based selection strategy_zero_crossing = DistanceStrategy() - strategy_zero_crossing.form_pairs(data_pairs_formation, method='zero_crossing', num_top=20, skip_top=5) + strategy_zero_crossing.form_pairs(data_pairs_formation, method='zero_crossing', + industry_dict=industry_dict, num_top=20, skip_top=5) # Checking a list of pairs that were created pairs = strategy.get_pairs() + # Checking a list of pairs with the number of zero crossings + num_crossing = strategy.get_num_crossing() + # Now generating signals for formed pairs, using (2 * st. variation) as a threshold # to enter a position strategy.trade_pairs(data_signals_generation, divergence=2) diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index 235bc62a..d906e93c 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -64,7 +64,7 @@ def test_form_pairs(self): # Performing the pairs formation step strategy.form_pairs(self.train_data, num_top=5, skip_top=0) - strategy_industry.form_pairs(self.train_data, method='industry', + strategy_industry.form_pairs(self.train_data, method='standard', industry_dict=self.industry_dict, num_top=5, skip_top=0) strategy_zero_crossing.form_pairs(self.train_data, method='zero_crossing', num_top=5, skip_top=0) strategy_variance.form_pairs(self.train_data, method='variance', num_top=5, skip_top=0) @@ -248,10 +248,6 @@ def test_exceptions(self): with self.assertRaises(Exception): strategy.trade_pairs(self.test_data, divergence=2) - # When trying to form pairs based on industry approach without giving an industry dictionary as an input - with self.assertRaises(Exception): - strategy.form_pairs(self.train_data, method='industry', industry_dict=None) - # When trying to get pairs with inappropriate method with self.assertRaises(Exception): strategy._selection_method(method='wrong input',num_top=5,skip_top=0) From 00c2d4d9d5ec165a66f98c45a5c673c767757595 Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Thu, 11 Mar 2021 23:03:32 +0900 Subject: [PATCH 027/103] fix error for pylint fix error for pylint --- arbitragelab/distance_approach/basic_distance_approach.py | 4 ++-- tests/test_basic_distance_approach.py | 3 +-- 2 files changed, 3 insertions(+), 4 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index 17adf55a..6ccbcbd7 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -116,9 +116,9 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= # In case of a selection method other than standard or industry is used, sorting paris # based on the method - self._selection_method(method, num_top, skip_top) + self.selection_method(method, num_top, skip_top) - def _selection_method(self, method, num_top, skip_top): + def selection_method(self, method, num_top, skip_top): """ Select pairs based on the method. """ diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index d906e93c..7a265966 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -26,7 +26,6 @@ def setUp(self): """ # Using saved ETF price series for testing and trading - project_path = os.path.dirname(__file__) data_path = project_path + "/test_data/stock_prices.csv" data = pd.read_csv(data_path, parse_dates=True, index_col="Date") @@ -250,4 +249,4 @@ def test_exceptions(self): # When trying to get pairs with inappropriate method with self.assertRaises(Exception): - strategy._selection_method(method='wrong input',num_top=5,skip_top=0) + strategy.selection_method(method='wrong input',num_top=5,skip_top=0) From 29fb516b8173741c1fa890abf9da879df6098920 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Sat, 13 Mar 2021 15:55:15 +0530 Subject: [PATCH 028/103] Initiation of the Stochastic Control Approach Module. --- .../stochastic_control_approach/__init__.py | 5 +++++ .../stochastic_control_approach/ou_model_jurek.py | 15 +++++++++++++++ docs/source/index.rst | 7 +++++++ .../stochastic_control_approach/introduction.rst | 9 +++++++++ 4 files changed, 36 insertions(+) create mode 100644 arbitragelab/stochastic_control_approach/__init__.py create mode 100644 arbitragelab/stochastic_control_approach/ou_model_jurek.py create mode 100644 docs/source/stochastic_control_approach/introduction.rst diff --git a/arbitragelab/stochastic_control_approach/__init__.py b/arbitragelab/stochastic_control_approach/__init__.py new file mode 100644 index 00000000..369a8301 --- /dev/null +++ b/arbitragelab/stochastic_control_approach/__init__.py @@ -0,0 +1,5 @@ +""" +This module implements Stochastic Control Approach based Statistical Arbitrage strategies. +""" + +from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py new file mode 100644 index 00000000..e9cfc8ed --- /dev/null +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -0,0 +1,15 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html +""" +Module implements the optimal dynamic portfolio strategy for arbitrageurs with a finite horizon and +non-myopic preferences facing a mean-reverting arbitrage opportunity using OU process. + +This module is a realization of the methodology in the following paper: +`Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. In EFA 2006 Meetings Paper. +`__ +""" + +class StochasticControlJurek: + def __init__(self): + pass diff --git a/docs/source/index.rst b/docs/source/index.rst index 6051154f..f9e4cc7d 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -107,6 +107,13 @@ This project is licensed under an all rights reserved licence. copula_approach/mispricing_index_strategy copula_approach/utility_functions +.. toctree:: + :maxdepth: 2 + :caption: Stochastic Control Approach + :hidden: + + stochastic_control_approach/introduction + .. toctree:: :maxdepth: 2 :caption: Optimal Mean Reversion diff --git a/docs/source/stochastic_control_approach/introduction.rst b/docs/source/stochastic_control_approach/introduction.rst new file mode 100644 index 00000000..0f0eeea5 --- /dev/null +++ b/docs/source/stochastic_control_approach/introduction.rst @@ -0,0 +1,9 @@ +.. _stochastic_control_approach_strategies-introduction: + +============ +Introduction +============ + +Stochastic Control Approach Strategies +###################################### + From 475cadcc03efbea7a7772673bf8f244eb9bf3b87 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Sat, 13 Mar 2021 23:11:43 +0530 Subject: [PATCH 029/103] Added draft implementation of second paper. --- .../stochastic_control_approach/__init__.py | 1 + .../ou_model_mudchanatongsuk.py | 117 ++++++++++++++++++ 2 files changed, 118 insertions(+) create mode 100644 arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py diff --git a/arbitragelab/stochastic_control_approach/__init__.py b/arbitragelab/stochastic_control_approach/__init__.py index 369a8301..062df115 100644 --- a/arbitragelab/stochastic_control_approach/__init__.py +++ b/arbitragelab/stochastic_control_approach/__init__.py @@ -3,3 +3,4 @@ """ from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek +from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import StochasticControlMudchanatongsuk diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py new file mode 100644 index 00000000..9e4891dc --- /dev/null +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -0,0 +1,117 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html +""" +Module implements the optimal pairs trading strategy using Stochastic Control Approach. + +This module is a realization of the methodology in the following paper: +`Mudchanatongsuk, S., Primbs, J.A. and Wong, W., 2008, June. Optimal pairs trading: A stochastic control approach. + In 2008 American control conference (pp. 1035-1039). IEEE. +`__ +""" + +import numpy as np +import pandas as pd + +class StochasticControlMudchanatongsuk: + def __init__(self): + + self.ticker_A = None + self.ticker_B = None + self.S = None + self.spread = None + self.time_array = None + + self.delta_t = 1 / 251 + self.sigma = None + self.mu = None + self.k = None + self.theta = None + self.eta = None + self.rho = None + + self.gamma = None + + def fit(self, data: pd.DataFrame): + + # Preprocessing + #data = data.ffill() + #TODO : Might need to normalize input, estimate params is not running properly. + + self.time_array = np.arange(0, len(data)) / self.delta_t + self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] + self.S = np.log(data.loc[:, self.ticker_B]) + self.spread = np.log(data.loc[:, self.ticker_A]) - self.S + + self._estimate_params() + + def _estimate_params(self): + + N = len(self.spread) - 1 + + m = (self.S[N] - self.S[0]) / N + + S_squared = (np.power(np.diff(self.S), 2).sum() - 2 * m * (self.S[N] - self.S[0]) + N*m*m) / N + + + p = (1 / (N * np.power(self.spread[:-1], 2).sum() - self.spread[:-1].sum() ** 2)) * \ + (N * np.multiply(self.spread[1:], self.spread[:-1]).sum() - + (self.spread[N] - self.spread[0]) * np.sum(self.spread[:-1]) - self.spread[:-1].sum() ** 2) + + q = (self.spread[N] - self.spread[0] + (1 - p)*self.spread[:-1].sum()) / N + + V_squared = (1 / N) * (self.spread[N] ** 2 - self.spread[0] ** 2 + (1 + p ** 2)*np.power(self.spread[:-1], 2).sum() + - 2 * p * np.multiply(self.spread[1:], self.spread[:-1]).sum() - N*q) + + + C = (1/(N * np.sqrt(V_squared * S_squared))) * (np.multiply(self.spread[1:], np.diff(self.S)).sum() + - p * np.multiply(self.spread[:-1], np.diff(self.S)).sum() + - m * (self.spread[N] - self.spread[0]) + - m * (1 - p) * self.spread[:-1].sum()) + + self.sigma = np.sqrt(S_squared/self.delta_t) + + self.mu = (m/self.delta_t) + (0.5 * (self.sigma ** 2)) + + self.k = - np.log(p)/self.delta_t + + self.theta = q/(1 - p) + + self.eta = np.sqrt(2 * self.k * V_squared / (1 - p ** 2)) + + self.rho = self.k * C * np.sqrt(V_squared * S_squared) / (self.eta * self.sigma * (1 - p)) + + def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): + + self.gamma = gamma + t = np.arange(0, len(data)) / self.delta_t + x = np.log(data.iloc[:, 0]) - np.log(data.iloc[:, 1]) + + alpha_t = self._alpha_calc(t) + beta_t = self._beta_calc(t) + + h = None + return h + + def _alpha_calc(self, t): + + sqrt_gamma = np.sqrt(1 - self.gamma) + exp_calc = np.exp(2*self.k*(t[-1] - t)/sqrt_gamma) + + left_calc = self.k * (1 - sqrt_gamma) / (2 * (self.eta ** 2)) + + right_calc = 2 * sqrt_gamma / (1 - sqrt_gamma - (1 + sqrt_gamma)*exp_calc) + + return left_calc * (1 + right_calc) + + def _beta_calc(self, t): + + sqrt_gamma = np.sqrt(1 - self.gamma) + exp_calc = np.exp(2*self.k*(t[-1] - t)/sqrt_gamma) + + left_calc = 1/(2 * (self.eta ** 2) * ((1 - sqrt_gamma) - (1 + sqrt_gamma)*exp_calc)) + + right_calc = self.gamma * sqrt_gamma * (self.eta ** 2 + 2*self.rho*self.sigma*self.eta) * ((1 - exp_calc) ** 2) - \ + self.gamma * (self.eta ** 2 + 2*self.rho*self.sigma*self.eta + 2*self.k*self.theta) * (1 - exp_calc) + + return left_calc * right_calc From 16387144791c2935d248f196f1a03e2cd1074ce2 Mon Sep 17 00:00:00 2001 From: hansenpei Date: Sun, 14 Mar 2021 00:15:35 -0500 Subject: [PATCH 030/103] All functionality done for vinecop 1. Update requirements 2. All function docs 3. Halfway through unittests --- .../copula_approach/copula_calculation.py | 33 +- .../copula_approach/vinecop_generate.py | 108 +- .../copula_approach/vinecop_strategy.py | 392 ++- requirements.txt | 1 + tests/test_basic_copula_strategy_new.py | 6 +- tests/test_data/prices_10y_SP500.csv | 2505 +++++++++++++++++ tests/test_vinecop_generate.py | 178 ++ 7 files changed, 2932 insertions(+), 291 deletions(-) create mode 100644 tests/test_data/prices_10y_SP500.csv create mode 100644 tests/test_vinecop_generate.py diff --git a/arbitragelab/copula_approach/copula_calculation.py b/arbitragelab/copula_approach/copula_calculation.py index 9a162189..3f8b35b3 100644 --- a/arbitragelab/copula_approach/copula_calculation.py +++ b/arbitragelab/copula_approach/copula_calculation.py @@ -23,8 +23,9 @@ `__ """ # pylint: disable = invalid-name -from typing import Callable +from typing import Callable, Tuple import numpy as np +import pandas as pd import scipy.stats as ss from scipy.interpolate import interp1d from scipy.optimize import minimize @@ -102,6 +103,36 @@ def bounded_ecdf(x): # Vectorize it to work with arrays. return np.vectorize(bounded_ecdf) +def to_quantile(data: pd.DataFrame) -> Tuple[pd.DataFrame, list]: + """ + Convert the data frame to quantile by row. + + Not in place. Also returns the marginal cdfs of each column. This can work with more than just 2 columns. + + The method returns: + + - quantile_data: (pd.DataFrame) The calculated quantile data in a data frame with the original indexing. + - cdf_list: (list) The list of marginal cumulative density functions. + + :param data: (pd.DataFrame) The original data in DataFrame. + :return: (tuple) + quantile_data: (pd.DataFrame) The calculated quantile data in a data frame with the original indexing. + cdf_list: (list) The list of marginal cumulative density functions. + """ + + column_count = len(data.columns) # Number of columns. + cdf_lst = [None] * column_count # List to store all marginal cdf functions. + quantile_data_lst = [None] * column_count # List to store all quantile data in pd.Series. + + # Loop through all columns. + for i in range(column_count): + cdf_lst[i] = construct_ecdf_lin(data.iloc[:, i]) + quantile_data_lst[i] = data.iloc[:, i].map(cdf_lst[i]) + + quantile_data = pd.concat(quantile_data_lst, axis=1) # Form the quantile DataFrame. + + return quantile_data, cdf_lst + def ml_theta_hat(x: np.array, y: np.array, copula_name: str) -> float: """ Calculate empirical theta (theta_hat) for a type of copula by pseudo-maximum likelihood. diff --git a/arbitragelab/copula_approach/vinecop_generate.py b/arbitragelab/copula_approach/vinecop_generate.py index 06825101..a116cab3 100644 --- a/arbitragelab/copula_approach/vinecop_generate.py +++ b/arbitragelab/copula_approach/vinecop_generate.py @@ -7,30 +7,29 @@ Built on top of the :code:`pyvinecoplib` package. See https://github.com/vinecopulib/pyvinecopulib for more details. """ -from abc import ABC, abstractmethod from typing import List, Union from itertools import permutations -import numba import numpy as np import pandas as pd import pyvinecopulib as pv import scipy.integrate as integrate -class RVineCop(): + +class RVineCop: """ - R-Vine copula class, housing C-vine copula and D-vine copula as special subcases. + R-Vine copula class, housing C-vine copula and D-vine copula as special sub cases. """ - + def __init__(self): pass - + class CVineCop(RVineCop): """ Class for C-vine copulas. - + This is a wrapper class of pv.Vinecop that provides useful methods for statistical arbitrage. One key note is - that, to keep the notaion consistent with literature consensus, all variables started with pv are indexed from + that, to keep the notation consistent with literature consensus, all variables started with pv are indexed from 1, not 0. In this way it is easier to see the nodes of the tree. """ @@ -41,6 +40,7 @@ def __init__(self, cvine_cop: pv.Vinecop = None): :param cvine_cop: (pv.Vinecop) Optional. A fitted C-vine copula. Defaults to None. """ + super().__init__() # All the bivariate classes used to construct the vine copula. self._bicop_family = [pv.BicopFamily.bb1, pv.BicopFamily.bb6, pv.BicopFamily.bb7, pv.BicopFamily.bb8, pv.BicopFamily.clayton, pv.BicopFamily.student, pv.BicopFamily.frank, @@ -61,7 +61,7 @@ def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = :param data: (pd.DataFrame) The quantile data to be used to fit the C-vine copula. :param pv_target_idx: (int) Optional. The stock to be targeted for trading. This is indexed from 1, hence - 1 corresponds to the 0th column data in the data frame. Defalts to 1. + 1 corresponds to the 0th column data in the data frame. Defaults to 1. :param if_renew: (bool) Optional. Whether to update the class attribute cvine_cop. Defaults to True. :return: (pv.Vinecop) The fitted pv.Vinecop object. """ @@ -73,9 +73,9 @@ def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = possible_cvine_structures = self._get_possible_cvine_structs(data_dim, pv_target_idx) # Fit among all possible structures. - controls = pv.FitControlsVinecop(family_set = self._bicop_family) # Bivar copula constituents for the C-vine. + controls = pv.FitControlsVinecop(family_set=self._bicop_family) # Bivar copula constituents for the C-vine. aics = dict() # Dictionary for AIC values for all candidate C-vine copulas. - cvine_cops = dict() # Dictionary for storing all candiate C-vine copulas. + cvine_cops = dict() # Dictionary for storing all candidate C-vine copulas. for cvine_structure in possible_cvine_structures: temp_cvine_struct = pv.CVineStructure(order=cvine_structure) # Specific C-vine structure temp_cvine_cop = pv.Vinecop(structure=temp_cvine_struct) # Construct the C-vine copula @@ -85,10 +85,10 @@ def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = # Select the structure that has the lowest aics aics = pd.Series(aics) - fitted_cvine_strcture = aics.idxmin() # aics indexed by the structure (tuple) + fitted_cvine_structure = aics.idxmin() # aics indexed by the structure (tuple) # Generate a C-vine copula for the system - fitted_cvine_cop = cvine_cops[fitted_cvine_strcture] + fitted_cvine_cop = cvine_cops[fitted_cvine_structure] if if_renew: # Whether to renew the class C-vine copula. self.cvine_cop = fitted_cvine_cop @@ -99,8 +99,8 @@ def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = def _get_possible_cvine_structs(data_dim: int, pv_target_idx: int) -> List[tuple]: """ Get all possible C-vine structures specified by the dimension and the targeted node. - - A C-vine copula is uniquelly determined by an ordered tuple, listing the center of each tree at every level + + A C-vine copula is uniquely determined by an ordered tuple, listing the center of each tree at every level read backwards. For example, for a 4-dim C-vine characterized by (4, 2, 1, 3), node 3 is the center for the 0th tree, node 1 is the center for the 1st tree and so on. The targeted node representing the stock of interest, cannot be the at the center of every tree (except the last) and thus has to be the 0th element in the @@ -114,14 +114,14 @@ def _get_possible_cvine_structs(data_dim: int, pv_target_idx: int) -> List[tuple # Initiating all_items = list(range(1, data_dim+1)) # All the nodes, indexed from 1 - all_structures = permutations(all_items) # All the possible stuctures, as permutations of the nodes + all_structures = permutations(all_items) # All the possible structures, as permutations of the nodes - # Loop thourgh all the structures + # Loop through all the structures valid_structures = [] for structure in all_structures: - if structure[0] == pv_target_idx: # Only keep the ones where the targeted index is the 0-th element + if structure[0] == pv_target_idx: # Only keep the ones where the targeted index is the 0-th element valid_structures.append(structure) - + return valid_structures def get_condi_probs(self, u: Union[pd.DataFrame, np.array], pv_target_idx: int = 1, @@ -152,11 +152,11 @@ def get_condi_probs(self, u: Union[pd.DataFrame, np.array], pv_target_idx: int = # The output is a float return condi_prob - # When tne input is a pd.Dataframe + # When the input is a pd.Dataframe condi_probs = u.apply(lambda row: self._get_condi_prob(row, pv_target_idx, eps), axis=1) # The result is a pd.Series with matching indices return condi_probs - + def _get_condi_prob(self, u: pd.Series, pv_target_idx: int = 1, eps: float = 1e-4) -> float: r""" Get the conditional probability of the C-vine copula for a target. @@ -180,11 +180,11 @@ def _get_condi_prob(self, u: pd.Series, pv_target_idx: int = 1, eps: float = 1e- target_idx = pv_target_idx - 1 # Indexing from 0 target = u[target_idx] # Upper lim of the integration others = np.delete(u, target_idx) # Those will be served as arguments in quad - + # The integrand function is the pdf - def pdf_func(target, others): + def pdf_func(target_local: float, others_local: np.array) -> float: # the pv.Vinecop.pdf only takes 2D arrays as input. Here it is assembled back - u_vec = np.insert(arr=others, obj=target_idx, values=target).reshape((1, 4)) + u_vec = np.insert(arr=others_local, obj=target_idx, values=target_local).reshape((1, len(u))) pdf = self.cvine_cop.pdf(u_vec)[0] return pdf @@ -192,13 +192,13 @@ def pdf_func(target, others): # Integrating along the margin and normalizing the conditional probability sum_prob = integrate.quad(pdf_func, 0, target, args=others)[0] total_prob = integrate.quad(pdf_func, 0, 1, args=others)[0] - condi_prob = sum_prob / total_prob - + condi_prob = sum_prob / total_prob + # Map the condi prob into [eps, 1-eps] wrapped_condi_prob = max(min(condi_prob, 1-eps), eps) return wrapped_condi_prob - + def get_cop_densities(self, u: Union[pd.DataFrame, np.array], num_threads: int = 1) -> Union[pd.Series, float]: """ Calculate probability density of the vine copula. @@ -228,7 +228,7 @@ def get_cop_densities(self, u: Union[pd.DataFrame, np.array], num_threads: int = # The result is a pd.Series with matching indices return pdfs_series - def get_cop_evals(self, u: pd.DataFrame, mcn: int = 1e4, num_threads: int = 1) -> pd.Series: + def get_cop_evals(self, u: pd.DataFrame) -> pd.Series: """ Calculate cumulative density of the vine copula. @@ -238,28 +238,26 @@ def get_cop_evals(self, u: pd.DataFrame, mcn: int = 1e4, num_threads: int = 1) - :param u: (Union[pd.DataFrame, np.array]) The quantiles data to be used. The input can be a pandas dataframe, or a numpy array vector. The formal case yields the result with in pandas series in matching indices, and the latter yields a single float number. - :param mcn: (int) Integer for the number of quasi-random numbers to draw to evaluate the distribution for the - Monte-Carlo integration. Defaults to 1e4. - :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. + :return: (Union[pd.Series, float]) The calculated cdf. If the input is a dataframe then the result is a series with matching indices. If the input is a 1D np.array then the result is a float. """ - + # When the input is a 1D np.array if isinstance(u, np.ndarray) and u.ndim == 1: u_np = u.reshape((1, -1)) - cdf = self.cvine_cop.cdf(u_np, mcn, num_threads)[0] + cdf = self.cvine_cop.cdf(u_np)[0] # The output is a float return cdf # When tne input is a pd.Dataframe u_np = np.array(u) - cdfs = self.cvine_cop.cdf(u_np, mcn, num_threads) + cdfs = self.cvine_cop.cdf(u_np) cdfs_series = pd.Series(cdfs, index=u.index) # The result is a pd.Series with matching indices return cdfs_series - - def simulate(self, n: int, qrn: bool = False, num_threads: int = 1, seeds: List[int] = []) -> np.ndarray: + + def simulate(self, n: int, qrn: bool = False, num_threads: int = 1, seeds: List[int] = None) -> np.ndarray: """ Simulate from a vine copula model. @@ -267,18 +265,21 @@ def simulate(self, n: int, qrn: bool = False, num_threads: int = 1, seeds: List[ :param qrn: (bool) Optional. Set to True for quasi-random numbers. Defaults to False. :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. :param seeds: (List[int]) Optional. Seeds of the random number generator. If empty then the random generator - will be seeded randomly. Defaults to False. + will be seeded randomly. Defaults to []. :return: (pd.ndarray) The generated random samples from the vine copula. """ + if seeds is None: + seeds = [] + simulated_samples = self.cvine_cop.simulate(n, qrn, num_threads, seeds) return simulated_samples - + def aic(self, u: pd.DataFrame, num_threads: int = 1) -> float: """ Evaluates the Akaike information criterion (AIC). - + :param u: (pd.DataFrame) The quantile data used for evaluation. :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. :return: (float) calculated AIC value. @@ -292,7 +293,7 @@ def aic(self, u: pd.DataFrame, num_threads: int = 1) -> float: def bic(self, u: pd.DataFrame, num_threads: int = 1) -> float: """ Evaluates the Bayesian information criterion (BIC). - + :param u: (pd.DataFrame) The quantile data used for evaluation. :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. :return: (float) calculated BIC value. @@ -306,7 +307,7 @@ def bic(self, u: pd.DataFrame, num_threads: int = 1) -> float: def loglik(self, u: pd.DataFrame, num_threads: int = 1) -> float: """ Evaluates the Sum of log-likelihood. - + :param u: (pd.DataFrame) The quantile data used for evaluation. :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. :return: (float) calculated sum of log-likelihood. @@ -316,28 +317,3 @@ def loglik(self, u: pd.DataFrame, num_threads: int = 1) -> float: loglik_value = self.cvine_cop.loglik(u_np, num_threads) return loglik_value - - - -# #%% -# print(cvine_cop.families) -# #%% -# test_quantiles = np.array([[0.1, 0.2, 0.3, 0.4], -# [0.5, 0.2, 0.3, 0.4], -# [1, 0.2, 0.3, 0.4]]) -# lower_input = np.array([[0.099, 0.2, 0.3, 0.4], -# [0.499, 0.6, 0.7, 0.8], -# [0.199, 0.3, 0.4, 0.8]]) -# upper_input = np.array([[0.101, 0.2, 0.3, 0.4], -# [0.501, 0.6, 0.7, 0.8], -# [0.201, 0.3, 0.4, 0.8]]) -# print(cvine_cop.pdf(u=test_quantiles)) -#%% - -# u = np.array([0, 0.2, 0.3, 0.4]) -# print(cvinecop._get_condi_prob(u, pv_target_idx = 1, eps=1e-4)) - -#%% - -#%% -#%% diff --git a/arbitragelab/copula_approach/vinecop_strategy.py b/arbitragelab/copula_approach/vinecop_strategy.py index 6d36302b..b3a8c924 100644 --- a/arbitragelab/copula_approach/vinecop_strategy.py +++ b/arbitragelab/copula_approach/vinecop_strategy.py @@ -8,135 +8,167 @@ """ from typing import List, Union, Callable, Tuple -from itertools import permutations from arbitragelab.copula_approach.vinecop_generate import CVineCop -import numpy as np +import arbitragelab.copula_approach.copula_calculation as ccalc import pandas as pd -import pyvinecopulib as pv -class CVineCopStrat(): + +class CVineCopStrat: """ Trading strategy class using vine copulas. """ - def __init__(self, cvinecop: CVineCop = None): + + def __init__(self, cvinecop: CVineCop = None, signal_to_position_table: pd.DataFrame = None): """ Create the trading strategy class. + + :param cvinecop: (CVineCop) Optional. A fitted C-vine copula model from the vinecop_generate module. + :param signal_to_position_table: (pd.DataFrame) Optional. The table that instructs how to generate positions + based on current signal and the immediate past position. By default it uses the table described above. """ + self.cvine_cop = cvinecop - self.past_obs = None - self.threshold_std = None - # Signal to position table: Row indexed by previous position, column indexed by signal - # Refer to doc string of self._signal_to_position() for more detail - self.signal_to_position_table = pd.DataFrame({1: {0: 1, 1: 1, -1: 0}, - -1: {0: -1, 1: 0, -1: -1}, - 0: {0: 0, 1: 0, -1: 0}, - 2: {0: 0, 1: 1, -1: -1}}) - + self.past_obs = None # Number of past observations for Bollinger band. + self.threshold_std = None # Standard deviation threshold for Bollinger band. + # Signal to position table: Row indexed by previous position, column indexed by signal. + # Refer to doc string of self._signal_to_position() for more detail. + if signal_to_position_table is None: + self.signal_to_position_table = pd.DataFrame({1: {0: 1, 1: 1, -1: 0}, + -1: {0: -1, 1: 0, -1: -1}, + 0: {0: 0, 1: 0, -1: 0}, + 2: {0: 0, 1: 1, -1: -1}}) + else: + self.signal_to_position_table = signal_to_position_table + def calc_mpi(self, returns: pd.DataFrame, cdfs: List[Callable], pv_target_idx: int = 1, subtract_mean: bool = False) -> pd.Series: """ Calculate mispricing indices from returns for the target stock. - Mispricing indices are technically cumulative conditional probabilities calculated from a copula based on - returns data. + Mispricing indices are technically cumulative conditional probabilities calculated from a vine copula based on + returns data. Note that MPIs are model dependent since they are conditional probabilities inferred from vine + copulas. + + :param returns: (pd.DataFrame) The returns data for stocks. + :param cdfs: (pd.DataFrame) The list of cdf functions for each stocks return, used to map returns to their + quantiles. + :param pv_target_idx: (int) Optional. The target stock's index. Defaults to 1. + :param subtract_mean: (bool) Optional. Whether to subtract the mean 0.5 of MPI from the calculation. + :return: (pd.Series) The MPIs calculated from returns and vine copula. """ - - # 1. Map all the returns to quantiles + + # 1. Map all the returns to quantiles. quantiles = pd.DataFrame(data=0, index=returns.index, columns=returns.columns) for i, column_name in enumerate(returns): quantiles[column_name] = returns[column_name].apply(cdfs[i]) - - # 2. Calculate the conditional probabilities + + # 2. Calculate the conditional probabilities. This step is relatively slow. mpis = self.cvine_cop.get_condi_probs(quantiles, pv_target_idx) - + if subtract_mean: mpis = mpis.subtract(0.5) return mpis - - def select_candidates(self): - pass - + def get_positions_bollinger(self, returns: pd.DataFrame, cdfs: List[Callable], pv_target_idx: int = 1, init_pos: int = 0, past_obs: int = 20, threshold_std: float = 1.0, - mpis: pd.Series = None, if_return_bollinger_band = False) -> pd.Series: + mpis: pd.Series = None, if_return_bollinger_band=False) \ + -> Union[pd.Series, Tuple[pd.Series, pd.DataFrame]]: """ Get positions based on the strategy suggested by [Bollinger, 1992]. - + Calculate the running mean and standard deviation of Cumulative mispricing index (CMPI) for the past 20 - observations (one month if it is daily data) and create the running Bollinger band as + observations (one month if it is daily data) and create the running Bollinger band as (mean - k*std, mean + k*std), k is the threshold_std variable. Trading logic is as follows: - + - Long if the CMPI crosses its lower Bollinger band (undervalued) - Short if the CMPI crosses its upper Bollinger band (overvalued) - Exit if the CMPI crosses the running mean of the Bollinger band (reversion to equilibrium) - + This is used for backtesting when one has access to all testing data at once. The first 20 observations ([0, 19]) will be used for calculating the Bollinger band and the trading signal generation starts from - observation 20. For live data feed please use self.get_cur_pos_bollinger(). + observation 20. For live data feed you can use self.get_cur_pos_bollinger() to save computation time. + + :param returns: (pd.DataFrame) The returns data for stocks. + :param cdfs: (pd.DataFrame) The list of cdf functions for each stocks return, used to map returns to their + quantiles. + :param pv_target_idx: (int) Optional. The target stock's index. Defaults to 1. + :param init_pos: (int) Optional. Initial trading position, 0 is None, 1 is Long, -1 is Short. Defaults to 0. + :param past_obs: (int) Optional. The number of observations used to calculate Bollinger band. Defaults to 20. + :param threshold_std: (float) Optional. How many std away from the running avg for the Bollinger band. Defaults + to 1. + :param mpis: (pd.Series) Optional. The MPI data for the target stock. Defaults to None, and it will be + from the returns automatically. This is used to preload MPIs to save computation time. + :param if_return_bollinger_band: (bool) Optional. Whether to return the Bollinger band data series together + with the positions data series. Defaults to False. + :return: (Union[pd.Series, Tuple[pd.Series]]) The MPIs calculated from returns and vine copula. Or the MPIs + together with the Bollinger band data. """ - - self.past_obs = past_obs - self.threshold_std = threshold_std - + + self.past_obs = past_obs # Number of past observations for the Bollinger band. + self.threshold_std = threshold_std # How many std away from the running avg for the Bollinger band. + # 1. Get the initial mean and std of CMPI if mpis is None: cmpis = self.calc_mpi(returns, cdfs, pv_target_idx, subtract_mean=True).cumsum() else: cmpis = mpis.cumsum() - init_mean = cmpis.iloc[:past_obs].mean() - init_std = cmpis.iloc[:past_obs].std() - + # init_mean = cmpis.iloc[:past_obs].mean() + # init_std = cmpis.iloc[:past_obs].std() + # 2. Get positions - # Initiating - trading_cmpis = cmpis.iloc[past_obs-1:] - bollinger_band = pd.DataFrame(data=0, index=trading_cmpis.index, columns=['LowerBound', 'Mean', 'UpperBound']) - bollinger_band.iloc[0] = [init_mean - threshold_std*init_std, init_mean, init_mean + threshold_std*init_std] - positions = pd.Series(data=0, index=trading_cmpis.index) - positions.iloc[0] = init_pos - # Loop through trading_cmpis to calculate positions - for idx in range(1, len(trading_cmpis)): - # Get signal + running_avg = cmpis.rolling(self.past_obs).mean() + running_std = cmpis.rolling(self.past_obs).std() + bollinger_band = pd.DataFrame({'LowerBound': running_avg - self.threshold_std * running_std, + 'Mean': running_avg, + 'UpperBound': running_avg + self.threshold_std * running_std}) + # Loop through the bollinger_band to get positions + positions = pd.Series(data=None, index=bollinger_band.index) + positions.iloc[self.past_obs - 1] = init_pos + for idx in range(past_obs, len(positions)): + # Get current trading signal from Bollinger band signal = self.get_cur_signal_bollinger( - past_pos=positions.iloc[idx-1], past_cmpi=trading_cmpis[idx-1], cur_cmpi=trading_cmpis[idx], - running_mean=bollinger_band['Mean'].iloc[idx-1], - upper_threshold=bollinger_band['UpperBound'].iloc[idx-1], - lower_threshold=bollinger_band['LowerBound'].iloc[idx-1]) + past_cmpi=cmpis[idx - 1], cur_cmpi=cmpis[idx], + running_mean=bollinger_band['Mean'].iloc[idx - 1], + upper_threshold=bollinger_band['UpperBound'].iloc[idx - 1], + lower_threshold=bollinger_band['LowerBound'].iloc[idx - 1]) # Translate signal to current position - positions.iloc[idx] = self._signal_to_position(past_pos=positions.iloc[idx-1], signal=signal) - - # Update the bollinger band - cur_returns_slice = cmpis.iloc[idx: idx+past_obs] - cur_mean = cur_returns_slice.mean() - cur_std = cur_returns_slice.std() - # Format: LowerBound, Mean, UpperBound - bollinger_band.iloc[idx] = [cur_mean - threshold_std*cur_std, cur_mean, cur_mean + threshold_std*cur_std] - + positions.iloc[idx] = self._signal_to_position(past_pos=positions.iloc[idx - 1], signal=signal) + # 3. Return positions (and the bollinger band) if if_return_bollinger_band: return positions, bollinger_band return positions - + @staticmethod - def get_cur_signal_bollinger(past_pos: int, past_cmpi: float, cur_cmpi: float, running_mean: float, + def get_cur_signal_bollinger(past_cmpi: float, cur_cmpi: float, running_mean: float, upper_threshold: float, lower_threshold: float) -> int: """ - Get the currrent trading signal based. - - Signal types {1: long, -1: short, 0: exit, 2: do nothing} + Get the current trading signal based on the bollinger band over CMPIs. + + Signal types {1: long, -1: short, 0: exit, 2: do nothing}. If the current CMPI > upper threshold, then short; + If the current CMPI < lower threshold, then long; If the current CMPI crosses with the running mean, then + exit; else do nothing. + + :param past_cmpi: (float) The immediate past CMPI value. + :param cur_cmpi: (float) The current CMPI value. + :param running_mean: (float) The running average for CMPI in the bollinger band. + :param upper_threshold: (float) The upper threshold of the bollinger band. + :param lower_threshold: (float) The lower threshold of the bollinger band. + :return: (int) The derived signal based on all the input info. """ - + signal = 2 # By default do nothing - + # Open signal if_long = (cur_cmpi < lower_threshold) if_short = (cur_cmpi > upper_threshold) - + # Exit signal: when the cmpi crosses with the running mean if_exit = ((past_cmpi - running_mean) * (cur_cmpi - running_mean) < 0) - + # Assemble the signal together if_any_signal = any([if_long, if_short, if_exit]) if if_any_signal: @@ -146,199 +178,117 @@ def get_cur_signal_bollinger(past_pos: int, past_cmpi: float, cur_cmpi: float, r # Return the default signal, which is do nothing return signal - def _signal_to_position(self, past_pos: int, signal: int, signal_to_position_table: pd.DataFrame = None) -> int: + def _signal_to_position(self, past_pos: int, signal: int) -> int: """ Map the signal to position, given the past position. - + The default map is: signal [long, short, exit, do-nothing], acting on previous positions being [0, 1, -1] respectively - + * long signal: {0: 1, 1: 1, -1: 0} * short signal: {0: -1, 1: 0, -1: 0} * exit signal: {0: 0, 1: 0, -1: 0} * do-nothing signal: {0: 0, 1: 1, -1: -1} + + :param signal: (int) Current signal {1: long, -1: short, 0: exit, 2: do nothing}. + :param past_pos: (int) The immediate past position {0: no position, 1: long, -1: short}. + :return: (int) The current position. """ - - if signal_to_position_table is not None: - self.signal_to_position_table = signal_to_position_table - - table = self.signal_to_position_table - - new_position = table.loc[past_pos, signal] - + + # Generate a new position according to the table. + new_position = self.signal_to_position_table.loc[past_pos, signal] + return new_position - + def get_cur_pos_bollinger(self, returns_slice: pd.DataFrame, cdfs: List[Callable], past_pos: int, - pv_target_idx: int = 1, past_cmpi: float = 0, threshold_std: float = 1.0) -> Tuple: + pv_target_idx: int = 1, past_cmpi: float = 0, threshold_std: float = 1.0) \ + -> Tuple[int, float]: """ Get the suggested position and updated bollinger band from cur_returns pandas DataFrame. - + If the dataframe has 21 rows, then the first 20 rows will be used to calculate the Bollinger band, then the position will be generated based on the last row. Then we calculate the updated Bollinger band. This is used for live data feed. + + :param returns_slice: (pd.DataFrame) The slice of the returns data frame. Everything except for the last data + point is used to calculate the bollinger band, and the last data point is used to generate the current + position. + :param cdfs: (List[Callable]) The list of CDFs for the returns data. + :param past_pos: (int) The immediate past position. + :param pv_target_idx: (int) Optional. The target stock index. For example, 1 means the target stock is the 0th + column in returns_slice. Defaults to 1. + :param past_cmpi: (float) Optional. The immediate past CMPI value. Defaults to 0. + :param threshold_std: (float) Optional. How many std away from the running avg for the Bollinger band. Defalts + to 1. + :return: (Tuple[int, float]) The current position and the new cmpi. """ - + # 1. Calculate the Bollinger band: mean and std - cmpis = past_cmpi + self.calc_mpi(returns_slice, cdfs, subtract_mean=True).cumsum() + cmpis = past_cmpi + self.calc_mpi(returns_slice, cdfs, subtract_mean=True, pv_target_idx=pv_target_idx).cumsum() init_mean = cmpis.iloc[: -1].mean() init_std = cmpis.iloc[: -1].std() # 2. Get positions from the last row of the dataframe past_cmpi = cmpis.iloc[-2] cur_cmpi = cmpis.iloc[-1] - signal = self.get_cur_signal_bollinger(past_pos, past_cmpi, cur_cmpi, running_mean=init_mean, - upper_threshold=init_mean + threshold_std*init_std, - lower_threshold=init_mean - threshold_std*init_std) + signal = self.get_cur_signal_bollinger(past_cmpi, cur_cmpi, running_mean=init_mean, + upper_threshold=init_mean + threshold_std * init_std, + lower_threshold=init_mean - threshold_std * init_std) new_position = self._signal_to_position(past_pos, signal) - + return new_position, cur_cmpi - + @staticmethod - def positions_to_units_cohort(prices_df: pd.DataFrame, positions: pd.Series, pv_target_idx: int = 1, - multiplier: float = 1) -> pd.DataFrame: + def positions_to_units_against_index(target_stock_prices: pd.Series, index_prices: pd.Series, positions: pd.Series, + multiplier: float = 1) -> pd.DataFrame: """ - Change the positions series into units held for each security for a dollar neutral strategy. - - For example., for 1 dollar investment of a 4-stock-cohort, long the target stock by 1/2 dollar and short every - other 3 by 1/6 dollar each. + Translate positions to units held for the target stock against an index fund. + + The translation is conducted under a dollar-neutral strategy against an index fund (typically SP500 index). For + example, for a long position, for each 1 dollar investment, long the target stock by 1/2 dollar, and short the + index fund by 1 dollar. Originally the positions calculated by this strategy is given with values in {0, 1, -1}. To be able to actually trade using the dollar neutral strategy as given by the authors in the paper, one needs to know at any given - time how much units to hold for each stock. The result will be returned in a pd.DataFrame. The user can also + time how much units to hold for the stock. The result will be returned in a pd.DataFrame. The user can also multiply the final result by changing the multiplier input. It means by default it uses 1 dollar for calculation unless changed. It also means there is no reinvestment on gains. - Note: This method assumes the 0th column in prices_df is the long unit (suppose it is called stock 1), 1st - column the shrot unit (suppose it is called stock 2). For example, 1 in positions means buy stock 1 with 0.5 - dollar and sell stock 2 to gain 0.5 dollar. - - Note2: The short units will be given in its actual value. i.e., short 0.54 units is given as -0.54 in the + Note: The short units will be given in its actual value. i.e., short 0.54 units is given as -0.54 in the output. - :param prices_df: (pd.DataFrame) Prices data frame for the two securities. - :param positions: (pd.Series) The suggested positions with values in {0, 1, -1}. Need to have the same length - as prices_df. - :param multiplier: (float) Optional. Multiply the calculated result by this amount. Defalts to 1. - :return: (pd.DataFrame) The calculated positions for each security. The row and column index will be taken - from prices_df. + :param target_stock_prices: (pd.Series) The target stock's price series. + :param index_prices: (pd.Series) The index fund's price. + :param positions: (pd.Series) The positions suggested by the strategy in integers. + :param multiplier: (float) Optional. Multiply the calculated result by this amount. Defaults to 1. + :return: (pd.DataFrame) The units to hold for the target stock and the index fund. """ - target_stock_prices = prices_df.iloc[:, pv_target_idx-1] - other_stocks_prices = prices_df.drop(columns=prices_df.columns[pv_target_idx-1]) - num_of_others = len(other_stocks_prices.columns) - target_stock_prices_np = target_stock_prices.to_numpy(dtype=np.float16) - other_stocks_prices_np = other_stocks_prices.to_numpy(dtype=np.float16) - - target_stock_units = pd.Series(data=0, index=target_stock_prices.index) - other_stocks_units = pd.DataFrame(data=0, index=other_stocks_prices.index, columns=other_stocks_prices.columns) - target_stock_units_np = target_stock_units.to_numpy(dtype=np.float16) - other_stocks_units_np = other_stocks_units.to_numpy(dtype=np.float16) + units_df = pd.DataFrame(data=0, index=target_stock_prices.index, columns=[target_stock_prices.name, + index_prices.name]) + prices_df = pd.concat([target_stock_prices, index_prices], axis=1) - target_stock_units_np[0] = 0.5 / target_stock_prices_np[0] * positions[0] - other_stocks_units_np[0, :] = - 0.5 / num_of_others /other_stocks_prices_np[0, :] * positions[0] - - nums = len(positions) - for i in range(1, nums): + units_df.iloc[0, 0] = 0.5 / prices_df.iloc[0, 0] * positions[0] + units_df.iloc[0, 1] = - 0.5 / prices_df.iloc[1, 0] * positions[0] + for i in range(1, len(positions)): # By default the new amount of units to be held is the same as the previous step. - target_stock_units_np[i] = target_stock_units_np[i-1] - other_stocks_units_np[i, :] = other_stocks_units_np[i-1, :] + units_df.iloc[i, :] = units_df.iloc[i - 1, :] # Updating if there are position changes. # From not short to short. - if positions[i-1] != -1 and positions[i] == -1: # Short target, long cohort - long_units = 0.5 / num_of_others / other_stocks_prices_np[i, :] - short_units = 0.5 / target_stock_prices_np[i] - target_stock_units_np[i] = - short_units - other_stocks_units_np[i, :] = long_units + if positions[i - 1] != -1 and positions[i] == -1: # Short 1, long 2 + long_units = 0.5 / prices_df.iloc[i, 1] + short_units = 0.5 / prices_df.iloc[i, 0] + units_df.iloc[i, 0] = - short_units + units_df.iloc[i, 1] = long_units # From not long to long. - if positions[i-1] != 1 and positions[i] == 1: # Short cohort, long target - long_units = 0.5 / target_stock_prices_np[i] - short_units = 0.5 / num_of_others / other_stocks_prices_np[i, :] - target_stock_units_np[i] = long_units - other_stocks_units_np[i, :] = - short_units + if positions[i - 1] != 1 and positions[i] == 1: # Short 2, long 1 + long_units = 0.5 / prices_df.iloc[i, 0] + short_units = 0.5 / prices_df.iloc[i, 1] + units_df.iloc[i, 0] = long_units + units_df.iloc[i, 1] = - short_units # From long/short to none. - if positions[i-1] != 0 and positions[i] == 0: # Exiting - target_stock_units_np[i] = 0 - other_stocks_units_np[i, :] = 0 - - return target_stock_units_np * multiplier, other_stocks_units_np * multiplier - -#%% test -import time -import arbitragelab.copula_approach.copula_strategy_basic as csb - -cvinecop = CVineCop() -stocks_universe = pd.read_csv(r'D:\Apprenticeship\data\dow_stocks.csv', parse_dates=True, - index_col='Date') -# Fit a vine copula -# Change to returns -returns_universe = stocks_universe.pct_change() -returns_universe.iloc[0] = 0 - -returns_sample = returns_universe[['AAPL', 'MSFT', 'BA', 'V']] - -train_returns = returns_sample.iloc[:1200] -test_returns = returns_sample.iloc[1200:] - -start_time = time.time() -# Change returns to pct -CSB = csb.BasicCopulaStrategy() -train_quantiles, cdfs = CSB.to_quantile(data=train_returns) -cvine_cop = cvinecop.fit_auto(train_quantiles) -print("--- %s seconds ---" % (time.time() - start_time)) -#%% -cvinecop = CVineCop(cvine_cop) -#%% Test mpi generation -import time -start_time = time.time() -cvcs = CVineCopStrat(cvinecop=cvinecop) -mpis = cvcs.calc_mpi(returns=test_returns, cdfs=cdfs, subtract_mean=True) -print("--- %s seconds ---" % (time.time() - start_time)) -#%% -start_time = time.time() -positions, bband = cvcs.get_positions_bollinger( - returns=test_returns, cdfs=cdfs, pv_target_idx=1, - init_pos=0, past_obs=20, threshold_std=2.0, mpis=mpis, - if_return_bollinger_band = True) -print("--- %s seconds ---" % (time.time() - start_time)) -#%% -import matplotlib.pyplot as plt -plt.style.use('seaborn') -fig, ax = plt.subplots(nrows=3, dpi=300, figsize=(10, 7), gridspec_kw={'height_ratios': [0.5, 0.2, 0.7]}, sharex=True) -ax[0].plot(stocks_universe['AAPL'].iloc[1200:] / stocks_universe['AAPL'].iloc[1200], label='Target Stock Price') -ax[0].plot(stocks_universe['MSFT'].iloc[1200:] / stocks_universe['MSFT'].iloc[1200], label='Cohort Stock 2', linewidth=1) -ax[0].plot(stocks_universe['BA'].iloc[1200:] / stocks_universe['BA'].iloc[1200], label='Cohort Stock 3', linewidth=1) -ax[0].plot(stocks_universe['V'].iloc[1200:] / stocks_universe['V'].iloc[1200], label='Cohort Stock 4',linewidth=1) -ax[1].plot(positions, label='positions') -ax[2].plot(mpis.cumsum(), label='CMPI') -ax[2].plot(bband['LowerBound'], label='B Band Bound', linewidth=1, color='brown') -ax[2].plot(bband['Mean'], label='B Band Mean') -ax[2].plot(bband['UpperBound'], linewidth=1, color='brown') -plt.tight_layout() -ax[0].legend() -ax[2].legend() -fig.show() - -#%% Positions to units -shifted_positions = positions.shift(1) -shifted_positions.iloc[0] = 0 -target_units, others_units = cvcs.positions_to_units_cohort( - prices_df=stocks_universe[['AAPL', 'MSFT', 'BA', 'V']].iloc[1219:], positions=shifted_positions, multiplier=4) - -#%% Equity curve plot -portfolio_pnl = (returns_sample['AAPL'].iloc[1219:].to_numpy() * target_units - + (returns_sample[['MSFT', 'BA', 'V']].iloc[1219:].to_numpy() * others_units).sum(axis=1)) -equity_pnl = pd.Series(data=portfolio_pnl.cumsum(), index=returns_sample['AAPL'].iloc[1219:].index) - -import matplotlib.pyplot as plt -fig, ax = plt.subplots(nrows=3, dpi=300, figsize=(10, 7), gridspec_kw={'height_ratios': [0.5, 0.2, 0.7]}, sharex=True) -ax[0].plot(stocks_universe['AAPL'].iloc[1200:] / stocks_universe['AAPL'].iloc[1200], label='Target Stock Price') -ax[0].plot(stocks_universe['MSFT'].iloc[1200:] / stocks_universe['MSFT'].iloc[1200], label='Cohort Stock 2', linewidth=1) -ax[0].plot(stocks_universe['BA'].iloc[1200:] / stocks_universe['BA'].iloc[1200], label='Cohort Stock 3', linewidth=1) -ax[0].plot(stocks_universe['V'].iloc[1200:] / stocks_universe['V'].iloc[1200], label='Cohort Stock 4',linewidth=1) -ax[1].plot(positions, label='positions') -ax[2].plot(equity_pnl, label='P&L', linewidth=1) - -plt.tight_layout() -ax[0].legend() -ax[2].legend() -fig.show() \ No newline at end of file + if positions[i - 1] != 0 and positions[i] == 0: # Exiting + units_df.iloc[i, 0] = 0 + units_df.iloc[i, 1] = 0 + + return units_df.multiply(multiplier) diff --git a/requirements.txt b/requirements.txt index c9345679..82a6a706 100644 --- a/requirements.txt +++ b/requirements.txt @@ -20,6 +20,7 @@ keras==2.3.1 tensorflow==2.2.1 arch==4.16.1 analytics-python==1.2.9 +pyvinecopulib==0.5.4 # Develop bump2version==1.0.1 diff --git a/tests/test_basic_copula_strategy_new.py b/tests/test_basic_copula_strategy_new.py index 61a3daf4..0f79ac08 100644 --- a/tests/test_basic_copula_strategy_new.py +++ b/tests/test_basic_copula_strategy_new.py @@ -47,7 +47,7 @@ def test_to_quantile(): 'col3': [np.nan, 1/5, 2/5, 3/5, 4/5, 1]} expected_df = pd.DataFrame.from_dict(expected) # Compare with expected result, up to 4 digits - pd.testing.assert_frame_equal(quantile_df, expected_df, check_dtype=False, check_less_precise=4) + pd.testing.assert_frame_equal(quantile_df, expected_df, check_dtype=False, atol=4) # Checking the cdfs test_input = pd.Series([-100, -1, 1.5, 2, 3, 10, np.nan]) @@ -55,8 +55,8 @@ def test_to_quantile(): quantiles_2 = test_input.map(cdfs[1]) expec_qt1 = pd.Series([0, 1e-5, 0.416667, 0.5, 0.666667, 1 - 1e-5, np.nan]) expec_qt2 = pd.Series([1e-5, 0.1, 0.35, 0.4, 0.5, 1 - 1e-5, np.nan]) - pd.testing.assert_series_equal(expec_qt1, quantiles_1, check_dtype=False, check_less_precise=4) - pd.testing.assert_series_equal(expec_qt2, quantiles_2, check_dtype=False, check_less_precise=4) + pd.testing.assert_series_equal(expec_qt1, quantiles_1, check_dtype=False, atol=4) + pd.testing.assert_series_equal(expec_qt2, quantiles_2, check_dtype=False, atol=4) def test_exit_trigger_or(self): """ diff --git a/tests/test_data/prices_10y_SP500.csv b/tests/test_data/prices_10y_SP500.csv new file mode 100644 index 00000000..42bc1bbd --- /dev/null +++ b/tests/test_data/prices_10y_SP500.csv @@ -0,0 +1,2505 @@ 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diff --git a/tests/test_vinecop_generate.py b/tests/test_vinecop_generate.py new file mode 100644 index 00000000..8774fdcf --- /dev/null +++ b/tests/test_vinecop_generate.py @@ -0,0 +1,178 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html +""" +Unit tests for vinecop_generate, vinecop_strategy +""" +import unittest +import pandas as pd +import numpy as np +import os +import warnings +import pyvinecopulib as pv +import arbitragelab.copula_approach.vinecop_generate as vg +import arbitragelab.copula_approach.copula_calculation as ccalc + + +class TestVineCop(unittest.TestCase): + """ + Testing vinecop_generate, vinecop_strategy. Not including the stocks selection module. + """ + + def setUp(self) -> None: + project_path = os.path.dirname(__file__) + data_path = project_path + "/test_data/prices_10y_SP500.csv" + sp500_prices = pd.read_csv(data_path, index_col=0, parse_dates=True).fillna(method='ffill') + sp500_returns = sp500_prices.pct_change().fillna(0) + + subsample = sp500_returns[['AAPL', 'ABT', 'V', 'AIZ']] + returns_train = subsample.iloc[:400] + returns_test = subsample.iloc[400:800] + + # Fit a c-vine copula in pv for future usage + bicop_family = [pv.BicopFamily.bb1, pv.BicopFamily.bb6, pv.BicopFamily.bb7, pv.BicopFamily.bb8, + pv.BicopFamily.clayton, pv.BicopFamily.student, pv.BicopFamily.frank, + pv.BicopFamily.gaussian, pv.BicopFamily.gumbel, pv.BicopFamily.indep] + cvine_structure = pv.CVineStructure(order=[1, 4, 3, 2]) + controls = pv.FitControlsVinecop(family_set=bicop_family) + pv_cvine_cop = pv.Vinecop(structure=cvine_structure) # Construct the C-vine copula + data_np, _ = ccalc.to_quantile(returns_train) + pv_cvine_cop.select(data=data_np, controls=controls) + + self.pv_cvine_cop = pv_cvine_cop + + @staticmethod + def test_to_quantile(): + """ + Testing the to_quantile method from ccalc module. + """ + + # Create sample data frame and compute the percentile + data = {'col1': [0, 1, 2, 3, 4, 5], 'col2': [0, 2, 4, 6, np.nan, 10], 'col3': [np.nan, 2, 4, 6, 8, 10]} + df = pd.DataFrame.from_dict(data) + quantile_df, cdfs = ccalc.to_quantile(df) + # Expected result + expected = {'col1': [1 / 6, 2 / 6, 3 / 6, 4 / 6, 5 / 6, 1], + 'col2': [1 / 5, 2 / 5, 3 / 5, 4 / 5, np.nan, 1], + 'col3': [np.nan, 1 / 5, 2 / 5, 3 / 5, 4 / 5, 1]} + expected_df = pd.DataFrame.from_dict(expected) + # Compare with expected result, up to 4 digits + pd.testing.assert_frame_equal(quantile_df, expected_df, check_dtype=False, atol=4) + + # Checking the cdfs + test_input = pd.Series([-100, -1, 1.5, 2, 3, 10, np.nan]) + quantiles_1 = test_input.map(cdfs[0]) + quantiles_2 = test_input.map(cdfs[1]) + expec_qt1 = pd.Series([0, 1e-5, 0.416667, 0.5, 0.666667, 1 - 1e-5, np.nan]) + expec_qt2 = pd.Series([1e-5, 0.1, 0.35, 0.4, 0.5, 1 - 1e-5, np.nan]) + pd.testing.assert_series_equal(expec_qt1, quantiles_1, check_dtype=False, atol=4) + pd.testing.assert_series_equal(expec_qt2, quantiles_2, check_dtype=False, atol=4) + + def test_get_possible_cvine_structs(self) -> None: + """ + Test CVineCop._get_possible_cvine_structs. + """ + + cvinecop = vg.CVineCop() + structures_5 = cvinecop._get_possible_cvine_structs(data_dim=5, pv_target_idx=2) + self.assertTrue(isinstance(structures_5, list)) + expected_structures_5 = {(2, 1, 3, 4, 5), (2, 1, 3, 5, 4), (2, 1, 4, 3, 5), (2, 1, 4, 5, 3), (2, 1, 5, 3, 4), + (2, 1, 5, 4, 3), (2, 3, 1, 4, 5), (2, 3, 1, 5, 4), (2, 3, 4, 1, 5), (2, 3, 4, 5, 1), + (2, 3, 5, 1, 4), (2, 3, 5, 4, 1), (2, 4, 1, 3, 5), (2, 4, 1, 5, 3), (2, 4, 3, 1, 5), + (2, 4, 3, 5, 1), (2, 4, 5, 1, 3), (2, 4, 5, 3, 1), (2, 5, 1, 3, 4), (2, 5, 1, 4, 3), + (2, 5, 3, 1, 4), (2, 5, 3, 4, 1), (2, 5, 4, 1, 3), (2, 5, 4, 3, 1)} + structures_5_set = set(structures_5) + self.assertEqual(structures_5_set, expected_structures_5) + + structures_3 = cvinecop._get_possible_cvine_structs(data_dim=3, pv_target_idx=1) + expected_structures_3 = {(1, 2, 3), (1, 3, 2)} + structures_3_set = set(structures_3) + self.assertEqual(structures_3_set, expected_structures_3) + + def test_get_condi_probs_priv(self) -> None: + """ + Test the _get_condi_probs function from vinecop_generate. + """ + + # Ignore possible integration warnings. + warnings.filterwarnings(action='ignore', message='The integral is probably divergent') + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + # Various inputs in quantile + u = np.array([[0, 0.1, 0.4, 0.6], [0.1, 0.1, 0.4, 0.6], [0.2, 0.1, 0.4, 0.6], [0.3, 0.1, 0.4, 0.6], + [0.9, 0.1, 0.4, 0.6], [1, 0.1, 0.4, 0.6], [0, 0.1, 0.4, 1], [0.1, 1, 0.4, 1], [0, 0, 1, 1], + [1, 0, 0, 0]]) + expected_results = np.array([0.0001, 0.07678050591604534, 0.17637106968139507, 0.283373927184108, + 0.9155297176502054, 0.9999, 0.0001, 0.03269281901703475, 0.0001, 0.9999]) + + condi_probs = np.array([cvinecop._get_condi_prob(ui, pv_target_idx=1) for ui in u]) + np.testing.assert_array_almost_equal(condi_probs, expected_results, decimal=3) + + def test_get_condi_probs(self) -> None: + """ + Test the get_condi_probs function from vinecop_generate. + """ + + # Ignore possible integration warnings. + warnings.filterwarnings(action='ignore', message='The integral is probably divergent') + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + + # Test 1D numpy array input + u_array = np.array([0.2, 0.1, 0.4, 0.6]) + expected_condi_prob = 0.17637106968139507 + condi_prob_single = cvinecop.get_condi_probs(u=u_array) + self.assertAlmostEqual(expected_condi_prob, condi_prob_single, places=4) + + # Test pd.DataFrame input + u_df = pd.DataFrame([[0, 0.1, 0.4, 0.6], [0.1, 0.1, 0.4, 0.6], [0.2, 0.1, 0.4, 0.6], [0.3, 0.1, 0.4, 0.6], + [0.9, 0.1, 0.4, 0.6], [1, 0.1, 0.4, 0.6], [0, 0.1, 0.4, 1], [0.1, 1, 0.4, 1], [0, 0, 1, 1], + [1, 0, 0, 0]]) + expected_results = pd.Series([0.0001, 0.07678050591604534, 0.17637106968139507, 0.283373927184108, + 0.9155297176502054, 0.9999, 0.0001, 0.03269281901703475, 0.0001, 0.9999]) + condi_probs = cvinecop.get_condi_probs(u=u_df) + pd.testing.assert_series_equal(expected_results, condi_probs, check_dtype=False, atol=4) + + def test_get_cop_densities(self) -> None: + """ + Test the get_cop_densities function from vinecop_generate. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + + # Test 1D numpy array input + u_array = np.array([0.2, 0.1, 0.4, 0.6]) + expected_cop_density = 0.8593039707767826 + cop_density_single = cvinecop.get_cop_densities(u=u_array) + self.assertAlmostEqual(expected_cop_density, cop_density_single, places=4) + + # Test pd.DataFrame input + u_df = pd.DataFrame([[0, 0.1, 0.4, 0.6], [0.1, 0.1, 0.4, 0.6], [0.2, 0.1, 0.4, 0.6], [0.3, 0.1, 0.4, 0.6], + [0.9, 0.1, 0.4, 0.6], [1, 0.1, 0.4, 0.6], [0, 0.1, 0.4, 1], [0.1, 1, 0.4, 1], [0, 0, 1, 1], + [1, 0, 0, 0]]) + cop_densities = cvinecop.get_cop_densities(u_df) + expected_cop_densities = pd.Series([3.272297e-03, 7.724320e-01, 8.593040e-01, 9.017561e-01, 7.418892e-01, + 4.308034e-01, 2.886153e-11, 6.266201e+07, 5.009017e-06, 1.229496e+15]) + pd.testing.assert_series_equal(expected_cop_densities, cop_densities, check_dtype=False, rtol=1e-3) + + def test_get_cop_evals(self) -> None: + """ + Test the get_cop_evals function from vinecop_generate. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + + # Test 1D numpy array input + u_array = np.array([0.2, 0.1, 0.4, 0.6]) + expected_cop_eval = 0.037 + cop_eval_single = cvinecop.get_cop_evals(u=u_array) + self.assertAlmostEqual(expected_cop_eval, cop_eval_single, places=2) + + # Test pd.DataFrame input + u_df = pd.DataFrame([[0, 0.1, 0.4, 0.6], [0.1, 0.1, 0.4, 0.6], [0.2, 0.1, 0.4, 0.6], [0.3, 0.1, 0.4, 0.6], + [0.9, 0.1, 0.4, 0.6], [1, 0.1, 0.4, 0.6], [0, 0.1, 0.4, 1], [0.1, 1, 0.4, 1], [0, 0, 1, 1], + [1, 0, 0, 0]]) + cop_evals = cvinecop.get_cop_densities(u_df) + expected_cop_evals = pd.Series([3.272297e-03, 7.724320e-01, 8.593040e-01, 9.017561e-01, 7.418892e-01, + 4.308034e-01, 2.886153e-11, 6.266201e+07, 5.009017e-06, 1.229496e+15]) + pd.testing.assert_series_equal(expected_cop_evals, cop_evals, check_dtype=False, rtol=1e-3) From 3905849528dcf031e6ad42a18e41882da722f940 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Sun, 14 Mar 2021 23:09:11 +0530 Subject: [PATCH 031/103] Added implementation of parameter estimation in first paper. --- .../ou_model_jurek.py | 54 ++++++++++++++++++- 1 file changed, 53 insertions(+), 1 deletion(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index e9cfc8ed..194cfcac 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -10,6 +10,58 @@ `__ """ +import numpy as np +import pandas as pd + class StochasticControlJurek: def __init__(self): - pass + + self.ticker_A = None + self.ticker_B = None + self.spread = None + self.time_array = None + + self.delta_t = 1 / 251 #TODO : Is this value correct for this paper? + self.sigma = None + self.mu = None + self.k = None + + self.gamma = None + + def fit(self, data: pd.DataFrame): + + self.time_array = np.arange(0, len(data)) / self.delta_t + self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] + + returns_df = data.pct_change() + returns_df = returns_df.replace([np.inf, -np.inf], np.nan).ffill().dropna() + + total_return_indices = data.copy() + total_return_indices.iloc[0, :] = 1 + total_return_indices.iloc[1:, :] = pd.DataFrame.cumprod(1 + returns_df, axis=0) + + # df = data.iloc[:round(len(data) * 0.1), :].mean(axis=0) + # mispricing_percent = df[self.ticker_B] / df[self.ticker_A] + # print(mispricing_percent) + # total_return_indices[self.ticker_A] *= mispricing_percent + + #TODO : Need to figure out weights for return indices for spread calcuation + + self.spread = total_return_indices[self.ticker_A] - total_return_indices[self.ticker_B] + + self._estimate_params() + + def _estimate_params(self): + + N = len(self.spread) + + self.mu = self.spread.mean() + + self.k = (-1 / self.delta_t) * np.log(np.multiply(self.spread[1:] - self.mu, self.spread[:-1] - self.mu).sum() + / np.power(self.spread[1:] - self.mu, 2).sum()) + + sigma_calc_sum = np.power(self.spread[1:] - self.mu - np.exp(-self.k*self.delta_t)*(self.spread[:-1] - self.mu) + / np.exp(-self.k*self.delta_t), 2).sum() + #TODO : Check for error in paper for this summation? + + self.sigma = np.sqrt(2*self.k*sigma_calc_sum/((np.exp(2*self.k*self.delta_t) - 1)*(N - 2))) From 553622bf09a103fb050bda22122d3b1960012cde Mon Sep 17 00:00:00 2001 From: hansenpei Date: Sun, 14 Mar 2021 16:22:48 -0400 Subject: [PATCH 032/103] Unit test finished 1. Unittest for vine copula module is finished. 2. Monir changes for naming convention. --- .../copula_approach/vinecop_generate.py | 1 + .../copula_approach/vinecop_strategy.py | 10 +- tests/test_vinecop_generate.py | 343 +++++++++++++++++- 3 files changed, 342 insertions(+), 12 deletions(-) diff --git a/arbitragelab/copula_approach/vinecop_generate.py b/arbitragelab/copula_approach/vinecop_generate.py index a116cab3..d074d13f 100644 --- a/arbitragelab/copula_approach/vinecop_generate.py +++ b/arbitragelab/copula_approach/vinecop_generate.py @@ -7,6 +7,7 @@ Built on top of the :code:`pyvinecoplib` package. See https://github.com/vinecopulib/pyvinecopulib for more details. """ +# pylint: disable = invalid-name from typing import List, Union from itertools import permutations import numpy as np diff --git a/arbitragelab/copula_approach/vinecop_strategy.py b/arbitragelab/copula_approach/vinecop_strategy.py index b3a8c924..b6566ab0 100644 --- a/arbitragelab/copula_approach/vinecop_strategy.py +++ b/arbitragelab/copula_approach/vinecop_strategy.py @@ -9,8 +9,8 @@ from typing import List, Union, Callable, Tuple from arbitragelab.copula_approach.vinecop_generate import CVineCop -import arbitragelab.copula_approach.copula_calculation as ccalc import pandas as pd +import numpy as np class CVineCopStrat: @@ -27,7 +27,7 @@ def __init__(self, cvinecop: CVineCop = None, signal_to_position_table: pd.DataF based on current signal and the immediate past position. By default it uses the table described above. """ - self.cvine_cop = cvinecop + self.cvinecop = cvinecop self.past_obs = None # Number of past observations for Bollinger band. self.threshold_std = None # Standard deviation threshold for Bollinger band. # Signal to position table: Row indexed by previous position, column indexed by signal. @@ -63,7 +63,7 @@ def calc_mpi(self, returns: pd.DataFrame, cdfs: List[Callable], pv_target_idx: i quantiles[column_name] = returns[column_name].apply(cdfs[i]) # 2. Calculate the conditional probabilities. This step is relatively slow. - mpis = self.cvine_cop.get_condi_probs(quantiles, pv_target_idx) + mpis = self.cvinecop.get_condi_probs(quantiles, pv_target_idx) if subtract_mean: mpis = mpis.subtract(0.5) @@ -112,7 +112,7 @@ def get_positions_bollinger(self, returns: pd.DataFrame, cdfs: List[Callable], p if mpis is None: cmpis = self.calc_mpi(returns, cdfs, pv_target_idx, subtract_mean=True).cumsum() else: - cmpis = mpis.cumsum() + cmpis = mpis.subtract(0.5).cumsum() # init_mean = cmpis.iloc[:past_obs].mean() # init_std = cmpis.iloc[:past_obs].std() @@ -124,7 +124,7 @@ def get_positions_bollinger(self, returns: pd.DataFrame, cdfs: List[Callable], p 'Mean': running_avg, 'UpperBound': running_avg + self.threshold_std * running_std}) # Loop through the bollinger_band to get positions - positions = pd.Series(data=None, index=bollinger_band.index) + positions = pd.Series(data=np.nan, index=bollinger_band.index) positions.iloc[self.past_obs - 1] = init_pos for idx in range(past_obs, len(positions)): # Get current trading signal from Bollinger band diff --git a/tests/test_vinecop_generate.py b/tests/test_vinecop_generate.py index 8774fdcf..8bacbe2b 100644 --- a/tests/test_vinecop_generate.py +++ b/tests/test_vinecop_generate.py @@ -4,13 +4,16 @@ """ Unit tests for vinecop_generate, vinecop_strategy """ + +# pylint: disable = invalid-name, protected-access, consider-using-enumerate import unittest -import pandas as pd -import numpy as np import os import warnings +import pandas as pd +import numpy as np import pyvinecopulib as pv import arbitragelab.copula_approach.vinecop_generate as vg +import arbitragelab.copula_approach.vinecop_strategy as vs import arbitragelab.copula_approach.copula_calculation as ccalc @@ -36,11 +39,20 @@ def setUp(self) -> None: cvine_structure = pv.CVineStructure(order=[1, 4, 3, 2]) controls = pv.FitControlsVinecop(family_set=bicop_family) pv_cvine_cop = pv.Vinecop(structure=cvine_structure) # Construct the C-vine copula - data_np, _ = ccalc.to_quantile(returns_train) + data_np, cdfs = ccalc.to_quantile(returns_train) pv_cvine_cop.select(data=data_np, controls=controls) self.pv_cvine_cop = pv_cvine_cop + # Data stored as class attributes + self.quantiles_data_train = data_np + self.quantiles_data_test, _ = ccalc.to_quantile(returns_test) + self.returns_train = returns_train + self.returns_test = returns_test + self.cdfs = cdfs + self.target_stock_prices = sp500_prices['AAPL'] + self.index_prices = sp500_prices['SPY'] + @staticmethod def test_to_quantile(): """ @@ -91,7 +103,7 @@ def test_get_possible_cvine_structs(self) -> None: def test_get_condi_probs_priv(self) -> None: """ - Test the _get_condi_probs function from vinecop_generate. + Test the _get_condi_probs function from CVineCop. """ # Ignore possible integration warnings. @@ -110,7 +122,7 @@ def test_get_condi_probs_priv(self) -> None: def test_get_condi_probs(self) -> None: """ - Test the get_condi_probs function from vinecop_generate. + Test the get_condi_probs function from CVineCop. """ # Ignore possible integration warnings. @@ -135,7 +147,7 @@ def test_get_condi_probs(self) -> None: def test_get_cop_densities(self) -> None: """ - Test the get_cop_densities function from vinecop_generate. + Test the get_cop_densities function from CVineCop. """ cvinecop = vg.CVineCop(self.pv_cvine_cop) @@ -157,7 +169,7 @@ def test_get_cop_densities(self) -> None: def test_get_cop_evals(self) -> None: """ - Test the get_cop_evals function from vinecop_generate. + Test the get_cop_evals function from CVineCop. """ cvinecop = vg.CVineCop(self.pv_cvine_cop) @@ -176,3 +188,320 @@ def test_get_cop_evals(self) -> None: expected_cop_evals = pd.Series([3.272297e-03, 7.724320e-01, 8.593040e-01, 9.017561e-01, 7.418892e-01, 4.308034e-01, 2.886153e-11, 6.266201e+07, 5.009017e-06, 1.229496e+15]) pd.testing.assert_series_equal(expected_cop_evals, cop_evals, check_dtype=False, rtol=1e-3) + + def test_simulate(self) -> None: + """ + Test the simulate function from CVineCop. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + + # Simulate with seeds, quasi random number + samples_1 = cvinecop.simulate(n=5, qrn=True, seeds=[1], num_threads=2) + expected_samples_1 = np.array([[0.81371918, 0.71286734, 0.04834333, 0.07197967], + [0.30703092, 0.04620067, 0.23234878, 0.22256818], + [0.60524091, 0.37953401, 0.22861292, 0.77214559], + [0.48694196, 0.82397845, 0.88019649, 0.66608806], + [0.73964397, 0.15731178, 0.25048662, 0.54705984]]) + np.testing.assert_array_almost_equal(samples_1, expected_samples_1, decimal=5) + + # Simulate with seeds, no quasi random number + samples_2 = cvinecop.simulate(n=5, qrn=False, seeds=[1]) + expected_samples_2 = np.array([[0.28040356, 0.18609166, 0.18793118, 0.08634828], + [0.42191178, 0.14888814, 0.10004586, 0.46644944], + [0.41231885, 0.5561528, 0.98162344, 0.936266], + [0.10936174, 0.51577398, 0.3811335, 0.69293515], + [0.77400811, 0.5948096, 0.50113537, 0.31332545]]) + np.testing.assert_array_almost_equal(samples_2, expected_samples_2, decimal=5) + + # Simulate with no seeds, quasi random number + samples_3 = cvinecop.simulate(n=5, qrn=True) + self.assertIsInstance(samples_3, np.ndarray) + self.assertEqual(samples_3.shape, (5, 4)) + + # Simulate with no seeds, no quasi random number + samples_4 = cvinecop.simulate(n=5, qrn=False) + self.assertIsInstance(samples_4, np.ndarray) + self.assertEqual(samples_4.shape, (5, 4)) + + def test_aic_bic_loglik(self) -> None: + """ + Test the aic, bic and loglik function in CVineCop class. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + + # Calculate aic, bic, log-likelihood value on test data + aic_value = cvinecop.aic(u=self.quantiles_data_train, num_threads=2) + bic_value = cvinecop.bic(u=self.quantiles_data_train, num_threads=2) + loglik_value = cvinecop.loglik(u=self.quantiles_data_train, num_threads=2) + + calculated = np.array([aic_value, bic_value, loglik_value]) + expected = np.array([-382.98496652926514, -355.04471469950926, 198.49248326463257]) + + np.testing.assert_array_almost_equal(calculated, expected, decimal=3) + + def test_fit_auto(self) -> None: + """ + Test the fit_auto function in CVinecop class. + """ + + cvinecop = vg.CVineCop() + + # 1. With renewal + cvinecop.fit_auto(data=self.quantiles_data_train, pv_target_idx=1, if_renew=True) + # Check its aic value on the training data + aic_1 = cvinecop.aic(u=self.quantiles_data_train, num_threads=1) + expected_aic_1 = -382.98496652926514 + self.assertAlmostEqual(aic_1, expected_aic_1, places=3) + + # 2. Without renewal, fit the cvine copula using the test set. + cvinecop.fit_auto(data=self.quantiles_data_test, pv_target_idx=1, if_renew=False) + # Check its aic value on the training data. Should still get the same result. + aic_2 = cvinecop.aic(u=self.quantiles_data_train, num_threads=1) + expected_aic_2 = -382.98496652926514 + self.assertAlmostEqual(aic_2, expected_aic_2, places=3) + + def test_strat_init(self) -> None: + """ + Test the __init__ function from CVineCopStrat. + """ + + # 1. Instantiate with a given CVineCop, using default table + cvinecop = vg.CVineCop(self.pv_cvine_cop) + cvstrat = vs.CVineCopStrat(cvinecop) + self.assertIsInstance(cvstrat.cvinecop, vg.CVineCop) + default_signal_to_position_table = pd.DataFrame({1: {0: 1, 1: 1, -1: 0}, + -1: {0: -1, 1: 0, -1: -1}, + 0: {0: 0, 1: 0, -1: 0}, + 2: {0: 0, 1: 1, -1: -1}}) + pd.testing.assert_frame_equal(default_signal_to_position_table, cvstrat.signal_to_position_table, atol=1e-4) + + # 2. Instantiate with no CVineCop, using a new table + signal_to_position_table = pd.DataFrame({1: {0: 1, 1: 1, -1: 1}, + -1: {0: -1, 1: 0, -1: -1}, + 0: {0: 0, 1: 0, -1: 0}, + 2: {0: 0, 1: 1, -1: -1}}) + cvinecop = vg.CVineCop() + cvstrat = vs.CVineCopStrat(signal_to_position_table=signal_to_position_table) + self.assertIsNone(cvstrat.cvinecop) + pd.testing.assert_frame_equal(signal_to_position_table, cvstrat.signal_to_position_table, atol=1e-4) + + def test_calc_mpi(self) -> None: + """ + Test the calc_mpi method for CVineCopStrat. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + cvstrat = vs.CVineCopStrat(cvinecop) + dataset = self.returns_test.iloc[:10] # Use only 10 data points to speed up calculation. + + # 1. MPIs with no mean subtraction + mpis_1 = cvstrat.calc_mpi(returns=dataset, cdfs=self.cdfs, pv_target_idx=1, subtract_mean=False) + expected_mpis_1 = np.array([0.319452, 0.510193, 0.498257, 0.864428, 0.169004, 0.669175, 0.479996, 0.216829, + 0.338173, 0.872803]) + np.testing.assert_array_almost_equal(mpis_1.to_numpy(), expected_mpis_1) + + # 2. MPIs with mean subtraction + mpis_2 = cvstrat.calc_mpi(returns=dataset, cdfs=self.cdfs, pv_target_idx=1, subtract_mean=True) + expected_mpis_2 = np.array([0.319452, 0.510193, 0.498257, 0.864428, 0.169004, 0.669175, 0.479996, 0.216829, + 0.338173, 0.872803]) - 0.5 + np.testing.assert_array_almost_equal(mpis_2.to_numpy(), expected_mpis_2) + + # 3. MPIs with target index being 2 + mpis_3 = cvstrat.calc_mpi(returns=dataset, cdfs=self.cdfs, pv_target_idx=2, subtract_mean=False) + expected_mpis_3 = np.array([0.38365451, 0.64834723, 0.65025266, 0.89930077, 0.27221104, 0.79938626, + 0.25941534, 0.79929461, 0.65683873, 0.60624597]) + np.testing.assert_array_almost_equal(mpis_3.to_numpy(), expected_mpis_3) + + def test_signal_to_position_priv(self) -> None: + """ + Test _signal_to_position method for CVineCopStrat. + """ + + past_positions = [0, 1, -1] + signals = [0, 1, -1, 2] + + # 1. Default table. + cvinecop = vg.CVineCop(self.pv_cvine_cop) + cvstrat = vs.CVineCopStrat(cvinecop) + new_positions = [] + for past_pos in past_positions: + for signal in signals: + new_positions.append(cvstrat._signal_to_position(past_pos, signal)) + + new_positions = np.array(new_positions, dtype=int) + expected_new_positions = np.array([0, 1, -1, 0, 0, 1, 0, 1, 0, 0, -1, -1], dtype=int) + + np.testing.assert_array_equal(new_positions, expected_new_positions) + + # 2. Custom table. + signal_to_position_table = pd.DataFrame({1: {0: 1, 1: 1, -1: 1}, + -1: {0: -1, 1: 0, -1: -1}, + 0: {0: 0, 1: 0, -1: 0}, + 2: {0: 0, 1: 1, -1: -1}}) + cvinecop = vg.CVineCop(self.pv_cvine_cop) + cvstrat = vs.CVineCopStrat(cvinecop, signal_to_position_table) + new_positions_2 = [] + for past_pos in past_positions: + for signal in signals: + new_positions_2.append(cvstrat._signal_to_position(past_pos, signal)) + + new_positions_2 = np.array(new_positions_2, dtype=int) + expected_new_positions_2 = np.array([0, 1, -1, 0, 0, 1, 0, 1, 0, 1, -1, -1], dtype=int) + + np.testing.assert_array_equal(new_positions_2, expected_new_positions_2) + + def test_get_cur_signal_bollinger(self) -> None: + """ + Test the get_cur_signal_bollinger method for CVineCopStrat. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + cvstrat = vs.CVineCopStrat(cvinecop) + + # All possible past CMPI and current CMPI value. + past_cmpis = [1.2, 1.2, 1.2, 1.2, 0.6, 0.6, 0.6, 0.6, -1.2, -1.2, -1.2, -1.2, -0.6, -0.6, -0.6, -0.6] + cur_cmpis = [1.3, 0.8, -0.8, -1.2, 0.8, 1.2, -0.6, -1.2, -1.3, -0.8, 0.8, 1.2, -0.8, -1.2, 0.6, 1.2] + + # Set the Bollinger band be: lower bound=-1, running mean=0, upper_bound=1, for eaiser comparison. + signals = [] + for p in range(len(past_cmpis)): + signals.append(cvstrat.get_cur_signal_bollinger(past_cmpis[p], cur_cmpis[p], running_mean=0, + upper_threshold=1, lower_threshold=-1)) + + signals = np.array(signals, dtype=int) + expected_signals = np.array([-1, 2, 0, 0, 2, -1, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0], dtype=int) + + np.testing.assert_array_equal(signals, expected_signals) + + def test_get_positions_bollinger(self) -> None: + """ + Test the get_positions_bollonger method for CVineCopStrat. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + cvstrat = vs.CVineCopStrat(cvinecop) + + returns = self.returns_test.iloc[:50] + cdfs = self.cdfs + + # 1. No side-loaded MPIs, No returning Bollinger band data + positions_1 = cvstrat.get_positions_bollinger(returns=returns, cdfs=cdfs, init_pos=0, past_obs=20, + threshold_std=1.0, mpis=None, if_return_bollinger_band=False) + positions_1 = np.array(positions_1) + expected_positions_1 = np.array([np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, + np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 0, 0, + 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, + 0, 0, -1, -1, -1, -1]) + np.testing.assert_array_almost_equal(positions_1, expected_positions_1) + + # 2. No side-loaded MPIs, returning Bollinger band data + positions_2, bband_2 = cvstrat.get_positions_bollinger(returns=returns, cdfs=cdfs, init_pos=0, past_obs=20, + threshold_std=1.0, mpis=None, + if_return_bollinger_band=True) + positions_2 = np.array(positions_2) + expected_bband_2 = np.array( + [[np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], + [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], + [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], + [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], + [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], + [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], [np.nan, np.nan, np.nan], + [np.nan, np.nan, np.nan], [-0.99804174, -0.51242996, -0.02681818], + [-1.01389355, -0.53421688, -0.0545402], [-1.01410921, -0.53519172, -0.05627423], + [-1.01585547, -0.54073564, -0.06561581], [-1.01443563, -0.5431882, -0.07194077], + [-1.01440765, -0.53871901, -0.06303036], [-1.01355233, -0.54504716, -0.07654198], + [-1.02009377, -0.56974981, -0.11940585], [-1.02381349, -0.57755538, -0.13129726], + [-1.03164991, -0.58661169, -0.14157347], [-1.05140426, -0.62233172, -0.19325919], + [-1.07200258, -0.64781845, -0.22363432], [-1.06415267, -0.63549678, -0.20684088], + [-1.07106441, -0.64187137, -0.21267833], [-1.06701021, -0.63792586, -0.20884152], + [-1.03268445, -0.61200584, -0.19132723], [-1.00132712, -0.59859125, -0.19585537], + [-1.02406425, -0.60640481, -0.18874537], [-0.99048707, -0.59439837, -0.19830968], + [-0.98614651, -0.59228322, -0.19841993], [-0.96288318, -0.57358595, -0.18428872], + [-0.96237537, -0.57312583, -0.18387629], [-0.97926186, -0.59957237, -0.21988287], + [-0.98888191, -0.61657377, -0.24426563], [-0.97483941, -0.64025171, -0.30566401], + [-0.96810442, -0.65350625, -0.33890809], [-0.96208956, -0.67228683, -0.38248409], + [-0.96345298, -0.65933248, -0.35521197], [-0.96573728, -0.64677872, -0.32782015], + [-0.98176343, -0.60250981, -0.22325619], [-0.97292103, -0.55106804, -0.12921505]]) + + np.testing.assert_array_almost_equal(positions_2, expected_positions_1) + np.testing.assert_array_almost_equal(bband_2.to_numpy(), expected_bband_2) + + # 3. Side loading CMPIs, output Bollinger Band + mpis = cvstrat.calc_mpi(returns=returns, cdfs=self.cdfs, pv_target_idx=1, subtract_mean=False) + positions_3, bband_3 = cvstrat.get_positions_bollinger( + returns=returns, cdfs=cdfs, init_pos=0, past_obs=20, threshold_std=1.0, mpis=mpis, + if_return_bollinger_band=True) + + np.testing.assert_array_almost_equal(positions_3, expected_positions_1) + np.testing.assert_array_almost_equal(bband_3.to_numpy(), expected_bband_2) + + def test_get_cur_pos_bollinger(self) -> None: + """ + Test the get_cur_position_bollinger method in CVineCopStrat. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + cvstrat = vs.CVineCopStrat(cvinecop) + + new_position, cur_cmpi = cvstrat.get_cur_pos_bollinger( + returns_slice=self.returns_test.iloc[:21], cdfs=self.cdfs, past_pos=0, pv_target_idx=1, past_cmpi=0, + threshold_std=1.0) + + past_positions = [0, -1, 1] + past_cmpis = [-1.6, -0.6, 0.4] + new_positions = [] + cur_cmpis = [] + for past_pos in past_positions: + for past_cmpi in past_cmpis: + new_position, cur_cmpi = cvstrat.get_cur_pos_bollinger( + returns_slice=self.returns_test.iloc[:21], cdfs=self.cdfs, past_pos=past_pos, pv_target_idx=1, + past_cmpi=past_cmpi, threshold_std=1.0) + new_positions.append(new_position) + cur_cmpis.append(cur_cmpi) + + expected_new_positions = [0, 0, 0, -1, -1, -1, 1, 1, 1] + expected_cur_cmpis = [-2.2162865028946586, -1.2162865028946583, -0.21628650289465834, -2.2162865028946586, + -1.2162865028946583, -0.21628650289465834, -2.2162865028946586, -1.2162865028946583, + -0.21628650289465834] + + np.testing.assert_array_almost_equal(new_positions, expected_new_positions) + np.testing.assert_array_almost_equal(cur_cmpis, expected_cur_cmpis) + + def test_positions_to_units_against_index(self) -> None: + """ + Test the positions_to_units_against_index method in CVineCopStrat. + """ + + cvinecop = vg.CVineCop(self.pv_cvine_cop) + cvstrat = vs.CVineCopStrat(cvinecop) + target_stock_prices = self.target_stock_prices.iloc[:50] + index_prices = self.index_prices[:50] + + positions = cvstrat.get_positions_bollinger(returns=self.returns_test[:50], cdfs=self.cdfs, init_pos=0, + past_obs=10, threshold_std=1.0, mpis=None, + if_return_bollinger_band=False) + + units_df = cvstrat.positions_to_units_against_index(target_stock_prices, index_prices, positions, + multiplier=10000) + expected_units = np.array([[np.nan, np.nan], [np.nan, np.nan], [np.nan, np.nan], [np.nan, np.nan], + [np.nan, np.nan], [np.nan, np.nan], [np.nan, np.nan], [np.nan, np.nan], + [np.nan, np.nan], [0., 0.], [0., 0.], [465.89015937, -42.29402765], + [465.89015937, - 42.29402765], [465.89015937, - 42.29402765], + [465.89015937, - 42.29402765], [465.89015937, - 42.29402765], + [465.89015937, - 42.29402765], [465.89015937, - 42.29402765], + [465.89015937, - 42.29402765], [465.89015937, - 42.29402765], + [465.89015937, - 42.29402765], [0., 0.], [-441.02822241, 40.68679327], + [-441.02822241, 40.68679327], [-441.02822241, 40.68679327], + [-441.02822241, 40.68679327], [-441.02822241, 40.68679327], + [-441.02822241, 40.68679327], [-441.02822241, 40.68679327], + [0., 0.], [437.00834394, - 40.29008913], [437.00834394, - 40.29008913], + [0., 0.], [0., 0.], [0., 0.], [0., 0.], [432.63286684, - 39.80891768], + [432.63286684, - 39.80891768], [432.63286684, - 39.80891768], + [0., 0.], [0., 0.], [0., 0.], [0., 0.], [-422.59046387, 39.37627869], + [-422.59046387, 39.37627869], [-422.59046387, 39.37627869], + [-422.59046387, 39.37627869], [-422.59046387, 39.37627869], + [-422.59046387, 39.37627869], [-422.59046387, 39.37627869]]) + + np.testing.assert_array_almost_equal(units_df.to_numpy(), expected_units) From 4df014187b8743a4fc5f9eb0059202045a9f73de Mon Sep 17 00:00:00 2001 From: hansenpei Date: Sun, 14 Mar 2021 16:36:19 -0400 Subject: [PATCH 033/103] Import order fix Minor import order fix --- arbitragelab/copula_approach/vinecop_strategy.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/arbitragelab/copula_approach/vinecop_strategy.py b/arbitragelab/copula_approach/vinecop_strategy.py index b6566ab0..602a2091 100644 --- a/arbitragelab/copula_approach/vinecop_strategy.py +++ b/arbitragelab/copula_approach/vinecop_strategy.py @@ -8,9 +8,9 @@ """ from typing import List, Union, Callable, Tuple -from arbitragelab.copula_approach.vinecop_generate import CVineCop import pandas as pd import numpy as np +from arbitragelab.copula_approach.vinecop_generate import CVineCop class CVineCopStrat: From 2dade317a6367d7c6ed65b255afd97bdbe984dad Mon Sep 17 00:00:00 2001 From: hansenpei Date: Sun, 14 Mar 2021 17:08:40 -0400 Subject: [PATCH 034/103] Minor bug fix in unittest Also added auto import in __init__ --- arbitragelab/copula_approach/__init__.py | 4 +++- tests/test_vinecop_generate.py | 7 +++---- 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/arbitragelab/copula_approach/__init__.py b/arbitragelab/copula_approach/__init__.py index b01fd79c..97dc3df4 100644 --- a/arbitragelab/copula_approach/__init__.py +++ b/arbitragelab/copula_approach/__init__.py @@ -4,10 +4,12 @@ from arbitragelab.copula_approach.copula_calculation import ( find_marginal_cdf, ml_theta_hat, log_ml, sic, aic, hqic, construct_ecdf_lin, fit_nu_for_t_copula, scad_penalty, - scad_derivative, adjust_weights) + scad_derivative, adjust_weights, to_quantile) from arbitragelab.copula_approach.copula_generate import ( Copula, Gumbel, Frank, Clayton, Joe, N13, N14, Gaussian, Student, Switcher) from arbitragelab.copula_approach.copula_strategy import CopulaStrategy from arbitragelab.copula_approach.copula_strategy_basic import BasicCopulaStrategy from arbitragelab.copula_approach.copula_strategy_mpi import CopulaStrategyMPI from arbitragelab.copula_approach.copula_generate_mixedcopula import (MixedCopula, CFGMixCop, CTGMixCop) +from arbitragelab.copula_approach.vinecop_generate import (RVineCop, CVineCop) +from arbitragelab.copula_approach.vinecop_strategy import CVineCopStrat diff --git a/tests/test_vinecop_generate.py b/tests/test_vinecop_generate.py index 8bacbe2b..83f93be8 100644 --- a/tests/test_vinecop_generate.py +++ b/tests/test_vinecop_generate.py @@ -184,10 +184,9 @@ def test_get_cop_evals(self) -> None: u_df = pd.DataFrame([[0, 0.1, 0.4, 0.6], [0.1, 0.1, 0.4, 0.6], [0.2, 0.1, 0.4, 0.6], [0.3, 0.1, 0.4, 0.6], [0.9, 0.1, 0.4, 0.6], [1, 0.1, 0.4, 0.6], [0, 0.1, 0.4, 1], [0.1, 1, 0.4, 1], [0, 0, 1, 1], [1, 0, 0, 0]]) - cop_evals = cvinecop.get_cop_densities(u_df) - expected_cop_evals = pd.Series([3.272297e-03, 7.724320e-01, 8.593040e-01, 9.017561e-01, 7.418892e-01, - 4.308034e-01, 2.886153e-11, 6.266201e+07, 5.009017e-06, 1.229496e+15]) - pd.testing.assert_series_equal(expected_cop_evals, cop_evals, check_dtype=False, rtol=1e-3) + cop_evals = cvinecop.get_cop_evals(u_df) + expected_cop_evals = pd.Series([0., 0.0246, 0.0373, 0.0444, 0.0673, 0.069, 0., 0.0739, 0., 0.]) + pd.testing.assert_series_equal(expected_cop_evals, cop_evals, check_dtype=False, atol=1e-2) def test_simulate(self) -> None: """ From 599b5b524b3a71decd492c5878a9e168838c0d9a Mon Sep 17 00:00:00 2001 From: hansenpei Date: Mon, 15 Mar 2021 00:24:29 -0400 Subject: [PATCH 035/103] Finished Doc Vine Copula Intro Documentation for vine copula intro is done. Only the intro to the trading strategy is left. --- .../images/3d_vinecop_decomposition.png | Bin 0 -> 140312 bytes .../images/C_vine_D_vine_structure.png | Bin 0 -> 213244 bytes .../copula_approach/images/Cvine_tuple.png | Bin 0 -> 47188 bytes .../images/R_vine_structure.png | Bin 0 -> 179330 bytes .../images/Rvine_Cvine_Dvine.png | Bin 0 -> 73772 bytes .../copula_approach/vine_copula_intro.rst | 405 ++++++++++++++++++ docs/source/index.rst | 2 + 7 files changed, 407 insertions(+) create mode 100644 docs/source/copula_approach/images/3d_vinecop_decomposition.png create mode 100644 docs/source/copula_approach/images/C_vine_D_vine_structure.png create mode 100644 docs/source/copula_approach/images/Cvine_tuple.png create mode 100644 docs/source/copula_approach/images/R_vine_structure.png create mode 100644 docs/source/copula_approach/images/Rvine_Cvine_Dvine.png create mode 100644 docs/source/copula_approach/vine_copula_intro.rst diff --git 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z4|DUhaaAc4G?ucLD`+1fWdXd-2d9@(7SeugpuoaH`l_zR?xt?1*5uCY0-P&rPC%iT z00h|HmS!I*iaQ>aAwUofvNBHRl&bs4eF&13x7hcKuNuC2Pm;ZIs$(Yav;q%QK?j# zjKoO=m{NY011GX|RVdji8fnoG)dC{-cA$V(z++@iV-_W1u%>icxu}e_HPHxM&I-&c zlLuT=_E)UT;cWtlvwZhpt3p-YF@2Eg5sj*j+@eBBMv?1#hvf2G7j{Cnv9$>?Y&K7Y zX$B>?c7USmcVN8!fy~Q1QUw>lEO;XaW{?7hoQDWNY5Fv8VizfoSEt6JXLjM67t{gJ zeWi#5wH}=<@gy88yfF~szp*um+z-Z9AizX2g2kB#ihuNi0%rXzFcol0Sd8N0_6%Cx zW$8&gKx`yoQzKf3eL2#k$w1Jh#0zn&TkaN&>q+mcpp&f+wIyFL4&MYt3oaC;_yxfa zuFle1pkpRUXIu;K7KZMY-ck}EhCRz5Tz+-CY+kqoZ6Lkg{>pz`kwILz1~7YEpGYKH jFbgnikQIg0mDAVVeo+g`__ +* `Joe, H. and Kurowicka, D. eds., 2011. Dependence modeling: vine copula handbook. World Scientific. `__ +* `Yu, R., Yang, R., Zhang, C., Špoljar, M., Kuczyńska-Kippen, N. and Sang, G., 2020. A Vine Copula-Based Modeling for Identification of Multivariate Water Pollution Risk in an Interconnected River System Network. Water, 12(10), p.2741. `__ +* `Dissmann, J., Brechmann, E.C., Czado, C. and Kurowicka, D., 2013. Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59, pp.52-69. `__ \ No newline at end of file diff --git a/docs/source/index.rst b/docs/source/index.rst index 6051154f..4818a21c 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -105,6 +105,8 @@ This project is licensed under an all rights reserved licence. copula_approach/copula_deeper_intro copula_approach/basic_trading_strategy copula_approach/mispricing_index_strategy + copula_approach/vine_copula_intro + copula_approach/cvine_copula_strategy copula_approach/utility_functions .. toctree:: From a2f83272481b97159eec1ade690e6984830de67c Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 15 Mar 2021 16:07:09 +0530 Subject: [PATCH 036/103] Added draft implementation of optimal portfolio weights for utility of terminal wealth. --- .../ou_model_jurek.py | 115 ++++++++++++++++++ .../ou_model_mudchanatongsuk.py | 36 +++--- 2 files changed, 135 insertions(+), 16 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 194cfcac..98fd0651 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -16,18 +16,23 @@ class StochasticControlJurek: def __init__(self): + #Training Data. self.ticker_A = None self.ticker_B = None self.spread = None self.time_array = None self.delta_t = 1 / 251 #TODO : Is this value correct for this paper? + # Estimated params from training data. self.sigma = None self.mu = None self.k = None + # Params inputted by user. + self.r = None self.gamma = None + def fit(self, data: pd.DataFrame): self.time_array = np.arange(0, len(data)) / self.delta_t @@ -51,6 +56,7 @@ def fit(self, data: pd.DataFrame): self._estimate_params() + def _estimate_params(self): N = len(self.spread) @@ -65,3 +71,112 @@ def _estimate_params(self): #TODO : Check for error in paper for this summation? self.sigma = np.sqrt(2*self.k*sigma_calc_sum/((np.exp(2*self.k*self.delta_t) - 1)*(N - 2))) + + + def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type = 1, r = 0.05, gamma = 1): + """ + utility_type = 1 implies agent with utility of terminal wealth. + utility_type = 2 implies agent whose utility is defined over intermediate consumption. + """ + + self.r = r + self.gamma = gamma + t = np.arange(0, len(data)) / self.delta_t + tau = t[:-1] - t + + W = np.zeros(len(t)) #TODO : Need to figure out how to calculate W + S = np.zeros(len(t)) #TODO : Calculate this spread after the spread calc in fit is finalized. + + A = None + B = None + if self.gamma != 1: + # For the case of gamma = 1, A & B are not used in the final optimal portfolio calculation, + # so the corresponding calculations are skipped. + if utility_type == 1: + A, B = self._AB_calc_1(tau) + + elif utility_type == 2: + A, B = self._AB_calc_2(tau) + + N = None + if self.gamma == 1: + N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2)) * W + + else: + N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2) + (2 * A * S + B) / self.gamma) * W + + return N + + + def _AB_calc_1(self, tau): + + c_1 = 2 * self.sigma ** 2 / self.gamma + c_2 = -(self.k / self.gamma + self.r * (1 - self.gamma) / self.gamma) + c_3 = 0.5 * ((1 - self.gamma) / self.gamma) * (((self.k + self.r) / self.sigma) ** 2) + det = 4 * (self.k ** 2 - self.r ** 2 * (1 - self.gamma)) / self.gamma + gamma_0 = 1 - (self.k / self.r) ** 2 + + A = self._A_calc_1(tau, c_1, c_2, c_3, det, gamma_0) + B = self._B_calc_1(tau, c_1, c_2, c_3, det, gamma_0) + return A, B + + + def _A_calc_1(self, tau, c_1, c_2, c_3, det, gamma_0): + + A = None + if 0 < self.gamma < gamma_0: + A = -c_2 / c_1 + (np.sqrt(-det) / (2 * c_1)) * np.tan(np.sqrt(-det) * tau / 2 + np.arctan(2 * c_2 / np.sqrt(-det))) + + elif self.gamma == gamma_0: + A = -(c_2 / c_1) * (1 + 1 / (c_2 * tau - 1)) + + elif gamma_0 < self.gamma < 1: + # coth = 1/tanh and arccoth(x) = arctanh(1/x) + # For reference : https://www.efunda.com/math/hyperbolic/hyperbolic.cfm + + A = -c_2 / c_1 + (np.sqrt(det) / (2 * c_1)) * (1 / np.tanh(-np.sqrt(det) * tau / 2 + np.arctanh(np.sqrt(det) / (2 * c_2)))) + + elif self.gamma > 1: + A = -c_2 / c_1 + (np.sqrt(det) / (2 * c_1)) * np.tanh(-np.sqrt(det) * tau / 2 + np.arctanh(2 * c_2 / np.sqrt(det))) + + return A + + + def _B_calc_1(self, tau, c_1, c_2, c_3, det, gamma_0): + + c_4 = 2 * self.k * self.mu / self.gamma + c_5 = -((self.k + self.r) / self.sigma ** 2) * ((1 - self.gamma) / self.gamma) * self.k * self.mu + + B = None + if 0 < self.gamma < gamma_0: + phi_1 = np.sqrt(-det) * (np.cos(np.sqrt(-det) * tau / 2) - 1) + 2 * c_2 * np.sin(np.sqrt(-det) * tau / 2) + phi_2 = np.arctanh(np.tan(0.25 * (np.sqrt(-det) * tau - 2 * np.arctan(2 * c_2 / np.sqrt(-det))))) + \ + np.arctanh(np.tan(0.5 * np.arctan(2 * c_2 / np.sqrt(-det)))) + + B = c_4 * phi_1 / (c_1 * np.sqrt(-det)) + (4 * phi_2 / np.sqrt(-det)) * (c_5 - c_4 / c_1) * \ + np.cos(np.sqrt(-det) * tau / 2 - np.arctan(c_2 / np.sqrt(-det))) + + elif self.gamma == gamma_0: + B = (c_1 * c_5 * (c_2 * tau - 2) - (c_2 ** 2) * c_4) * tau / (2 * c_1 * (c_2 * tau - 1)) + + elif self.gamma > gamma_0: + B = (4 * (c_2 * c_5 - c_3 * c_4 + (c_3 * c_4 - c_2 * c_5) * np.cosh(np.sqrt(det) * tau / 2)) + + 2 * c_5 * np.sqrt(det) * np.sinh(np.sqrt(det) * tau / 2)) \ + / (det * np.cosh(np.sqrt(det) * tau / 2) - 2 * c_2 * np.sqrt(det) * np.sinh(np.sqrt(det) * tau / 2)) + + return B + + + def _AB_calc_2(self, tau): + + A = self._A_calc_2(tau) + B = self._B_calc_2(tau) + return A, B + + + def _A_calc_2(self, tau): + pass + + + def _B_calc_2(self, tau): + pass diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 9e4891dc..ddfd821f 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -58,10 +58,10 @@ def _estimate_params(self): (N * np.multiply(self.spread[1:], self.spread[:-1]).sum() - (self.spread[N] - self.spread[0]) * np.sum(self.spread[:-1]) - self.spread[:-1].sum() ** 2) - q = (self.spread[N] - self.spread[0] + (1 - p)*self.spread[:-1].sum()) / N + q = (self.spread[N] - self.spread[0] + (1 - p) * self.spread[:-1].sum()) / N - V_squared = (1 / N) * (self.spread[N] ** 2 - self.spread[0] ** 2 + (1 + p ** 2)*np.power(self.spread[:-1], 2).sum() - - 2 * p * np.multiply(self.spread[1:], self.spread[:-1]).sum() - N*q) + V_squared = (1 / N) * (self.spread[N] ** 2 - self.spread[0] ** 2 + (1 + p ** 2) * np.power(self.spread[:-1], 2).sum() + - 2 * p * np.multiply(self.spread[1:], self.spread[:-1]).sum() - N * q) C = (1/(N * np.sqrt(V_squared * S_squared))) * (np.multiply(self.spread[1:], np.diff(self.S)).sum() @@ -69,13 +69,13 @@ def _estimate_params(self): - m * (self.spread[N] - self.spread[0]) - m * (1 - p) * self.spread[:-1].sum()) - self.sigma = np.sqrt(S_squared/self.delta_t) + self.sigma = np.sqrt(S_squared / self.delta_t) - self.mu = (m/self.delta_t) + (0.5 * (self.sigma ** 2)) + self.mu = (m / self.delta_t) + (0.5 * (self.sigma ** 2)) - self.k = - np.log(p)/self.delta_t + self.k = - np.log(p) / self.delta_t - self.theta = q/(1 - p) + self.theta = q / (1 - p) self.eta = np.sqrt(2 * self.k * V_squared / (1 - p ** 2)) @@ -85,29 +85,33 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): self.gamma = gamma t = np.arange(0, len(data)) / self.delta_t + tau = t[:-1] - t x = np.log(data.iloc[:, 0]) - np.log(data.iloc[:, 1]) - alpha_t = self._alpha_calc(t) - beta_t = self._beta_calc(t) + alpha_t, beta_t = self._alpha_beta_calc(tau) h = None return h - def _alpha_calc(self, t): + def _alpha_beta_calc(self, tau): sqrt_gamma = np.sqrt(1 - self.gamma) - exp_calc = np.exp(2*self.k*(t[-1] - t)/sqrt_gamma) + exp_calc = np.exp(2 * self.k * tau / sqrt_gamma) + + alpha_t = self._alpha_calc(sqrt_gamma, exp_calc) + beta_t = self._beta_calc(sqrt_gamma, exp_calc) + + return alpha_t, beta_t + + def _alpha_calc(self, sqrt_gamma, exp_calc): left_calc = self.k * (1 - sqrt_gamma) / (2 * (self.eta ** 2)) - right_calc = 2 * sqrt_gamma / (1 - sqrt_gamma - (1 + sqrt_gamma)*exp_calc) + right_calc = 2 * sqrt_gamma / (1 - sqrt_gamma - (1 + sqrt_gamma) * exp_calc) return left_calc * (1 + right_calc) - def _beta_calc(self, t): - - sqrt_gamma = np.sqrt(1 - self.gamma) - exp_calc = np.exp(2*self.k*(t[-1] - t)/sqrt_gamma) + def _beta_calc(self, sqrt_gamma, exp_calc): left_calc = 1/(2 * (self.eta ** 2) * ((1 - sqrt_gamma) - (1 + sqrt_gamma)*exp_calc)) From ed9f3983409456b4edaf96b65a27edc4b41b9511 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 15 Mar 2021 16:55:08 +0530 Subject: [PATCH 037/103] Added comments and made small changes to code structure. --- .../ou_model_jurek.py | 52 ++++++++++++++----- 1 file changed, 40 insertions(+), 12 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 98fd0651..922d892d 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -76,7 +76,13 @@ def _estimate_params(self): def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type = 1, r = 0.05, gamma = 1): """ utility_type = 1 implies agent with utility of terminal wealth. - utility_type = 2 implies agent whose utility is defined over intermediate consumption. + gamma = 1 implies log utility investor. + gamma != 1 implies general CRRA investor. + + utility_type = 2 implies agent whose utility is defined over intermediate consumption + with agent’s preferences described by Epstein-Zin recursive utility with phi = 1. + gamma = 1 reduces to standard log utility. + gamma ! = 1 """ self.r = r @@ -87,28 +93,35 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type = 1, r = 0. W = np.zeros(len(t)) #TODO : Need to figure out how to calculate W S = np.zeros(len(t)) #TODO : Calculate this spread after the spread calc in fit is finalized. - A = None - B = None - if self.gamma != 1: + N = None + # The optimal weights equation is the same for both types of utility functions. + # For gamma = 1, the outputs weights are identical for both types of utility functions, + # whereas for gamma != 1, the calculation of A and B functions are different. + if self.gamma == 1: + N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2)) * W + + else: # For the case of gamma = 1, A & B are not used in the final optimal portfolio calculation, # so the corresponding calculations are skipped. + + A = None + B = None if utility_type == 1: A, B = self._AB_calc_1(tau) elif utility_type == 2: A, B = self._AB_calc_2(tau) - N = None - if self.gamma == 1: - N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2)) * W - - else: N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2) + (2 * A * S + B) / self.gamma) * W return N def _AB_calc_1(self, tau): + """ + For utility_type = 1. + Follows Appendix A.2 in the paper. + """ c_1 = 2 * self.sigma ** 2 / self.gamma c_2 = -(self.k / self.gamma + self.r * (1 - self.gamma) / self.gamma) @@ -144,6 +157,8 @@ def _A_calc_1(self, tau, c_1, c_2, c_3, det, gamma_0): def _B_calc_1(self, tau, c_1, c_2, c_3, det, gamma_0): + #Note : When self.mu = 0, c_4 and c_5 become zero and consequently B becomes zero. + c_4 = 2 * self.k * self.mu / self.gamma c_5 = -((self.k + self.r) / self.sigma ** 2) * ((1 - self.gamma) / self.gamma) * self.k * self.mu @@ -168,14 +183,27 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, det, gamma_0): def _AB_calc_2(self, tau): + """ + For utility_type = 2. + Follows appendix B.1 in the paper. + """ + + c_1 = 2 * self.sigma ** 2 / self.gamma + #TODO : Figure out how to calculate beta and subsequently c_2, c_3, etc. + c_2 = 0 + c_3 = 0 + det = 0 + gamma_0 = 0 - A = self._A_calc_2(tau) + A = self._A_calc_2(tau, c_1, c_2, c_3, det, gamma_0) B = self._B_calc_2(tau) return A, B - def _A_calc_2(self, tau): - pass + def _A_calc_2(self, tau, c_1, c_2, c_3, det, gamma_0): + + # Same calculation as for general CRRA Investor. + return self._A_calc_1(tau, c_1, c_2, c_3, det, gamma_0) def _B_calc_2(self, tau): From 1c22de2da2e8f2fbc3759878c829293498d0d300 Mon Sep 17 00:00:00 2001 From: hansenpei Date: Mon, 15 Mar 2021 17:33:18 -0400 Subject: [PATCH 038/103] Vine cop trading strategy doc 1. Finished documentation of vine copula trading strategy. 2. Minor changes in function doc strings. --- .../copula_approach/vinecop_strategy.py | 9 +- .../copula_approach/cvine_copula_strategy.rst | 348 ++++++++++++++++++ .../images/Bollinger_band_example.png | Bin 0 -> 394336 bytes .../images/CMPI_vs_log_prices.png | Bin 0 -> 286157 bytes .../images/Equity_curve_cvinecop.png | Bin 0 -> 314913 bytes .../images/workflow_getdata.png | Bin 0 -> 70773 bytes .../images/workflow_select_structure.png | Bin 0 -> 113469 bytes .../images/workflow_vinecop_density.png | Bin 0 -> 92976 bytes .../copula_approach/vine_copula_intro.rst | 32 +- 9 files changed, 372 insertions(+), 17 deletions(-) create mode 100644 docs/source/copula_approach/cvine_copula_strategy.rst create mode 100644 docs/source/copula_approach/images/Bollinger_band_example.png create mode 100644 docs/source/copula_approach/images/CMPI_vs_log_prices.png create mode 100644 docs/source/copula_approach/images/Equity_curve_cvinecop.png create mode 100644 docs/source/copula_approach/images/workflow_getdata.png create mode 100644 docs/source/copula_approach/images/workflow_select_structure.png create mode 100644 docs/source/copula_approach/images/workflow_vinecop_density.png diff --git a/arbitragelab/copula_approach/vinecop_strategy.py b/arbitragelab/copula_approach/vinecop_strategy.py index 602a2091..dda58fb1 100644 --- a/arbitragelab/copula_approach/vinecop_strategy.py +++ b/arbitragelab/copula_approach/vinecop_strategy.py @@ -2,9 +2,10 @@ # All rights reserved # Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html """ -Module that generates vine copulas. +Module that houses vine copula trading strategies. -Built on top of the :code:`pyvinecoplib` package. See https://github.com/vinecopulib/pyvinecopulib for more details. +Method based on `Stübinger, J., Mangold, B. and Krauss, C., 2018. Statistical arbitrage with vine copulas. +`__ """ from typing import List, Union, Callable, Tuple @@ -15,7 +16,7 @@ class CVineCopStrat: """ - Trading strategy class using vine copulas. + Trading strategy class using C-vine copulas. """ def __init__(self, cvinecop: CVineCop = None, signal_to_position_table: pd.DataFrame = None): @@ -246,7 +247,7 @@ def positions_to_units_against_index(target_stock_prices: pd.Series, index_price The translation is conducted under a dollar-neutral strategy against an index fund (typically SP500 index). For example, for a long position, for each 1 dollar investment, long the target stock by 1/2 dollar, and short the - index fund by 1 dollar. + index fund by 1/2 dollar. Originally the positions calculated by this strategy is given with values in {0, 1, -1}. To be able to actually trade using the dollar neutral strategy as given by the authors in the paper, one needs to know at any given diff --git a/docs/source/copula_approach/cvine_copula_strategy.rst b/docs/source/copula_approach/cvine_copula_strategy.rst new file mode 100644 index 00000000..44591181 --- /dev/null +++ b/docs/source/copula_approach/cvine_copula_strategy.rst @@ -0,0 +1,348 @@ +.. _cvine_copula_strategy: + + +.. note:: + This document is an implementation of: + + Stübinger, J., Mangold, B. and Krauss, C. `Statistical arbitrage with vine copulas. `__ + Quantitative Finance, 2018. + +====================== +C-vine Copula Strategy +====================== + +With the power of vine copula, we are able to model the relation among several random variables. Speficifally +we aim to trade based on the information generated from the vine copula model. +Similar to traditional bivariate approaches, we use the conditional (cumulative) probability to gauge whether +the target stock is underpriced or overpriced against other stocks, and generate trading signal based on them +from a mean-reversion bet. + +We aim to cover the following topics: + + 1. Idea and typical workflow of the C-vine copula approach + 2. Strategy details + 3. Comments for this approach + +Overview of the C-vine Stategy +############################## + +At first, vine copula is a very flexible model for dealing with multi-variate dependencies. It decomposes +joint probability density into bivariate copula densities and marginal densities in a tree structure. +R-vine is the most generic structure that is shared by all vine copulas, and in application people use C-vine +and D-vine more often as special cases of a generic R-vine. + +.. Note:: + + With :math:`N` random variables, there are :math:`N(N − 1)(N − 2)! 2^{(N − 2)(N − 3)/2}/2` many possible + structures for R-vines. Therefore numerically fitting an R-vine structure directly from data becomes a + burden, and even if such a method exists and can be calculated in a reasonable time, it is likely subject to + overfit using financial market data. + In contrast, for a C-vine there are "only" :math:`N!` possible structures, and it has much better interpretability. + +Since C-vine has the star-like structure at each level of the tree, it is ideal for modeling dependencies where one +specific random variable is key. +Hence, although we are squeezing statistical arbitrage from an :math:`N` stocks cohort, we are using the "*1-vs-the rest*" +type of framework. +The D-vine or more general R-vine strategy handling mispricings all together, that dynamically trades every stock +based on the mispricing info, to the best of our knowlegde, is not yet developed, at least not available in literature. + +We have the workflow as follows: + + 1. Get data + 2. Figure out the C-vine structure + 3. Calculate probability density + 4. Calculate the conditional probability + 5. Generate signals and trade + +We will dive into the details for each part of the workflow. + +C-vine Copula Strategy Workflow +############################### + +For ease of demontration, assuming we are trading 4 stocks. + +Step 1: Get data +**************** + +We work with stocks' **daily returns data** exclusively. + +.. Note:: + + Selecting trading candidates is a serious topic, and can largely determine if a strategy is profitable or + not. There are 4 methods proposed in [Stübinger et al. 2018]: + pairwise Spearman's rho, multi-dimensional Spearman's rho, + sum of distance in quantile plots to hyper-diagonal, and a copula-chi-square test for dependence. + Loosely speaking, the goal is to find stocks cohorts that are heavily dependent, such that a mean-reversion bet + on relative mispricings is profitable. + For more details in implementation, please refer to [Vijay's document]. + + +Suppose we have chosen a few cohorts and in each cohort it has a key stock element. We then need to turn the translate +the stocks' returns data into its quantiles (pseudo-observations) using empirical CDFs (ECDFs). +We denote the pseudo-observations as :math:`u_i`'s, and they are all uniform in :math:`[0, 1]`. + +.. figure:: images/workflow_getdata.png + :scale: 40 % + :align: center + + (Fig 1: Generate pseudo-observations or quantiles and marginal ECDFs from returns data.) + + +Step 2: Figure out the C-vine Structure +*************************************** + +To start with, there are :math:`4! = 24` many possible C-vine structures. Without loss of generality assuming the stock 1 +is our target stock. In the end, we aim to come up with this conditional density that indicates relative mispricing for +stock 1 against 3 other stocks in this cohort: + +.. math:: + + h(u_1 | u_2, u_3, u_4) + = \mathbb{P}(U_1 \le u_1 | U_2=u_2, U_3=u_3, U_4=u_4) + +If :math:`h(u_1 | u_2, u_3, u_4) < 0.5` then that day's return for stock 1 is considered lower than the mean of what the +history tells and vice versa, similar to the "traditional" copula approaches with Mispricing Index. + +In [Stübinger et al. 2018], the authors claimed that in order to calculate :math:`h(u_1 | u_2, u_3, u_4)`, stock 1 must never be +at the center of every level of the tree. +Remember that C-vine can be fully characterized by an ordered tuple :math:`(c_4, c_3, c_2, c_1)` where :math:`c_1` is the +center for the level-1 tree, :math:`c_2` for level-2 and so on. +Therefore, to make stock 1 never at the center (except at the tree root), it is equivalent to check each possibility generated by +:math:`(1, c_3, c_2, c_1)`, where :math:`(c_3, c_2, c_1)` is a permutation of :math:`\{2, 3, 4\}`. Obviously there are :math:`3! = 6` many ways available. + +.. Note:: + + Disclaimer: I do not fully agree with the authors' argument here, because **all** vine copula allows one to calculate + the joint probability density :math:`f(u_1, u_2, u_3, u_4)`, for any given quantities :math:`(u_1, u_2, u_3, u_4)` in + order to calculate :math:`h` for any target stock, simply integrate along that marginal variable and then normalize by a + full integration in that direction. For example: + + .. math:: + + h(u_1 | u_2, u_3, u_4) + = \left( \int_0^{u_1} f(u, u_2, u_3, u_4) du \right) / \left( \int_0^{1} f(u, u_2, u_3, u_4) du \right) + + Moreover, I think if we treat stock 1 as the key stock, it should be **at the center of every level of the tree**, because + it makes intuitive sense to model all other stocks' and their bivariate copula densities relation given the stock 1's information. + Stock 1 is the object of interest, and therefore should be the governing quantity here. + I.e., 1 should be put at the end of the tuple, not at the beginning, and there are still 6 many possible structures for + 4 stocks. + + Currently we provide only the implementation in [Stübinger et al. 2018]. In the future we will provide the alternative method + that puts the target stock at the center. + +After chosen the 6 possible vine structures, we then fit everyone of them and calculate the associated AIC value. We choose +the final C-vine structure among candidates with the lowest AIC value. +It is equivalent in this case to directly comparing the log-likelihood and choose the one that constitutes the largest +log-likelihood value. +The exact fitting includes figuring out what type of (parametric) bivariate copula to use for every node, and the parameter(s) +value that fits best the data. + +.. figure:: images/workflow_select_structure.png + :scale: 60 % + :align: center + + (Fig 2: Determine the C-vine structure by AIC or maximum likelihood. Picture from [Stübinger et al. 2018].) + +Step 3: Probability Density +*************************** + +We aim to calculate :math:`f(u_1, u_2, u_3, u_4)`. +This is straightforward once we fit the C-vine to training data. Now we are working on the trading priod data. At first +we should map them into quantiles using the ECDFs trained in the training period. Then we can calculate directly the probability +density for pseudo-observations, say :math:`(u_1, u_2, u_3, u_4)`, by calculating every node at every level of the tree. +Note that each node constitues a probability density, either marginal density (top of the tree) or the copula density (not +top of the tree). And the final probability density is their product. + +.. figure:: images/workflow_vinecop_density.png + :scale: 50 % + :align: center + + (Fig 3: Determine the joint density :math:`f(u_1, u_2, u_3, u_4)` from the vine copula. Here the notation + :math:`f(x_1, x_2, x_3, x_4)` is okay since we start from the beginning only using quantiles data, so :math:`u_i = x_i`.) + +Step 4: Conditional Probability +******************************* + +We aim to calculate :math:`h(u_1| u_2, u_3, u_4)`, given that stock 1 is the target stock. Similarly we can compute for +other stocks if they are the target. +Here we use numerical integration for this value: + +.. math:: + + \begin{align} + h(u_1 | u_2, u_3, u_4) + &= \mathbb{P}(U_1 \le u_1 | U_2=u_2, U_3=u_3, U_4=u_4) \\ + &= \left( \int_0^{u_1} f(u, u_2, u_3, u_4) du \right) / \left( \int_0^{1} f(u, u_2, u_3, u_4) du \right) + \end{align} + +Keep in mind that this value is model dependent: it depends on which vine structure we are using, and the types of bivariate +copulas and their parameters in each node. Some people denote the conditional probability as :math:`h_C` to indicate that it +depends on a copula. + +.. Note:: + + Here we computed :math:`h` from the "bottom up" by marginal integration. The authors suggested computing from "top down" + by taking partial differentiations from the copula definition :math:`C(u_1, u_2, u_3, u_4)` (cumulative density): + + .. math:: + + h(u_1 | u_2, u_3, u_4) := \frac{\partial^3 C(u_1, u_2, u_3, u_4)}{\partial u_1 \partial u_2 \partial u_3} + + I do not agree with the author's approach for the following reason: + Mathematically speaking it is the same. However vine copula only allows one to compute the joint density :math:`f`, and + unlike "traditional" copula models where :math:`C` is defined by definition. For vine copula :math:`C` is found by + Monte-Carlo integrations from :math:`f`. + Also even if :math:`C` can be found analytically, taking 3 numerical partial + differentiations will likely yield more issues compared to numerically integrating just along 1 marginal variable. + + +Step 5: Generate Signals and Trade +********************************** + +For simplificaition say we have 2 cohorts after the stocks selection, each cohort has a target stock. +And we have fitted 2 C-vine copulas respectively for the 2 cohorts with their own target stock. +Without loss of generality, let us fix stock 1 for each cohort as its target stock. +For conditional probability :math:`h`: + + 1. If :math:`h > 0.5`, stock 1's return that day is higher than the historical average compared to other 3 stocks + in the cohort. + 2. If :math:`h < 0.5`, stock 1's return that day is higher than the historical average compared to other 3 stocks + in the cohort. + +Therefore, we adopt the cumulative mispricing index framework. For each cohort we calculate the **de-meaned** cumulative sum +of :math:`h` as :math:`CMPI`, and formulate the trading signal using a Bollinger band: +Denote the running average of :math:`CMPI` in the fixed-length, moving time window as :math:`\hat{\mu}(t)`, the running +standard deviation in the time window as :math:`\hat{\sigma}(t)`, and some positive constant :math:`k` to control the +Bollinger band's width. + + 1. Short signal: When :math:`CMPI > \hat{\mu}(t) + k \hat{\sigma}(t)`. + 2. Long signal: When :math:`CMPI < \hat{\mu}(t) - k \hat{\sigma}(t)`. + 3. Exit signal: When :math:`CMPI` crosses with :math:`\hat{\mu}(t)`. + 4. Do nothing: Else. + +.. figure:: images/Bollinger_band_example.png + :scale: 25 % + :align: center + + (Fig 4: Positions of the target stock and the associated Bollinger Band.) + +Now we total net positions for each key stock in each cohort. Then we formulate our dollar-neutral strategy by trading +against a cheap broad-based market index such as SPY, similar to the method used in [Avellaneda and Lee, 2010]. + +.. Note:: + + It is totally possible that different cohorts can share the same key stock. The cohort and key stock information + is generated from the stocks cohort selection methods. + +It is no surprise that :math:`CMPI` looks reasonably similar to cumulative log-returns of the target stock. This can be +used as a sanity check on whether our vine copula model is off. + +.. figure:: images/CMPI_vs_log_prices.png + :scale: 40 % + :align: center + + (Fig 5: CMPI and cumulative log returns of the target stock. Their shape looks very similar.) + +Comments +######## + +Vine copula provides a very flexible approach in modeling multi-variate dependencies. The C-vine structure specifically +highlights a dominant component at every level of the tree, ideal for our "1-vs-the rest" trading strategy for capturing +statistical arbitrage among multiple stocks, which non-quant strategies often omit or are still primative. + +As promising as it looks, just like any other methods it inevitably bears the some drawbacks: + + 1. High start-up cost: to understand this method, the user needs to understand copula modeling from scratch, and + also how to interprete vine copula models from end to end. + + 2. High computation cost: For a cohort of 4 stocks and 3 years of daily training data + 1 year of test data, it takes about + 30 seconds to fit and generate positions. This can hardly be optimized further since the fitting algorithm is already + written in an optimized C++ library. And the compuation time should scale up in :math:`O(N!)`. This is just for fitting and + generating positions without factoring into the time for stocks selection. + + 3. Interpretability: Since the exact fitting algorithms are quite complicated, the interpretability may suffer in + back tracking possible fitting issues and how to evaluate each fits. Also the high dimension makes it difficult + to produce an intuitive plot just to visually check if the model is correct, unlike bivariate copulas. + +.. figure:: images/Equity_curve_cvinecop.png + :scale: 32 % + :align: center + + (Fig 6: Equity curve for just 1 cohort with 4 stocks.) + +Implementation +############## + +.. automodule:: arbitragelab.copula_approach.vinecop_strategy + + .. autoclass:: CVineCopStrat + :members: __init__, calc_mpi, get_positions_bollinger, get_cur_signal_bollinger, get_cur_pos_bollinger, positions_to_units_against_index + +Example +******* + +.. code-block:: + + # Importing the module and other libraries + from arbitragelab.copula_approach.vinecop_generate import CVineCop + from arbitragelab.copula_approach.vinecop_strategy import CVineCopStrat + from arbitragelab.copula_approach.copula_calculation import to_quantile + import pandas as pd + import numpy as np + + # Loading stocks data. Use 1 cohort for example: suppose stocks 'AAPL', 'MSFT', 'AMZN', 'FB' + # form the cohort, and 'AAPL' is the target stock. + sp500_returns = pd.read_csv('all_sp500_returns.csv', index_col='Dates', parse_dates=True) + returns_train = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']][:800] + returns_test = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']][800:1100] + + prices_aapl_spy = pd.read_csv('all_sp500_prices.csv', + index_col='Dates', parse_dates=True)[['AAPL', 'SPY']][800:1100] + + rts_train_quantiles, cdfs = to_quantile(returns_train) + rts_test_quantiles, _ = to_quantile(returns_train) + + # Instantiate a CVineCop (C-vine copula) class to fit + cvinecop = CVineCop + + # Fit C-vine automatically, 'AAPL' is the target stock + # Note that pv_target_idx is indexed from 1 + vinecop_structure = cvinecop.fit_auto(data=rts_train_quantiles, pv_target_idx=1, if_renew=True) + # Print the vine copula structure as a sanity check. You can directly fit internally by just using + # cvinecop.fit_auto(data=rts_train_quantiles, pv_target_idx=1, if_renew=True) if you do not want to + # print structures. + print(vinecop_structure) + + # Instantiate a CVineCopStrat (trading) class from the fitted C-vine copula + cvstrat = CVineCopStrat(cvinecop) + + # Generate positions over the test data, return the Bollinger band for sanity check + # Note that the cdfs should be from the training set. + positions, bband = cvstrat.get_positions_bollinger(returns=returns_test, cdfs=cdfs, + if_return_bollinger_band=True) + positions = positions.shift(1) # Avoid look-back bias + + # Formulate units from the positions against the SPY index, with 100,000 dollar investment + units = cvstrat.positions_to_units_against_index(target_stock_prices=prices_aapl_spy['AAPL'], + index_prices=prices_aapl_spy['SPY'], + positions=positions, + multiplier=100000) + +Research Notebooks +################## + +The following research notebook can be used to better understand the basic copula strategy. + +* `Basic Copula Strategy`_ + +.. _`Basic Copula Strategy`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Copula%20Approach/Copula_Strategy_Basic.ipynb + +References +########## + +* `Stübinger, J., Mangold, B. and Krauss, C., 2018. Statistical arbitrage with vine copulas. Quantitative Finance, 18(11), pp.1831-1849. `__ +* `Joe, H. and Kurowicka, D. eds., 2011. Dependence modeling: vine copula handbook. World Scientific. `__ +* `Yu, R., Yang, R., Zhang, C., Špoljar, M., Kuczyńska-Kippen, N. and Sang, G., 2020. A Vine Copula-Based Modeling for Identification of Multivariate Water Pollution Risk in an Interconnected River System Network. Water, 12(10), p.2741. `__ +* `Dissmann, J., Brechmann, E.C., Czado, C. and Kurowicka, D., 2013. Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59, pp.52-69. `__ +* `Avellaneda, M. and Lee, J.H., 2010. Statistical arbitrage in the US equities market. 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Note:: - We only implemented C-vine structure, since it is the only vine structure that has curated trading strategies to the best - of our knowledge. For general R-vine, though one can still calculate cumulative densities and generate signals, how + We only implemented the C-vine structure, since it is the only vine structure that has curated trading strategies to the best + of our knowledge. For general R-vine, though one can still calculate conditional probabilities and generate signals, how the R-vine structure is determined becomes less interpretable. But this documentation is written as a general introduction that is not limited to C-vine, in the hope that the reader can achieve a more thorough picture on vine copula modeling. @@ -16,7 +16,7 @@ Copula is a great statistical tool to study the relation among multiple random v cumulative density of quantiles of marginals, we can bypass the idiosyncratic features of marginal distributions and directly look at how they are "related". Indeed, traders and analysts have been using copula to exploit statistical arbitrage under the pairs trading framework -for some time, and we have implemented the most popular methods in :code:`ArbitrageLab`. +for some time, and we have implemented some of the most popular methods in :code:`ArbitrageLab`. However, it is natural to expand beyond dealing with just a pair of stocks: There already exist a great amount of competing stat arb methods alongside with copula, thinning the potential alpha. It is also intuitive for human to think about relative pricing among 2 stocks, where as for higher dimensions it is not so easy, and left great chances for quantitative approaches. @@ -170,13 +170,13 @@ They can be visualized as follows: For an R-vine, for each level of the tree, it needs to satisfy the following conditions: - 1. Each layer of the tree must have :math:`N-1` edges for :math:`N` nodes, and all the nodes in this later must be + 1. Each layer of the tree must have :math:`N-1` edges for :math:`N` nodes, and all the nodes in this layer must be connected (i.e., you can travel from any node to any other node via edges in finite steps). 2. Proximity condition: Every edge will contribute to a joint density in the next layer. For example in Fig 1, at layer 1, node 1 and node 3 makes a (1,3) node in layer 2. -For a C-vine, it must be an R-vine at first, but every layer of the tree there is a center component. This structure +For a C-vine, it must be an R-vine at first, but for every layer of the tree there is a center component. This structure makes it possible to represend the C-vine structure using an ordered tuple: reading backwards, each number represents the centered component at each level of the tree. @@ -186,10 +186,11 @@ For a D-vine, each tree is a *path*: there is one road that goes through all the :scale: 28 % :align: center - (Fig 3: C-vine its tuple representation.) + (Fig 3: C-vine and its tuple representation.) The representation of a generic R-vine is slightly more complicated, and requires a lower triangular matrix (some places uses an upper triangular matrix for representation, and they are indeed identical). +Let's look at the following R-vine with 7 random variables for example: .. figure:: images/R_vine_structure.png :scale: 50 % @@ -213,18 +214,20 @@ The R-vine tree in Fig 4 can be represented by the following matrix: 6 & 3 & 3 & 2 & 2 & 2 & 2 \end{bmatrix} -The R-vine structure is read from the matrix as follows: +The R-vine structure is mapped to the matrix as follows: 1. Find a diagonal term :math:`a`. For example :math:`M_{2, 2} = 4`. 2. Follow that column downwards and stop somewhere :math:`b`, say we stop at :math:`M_{4, 5} = 1`. - 3. The leftover terms in that column are then conditions :math:`\{c_1, c_2, \cdots\}`. In this example + 3. The leftover terms below :math:`b` in that column are then conditions :math:`\{c_1, c_2, \cdots\}`. In this example we have :math:`\{2, 3\}` left. 4. The node :math:`(a, b | c_1, c_2, \cdots)` is in the R-vine. In this example, :math:`(1, 4 | 2, 3)` is at :math:`(T_4)`. +Working from the top of the tree you can also map the matrix back to a full R-vine. (Left as an exercise to +the reader.) Sometimes in literature you will see the same structure represented by the triangular matrix below: .. math:: @@ -295,7 +298,7 @@ This quantity needs to be calculated numerically by integrating the target varia .. math:: \begin{align} - h(u_1 | u_2, u_3) + h(u_1 | u_2, u_3, u_4) &= \mathbb{P}(U_1 \le u_1 | U_2=u_2, U_3=u_3, U_4=u_4) \\ &= \left( \int_0^{u_1} f(u, u_2, u_3, u_4) du \right) / \left( \int_0^{1} f(u, u_2, u_3, u_4) du \right) \end{align} @@ -320,12 +323,15 @@ Those are very interesting topics but are beyond our scope here. Interested read details. This is an active research field and involves a lot of heavy lifting. Luckily, a lot of great algorithms are already nicely blackboxed, handled automatically by softwares. Specifically, sample generation is a pretty much solved problem, whereas determine the best R-vine structure given data and determing all copula types and parameters are still discussed, but some algorithms are available. -Thus, samping is very fast, and fitting can be slow. +Thus, sampling is very fast, and fitting can be slow. .. Note:: - When working with copula models, whether it is a "traditional" copula model or vine copula, we always fit the + 1. When working with copula models, whether it is a "traditional" copula model or vine copula, we always fit the pseudo-observations, i.e., quanties data, instead of the real data. + + 2. For fitting a vine copula, we need to determine the best tree structure that reflects the data, along with specifying + the type of bivariate copulas and their parameters. The amount of calculation is huge. For data specific evaluations, we can always calculate the log-likelihood, and consequently AIC, BIC, and compare those results. @@ -358,7 +364,7 @@ Example # Loading stocks data sp500_returns = pd.read_csv('all_sp500_returns.csv', index_col='Dates', parse_dates=True) - subsample_returns = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'GOOGL']] + subsample_returns = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']] subsample_rts_quantiles, _ = to_quantile(subsample_returns) quantiles_example = pd.DataFrame([0.1, 0.2, 0.3, 0.8], [0.5, 0.1, 0.9, 0.2]) @@ -399,7 +405,7 @@ The following research notebook can be used to better understand the vine copula References ########## -* `Stübinger, J., Mangold, B. and Krauss, C., 2018. Statistical arbitrage with vine copulas. Quantitative Finance, 18(11), pp.1831-1849.. `__ +* `Stübinger, J., Mangold, B. and Krauss, C., 2018. Statistical arbitrage with vine copulas. Quantitative Finance, 18(11), pp.1831-1849. `__ * `Joe, H. and Kurowicka, D. eds., 2011. Dependence modeling: vine copula handbook. World Scientific. `__ * `Yu, R., Yang, R., Zhang, C., Špoljar, M., Kuczyńska-Kippen, N. and Sang, G., 2020. A Vine Copula-Based Modeling for Identification of Multivariate Water Pollution Risk in an Interconnected River System Network. Water, 12(10), p.2741. `__ * `Dissmann, J., Brechmann, E.C., Czado, C. and Kurowicka, D., 2013. Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59, pp.52-69. `__ \ No newline at end of file From 06a5b33731d70a801d526606245da2d38bc3b75e Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 16 Mar 2021 14:19:02 +0530 Subject: [PATCH 039/103] Added Partial implementation of Appendix B.1.2 in Jurek (2007). Added spacing and changed variable names. --- .../ou_model_jurek.py | 119 +++++++++++++----- 1 file changed, 85 insertions(+), 34 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 922d892d..5b36612e 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -31,6 +31,7 @@ def __init__(self): # Params inputted by user. self.r = None self.gamma = None + self.beta = None def fit(self, data: pd.DataFrame): @@ -66,27 +67,37 @@ def _estimate_params(self): self.k = (-1 / self.delta_t) * np.log(np.multiply(self.spread[1:] - self.mu, self.spread[:-1] - self.mu).sum() / np.power(self.spread[1:] - self.mu, 2).sum()) - sigma_calc_sum = np.power(self.spread[1:] - self.mu - np.exp(-self.k*self.delta_t)*(self.spread[:-1] - self.mu) - / np.exp(-self.k*self.delta_t), 2).sum() + sigma_calc_sum = np.power(self.spread[1:] - self.mu - np.exp(-self.k * self.delta_t) * (self.spread[:-1] - self.mu) + / np.exp(-self.k * self.delta_t), 2).sum() #TODO : Check for error in paper for this summation? - self.sigma = np.sqrt(2*self.k*sigma_calc_sum/((np.exp(2*self.k*self.delta_t) - 1)*(N - 2))) + self.sigma = np.sqrt(2 * self.k * sigma_calc_sum / ((np.exp(2 * self.k * self.delta_t) - 1) * (N - 2))) - def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type = 1, r = 0.05, gamma = 1): + def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, r = 0.05, gamma = 1): """ utility_type = 1 implies agent with utility of terminal wealth. gamma = 1 implies log utility investor. gamma != 1 implies general CRRA investor. utility_type = 2 implies agent whose utility is defined over intermediate consumption - with agent’s preferences described by Epstein-Zin recursive utility with phi = 1. + with agent’s preferences described by Epstein-Zin recursive utility with phi(elasticity of intertemporal substitution) = 1. gamma = 1 reduces to standard log utility. - gamma ! = 1 + gamma ! = 1, gamma > 1 implies more risk averse investors, whereas gamma < 1 implies more risk tolerance. + + What is beta? + 1)subjective rate of time preference. + + 2)beta signifies the constant fraction of total wealth an investor chooses to consume. This is analogous to a hedge fund investor + who cares both about terminal wealth in some risk-averse way and consumes a constant fraction, β, + of assets under management (the management fee). + + For utility_type = 2, C(Consumption) = beta * W """ self.r = r self.gamma = gamma + self.beta = beta t = np.arange(0, len(data)) / self.delta_t tau = t[:-1] - t @@ -124,21 +135,31 @@ def _AB_calc_1(self, tau): """ c_1 = 2 * self.sigma ** 2 / self.gamma + c_2 = -(self.k / self.gamma + self.r * (1 - self.gamma) / self.gamma) + c_3 = 0.5 * ((1 - self.gamma) / self.gamma) * (((self.k + self.r) / self.sigma) ** 2) - det = 4 * (self.k ** 2 - self.r ** 2 * (1 - self.gamma)) / self.gamma + + disc = 4 * (self.k ** 2 - self.r ** 2 * (1 - self.gamma)) / self.gamma + #Note : discriminant is always positive for gamma > 1. + gamma_0 = 1 - (self.k / self.r) ** 2 + #Note : gamma_0 is not always > 0. + + + A = self._A_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) + B = self._B_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) - A = self._A_calc_1(tau, c_1, c_2, c_3, det, gamma_0) - B = self._B_calc_1(tau, c_1, c_2, c_3, det, gamma_0) return A, B - def _A_calc_1(self, tau, c_1, c_2, c_3, det, gamma_0): + def _A_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): + + #Note : A<=0 and decreasing in tau for gamma > 1, and vice versa for gamma < 1. A = None if 0 < self.gamma < gamma_0: - A = -c_2 / c_1 + (np.sqrt(-det) / (2 * c_1)) * np.tan(np.sqrt(-det) * tau / 2 + np.arctan(2 * c_2 / np.sqrt(-det))) + A = -c_2 / c_1 + (np.sqrt(-disc) / (2 * c_1)) * np.tan(np.sqrt(-disc) * tau / 2 + np.arctan(2 * c_2 / np.sqrt(-disc))) elif self.gamma == gamma_0: A = -(c_2 / c_1) * (1 + 1 / (c_2 * tau - 1)) @@ -147,37 +168,39 @@ def _A_calc_1(self, tau, c_1, c_2, c_3, det, gamma_0): # coth = 1/tanh and arccoth(x) = arctanh(1/x) # For reference : https://www.efunda.com/math/hyperbolic/hyperbolic.cfm - A = -c_2 / c_1 + (np.sqrt(det) / (2 * c_1)) * (1 / np.tanh(-np.sqrt(det) * tau / 2 + np.arctanh(np.sqrt(det) / (2 * c_2)))) + A = -c_2 / c_1 + (np.sqrt(disc) / (2 * c_1)) * (1 / np.tanh(-np.sqrt(disc) * tau / 2 + np.arctanh(np.sqrt(disc) / (2 * c_2)))) elif self.gamma > 1: - A = -c_2 / c_1 + (np.sqrt(det) / (2 * c_1)) * np.tanh(-np.sqrt(det) * tau / 2 + np.arctanh(2 * c_2 / np.sqrt(det))) + A = -c_2 / c_1 + (np.sqrt(disc) / (2 * c_1)) * np.tanh(-np.sqrt(disc) * tau / 2 + np.arctanh(2 * c_2 / np.sqrt(disc))) return A - def _B_calc_1(self, tau, c_1, c_2, c_3, det, gamma_0): + def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): #Note : When self.mu = 0, c_4 and c_5 become zero and consequently B becomes zero. c_4 = 2 * self.k * self.mu / self.gamma + c_5 = -((self.k + self.r) / self.sigma ** 2) * ((1 - self.gamma) / self.gamma) * self.k * self.mu B = None if 0 < self.gamma < gamma_0: - phi_1 = np.sqrt(-det) * (np.cos(np.sqrt(-det) * tau / 2) - 1) + 2 * c_2 * np.sin(np.sqrt(-det) * tau / 2) - phi_2 = np.arctanh(np.tan(0.25 * (np.sqrt(-det) * tau - 2 * np.arctan(2 * c_2 / np.sqrt(-det))))) + \ - np.arctanh(np.tan(0.5 * np.arctan(2 * c_2 / np.sqrt(-det)))) + phi_1 = np.sqrt(-disc) * (np.cos(np.sqrt(-disc) * tau / 2) - 1) + 2 * c_2 * np.sin(np.sqrt(-disc) * tau / 2) + + phi_2 = np.arctanh(np.tan(0.25 * (np.sqrt(-disc) * tau - 2 * np.arctan(2 * c_2 / np.sqrt(-disc))))) + \ + np.arctanh(np.tan(0.5 * np.arctan(2 * c_2 / np.sqrt(-disc)))) - B = c_4 * phi_1 / (c_1 * np.sqrt(-det)) + (4 * phi_2 / np.sqrt(-det)) * (c_5 - c_4 / c_1) * \ - np.cos(np.sqrt(-det) * tau / 2 - np.arctan(c_2 / np.sqrt(-det))) + B = c_4 * phi_1 / (c_1 * np.sqrt(-disc)) + (4 * phi_2 / np.sqrt(-disc)) * (c_5 - c_4 / c_1) * \ + np.cos(np.sqrt(-disc) * tau / 2 - np.arctan(c_2 / np.sqrt(-disc))) elif self.gamma == gamma_0: B = (c_1 * c_5 * (c_2 * tau - 2) - (c_2 ** 2) * c_4) * tau / (2 * c_1 * (c_2 * tau - 1)) elif self.gamma > gamma_0: - B = (4 * (c_2 * c_5 - c_3 * c_4 + (c_3 * c_4 - c_2 * c_5) * np.cosh(np.sqrt(det) * tau / 2)) - + 2 * c_5 * np.sqrt(det) * np.sinh(np.sqrt(det) * tau / 2)) \ - / (det * np.cosh(np.sqrt(det) * tau / 2) - 2 * c_2 * np.sqrt(det) * np.sinh(np.sqrt(det) * tau / 2)) + B = (4 * (c_2 * c_5 - c_3 * c_4 + (c_3 * c_4 - c_2 * c_5) * np.cosh(np.sqrt(disc) * tau / 2)) + + 2 * c_5 * np.sqrt(disc) * np.sinh(np.sqrt(disc) * tau / 2)) \ + / (disc * np.cosh(np.sqrt(disc) * tau / 2) - 2 * c_2 * np.sqrt(disc) * np.sinh(np.sqrt(disc) * tau / 2)) return B @@ -189,22 +212,50 @@ def _AB_calc_2(self, tau): """ c_1 = 2 * self.sigma ** 2 / self.gamma - #TODO : Figure out how to calculate beta and subsequently c_2, c_3, etc. - c_2 = 0 - c_3 = 0 - det = 0 - gamma_0 = 0 - - A = self._A_calc_2(tau, c_1, c_2, c_3, det, gamma_0) - B = self._B_calc_2(tau) + + c_2 = (self.gamma * (2 * self.r - self.beta) - 2 * (self.k + self.r)) / (2 * self.gamma) + + c_3 = ((self.k + self.r) ** 2) * (1 - self.gamma) / (2 * self.gamma * (self.sigma ** 2)) + + disc = ((2 * self.k + self.beta) ** 2 + (self.gamma - 1) * ((-2 * self.r + self.beta) ** 2)) / self.gamma + + gamma_0 = 4 * (self.k + self.r) * (self.r - self.beta - self.k) / ((2 * self.r - self.beta) ** 2) + + + A = self._A_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) + B = self._B_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) + return A, B - def _A_calc_2(self, tau, c_1, c_2, c_3, det, gamma_0): + def _A_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): # Same calculation as for general CRRA Investor. - return self._A_calc_1(tau, c_1, c_2, c_3, det, gamma_0) + return self._A_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) + + + def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): + + # Note : When self.mu = 0, c_4 and c_6 become zero and consequently B becomes zero. + + c_4 = 2 * self.k * self.mu / self.gamma + + c_5 = -(self.k + self.r * (1 - self.gamma) + self.beta * self.gamma) / (2 * self.gamma) + + c_6 = self.k * (self.k + self.r) * (self.gamma - 1) * self.mu / (self.gamma * self.sigma ** 2) + + B = None + if 0 < self.gamma < gamma_0: + pass - def _B_calc_2(self, tau): - pass + elif self.gamma == gamma_0: + pass + + elif gamma_0 < self.gamma < 1: + pass + + elif self.gamma > 1: + pass + + return B From cbe02a7e3a528b0be39e01fba716ef88392a311e Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 16 Mar 2021 11:39:14 +0100 Subject: [PATCH 040/103] Minor code adjustment for Partner Selection Module --- arbitragelab/copula_approach/vine_copula_partner_selection.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index 6789c9a2..eebc9e38 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -218,7 +218,7 @@ def geometric(self, n_targets: int = 5) -> list: and this measure is just the sum of Euclidean distance for all data points to the y=x line (diagonal). For every target stock the quadruple with the lowest diagonal measure is returned. - :param n_targets: (int) number of target stocks to select. + :param n_targets: (int) Number of target stocks to select. :return: (list) List of all selected quadruples. """ From b42d7daf306e225136649dc672bf0d54acbf302f Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 16 Mar 2021 16:54:33 +0530 Subject: [PATCH 041/103] Added additional implementation of Appendix B.1.2 in Jurek (2007). --- .../ou_model_jurek.py | 57 ++++++++++++++++++- 1 file changed, 55 insertions(+), 2 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 5b36612e..226a9f32 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -76,6 +76,9 @@ def _estimate_params(self): def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, r = 0.05, gamma = 1): """ + + Implementation of Theorem 1 and Theorem 2 in Jurek (2007). + utility_type = 1 implies agent with utility of terminal wealth. gamma = 1 implies log utility investor. gamma != 1 implies general CRRA investor. @@ -247,15 +250,65 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): B = None if 0 < self.gamma < gamma_0: + # TODO : Finish this. pass elif self.gamma == gamma_0: + # TODO : Finish this. pass elif gamma_0 < self.gamma < 1: - pass + + rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) + rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) + rep_phrase_3 = np.arctanh(rep_phrase_2 / c_2) - tau * rep_phrase_2 + # arccoth(x) = arctanh(1/x) + rep_phrase_4 = np.exp(tau * c_2) + rep_phrase_5 = np.exp(tau * c_5) + + denominator = c_2 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) + + term_1 = rep_phrase_4 * rep_phrase_1 * c_6 * c_2 ** 2 + + term_2 = rep_phrase_4 * c_3 * rep_phrase_1 * c_4 + + term_3 = 2 * rep_phrase_5 * (1 / np.sinh(rep_phrase_3)) - rep_phrase_2 * (1 / np.tanh(rep_phrase_3)) * rep_phrase_1 + # csch = 1/sinh, coth = 1/tanh + + term_4 = rep_phrase_4 * rep_phrase_1 * c_5 + + term_5 = (1 / np.sinh(rep_phrase_3)) * (c_3 * c_4 * (rep_phrase_5 * rep_phrase_2 - rep_phrase_4 * np.sinh(tau * rep_phrase_2) * c_5) + + rep_phrase_5 * rep_phrase_2 * c_5 * c_6) + # csch = 1/sinh + + + B = np.exp(-tau * c_2) * (term_1 - (term_2 + (rep_phrase_2 * term_3 + term_4) * c_6) * c_2 + + term_5) / denominator elif self.gamma > 1: - pass + + rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1 + rep_phrase_2 = 0.5 * np.sqrt(disc) * tau - np.arctanh(2 * c_2 / np.sqrt(disc)) # Repeated Phrase 2 + + denominator = 2 * c_1 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator + + term_1 = 2 * np.exp(tau * c_2) * rep_phrase_1 * c_4 * c_5 * (c_2 + 0.5 * np.sqrt(disc) * np.tanh(rep_phrase_2)) + + term_2 = 2 * np.exp(tau * c_2) * rep_phrase_1 - 2 * np.exp(tau * c_5) * (1 / np.cosh(rep_phrase_2)) + # sech = 1 / cosh + + term_3 = np.exp(tau * c_5) * (1 / np.cosh(rep_phrase_2)) - 2 * np.exp(tau * c_2) * rep_phrase_1 + + term_4 = np.exp(tau * c_2) * np.sqrt(disc) * rep_phrase_1 * np.tanh(rep_phrase_2) + + term_5 = 2 * np.exp(tau * c_2) * rep_phrase_1 - np.exp(tau * c_5) * (1 / np.cosh(rep_phrase_2)) + + + B = np.exp(-tau * c_2) * (term_1 + + c_1 * ( c_6 * (c_2 * term_2 + + term_3 * c_5 + - term_4) + - c_3 * term_5 * c_4)) / denominator + return B From 507bd2f147d9589bc663441f652cea2a3ff35550 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 16 Mar 2021 21:17:14 +0530 Subject: [PATCH 042/103] Completed implementation of Theorem 1 and 2 in Jurek (2007). --- .../ou_model_jurek.py | 75 ++++++++++++++----- .../ou_model_mudchanatongsuk.py | 5 +- 2 files changed, 59 insertions(+), 21 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 226a9f32..f8307375 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -51,7 +51,8 @@ def fit(self, data: pd.DataFrame): # print(mispricing_percent) # total_return_indices[self.ticker_A] *= mispricing_percent - #TODO : Need to figure out weights for return indices for spread calcuation + #TODO : Need to figure out weights for return indices for spread calcuation. + # Use Engle cointergration in arbitragelab to calculate weights. self.spread = total_return_indices[self.ticker_A] - total_return_indices[self.ticker_B] @@ -69,7 +70,6 @@ def _estimate_params(self): sigma_calc_sum = np.power(self.spread[1:] - self.mu - np.exp(-self.k * self.delta_t) * (self.spread[:-1] - self.mu) / np.exp(-self.k * self.delta_t), 2).sum() - #TODO : Check for error in paper for this summation? self.sigma = np.sqrt(2 * self.k * sigma_calc_sum / ((np.exp(2 * self.k * self.delta_t) - 1) * (N - 2))) @@ -84,7 +84,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, gamma != 1 implies general CRRA investor. utility_type = 2 implies agent whose utility is defined over intermediate consumption - with agent’s preferences described by Epstein-Zin recursive utility with phi(elasticity of intertemporal substitution) = 1. + with agent’s preferences described by Epstein-Zin recursive utility with psi(elasticity of intertemporal substitution) = 1. gamma = 1 reduces to standard log utility. gamma ! = 1, gamma > 1 implies more risk averse investors, whereas gamma < 1 implies more risk tolerance. @@ -249,13 +249,50 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): B = None + rep_exp_1 = np.exp(tau * c_2) + rep_exp_2 = np.exp(tau * c_5) + if 0 < self.gamma < gamma_0: - # TODO : Finish this. - pass + + rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) + rep_phrase_2 = np.sqrt(c_1 * c_3) / rep_phrase_1 + rep_phrase_3 = rep_phrase_1 * tau + np.arctan(c_2 / rep_phrase_1) + + denominator = c_1 * rep_phrase_2 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) + + term_1 = rep_exp_1 * rep_phrase_2 * c_4 * c_5 * (c_2 - rep_phrase_1 * np.tan(rep_phrase_3)) + + term_2 = rep_exp_1 * rep_phrase_2 - 2 * rep_exp_2 * (1 / np.cos(rep_phrase_3)) + + term_3 = rep_exp_2 * (1 / np.cos(rep_phrase_3)) - rep_exp_1 * rep_phrase_2 + + term_4 = rep_exp_1 * rep_phrase_2 * rep_phrase_1 * np.tan(rep_phrase_3) + + term_5 = -term_3 + + + B = np.exp(-tau * c_2) * (term_1 + + c_1 * (c_6 * (c_2 * term_2 + + term_3 * c_5 + + term_4) + -c_3 * term_5 * c_4)) / denominator + elif self.gamma == gamma_0: - # TODO : Finish this. - pass + + denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 + + term_1 = rep_exp_1 * tau * c_4 * c_2 ** 3 + + term_2 = (c_4 * (rep_exp_1 * (tau * c_5 + 1) - rep_exp_2) + rep_exp_1 * tau * c_1 * c_6) * c_2 ** 2 + + term_3 = c_1 * (rep_exp_1 * tau * c_5 + 2 * (rep_exp_1 - rep_exp_2)) * c_6 * c_2 + + term_4 = (rep_exp_1 - rep_exp_2) * c_1 * c_5 * c_6 + + + B = (-term_1 + term_2 - term_3 + + term_4) / denominator elif gamma_0 < self.gamma < 1: @@ -263,22 +300,20 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) rep_phrase_3 = np.arctanh(rep_phrase_2 / c_2) - tau * rep_phrase_2 # arccoth(x) = arctanh(1/x) - rep_phrase_4 = np.exp(tau * c_2) - rep_phrase_5 = np.exp(tau * c_5) denominator = c_2 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) - term_1 = rep_phrase_4 * rep_phrase_1 * c_6 * c_2 ** 2 + term_1 = rep_exp_1 * rep_phrase_1 * c_6 * c_2 ** 2 - term_2 = rep_phrase_4 * c_3 * rep_phrase_1 * c_4 + term_2 = rep_exp_1 * c_3 * rep_phrase_1 * c_4 - term_3 = 2 * rep_phrase_5 * (1 / np.sinh(rep_phrase_3)) - rep_phrase_2 * (1 / np.tanh(rep_phrase_3)) * rep_phrase_1 + term_3 = 2 * rep_exp_2 * (1 / np.sinh(rep_phrase_3)) - rep_phrase_2 * (1 / np.tanh(rep_phrase_3)) * rep_phrase_1 # csch = 1/sinh, coth = 1/tanh - term_4 = rep_phrase_4 * rep_phrase_1 * c_5 + term_4 = rep_exp_1 * rep_phrase_1 * c_5 - term_5 = (1 / np.sinh(rep_phrase_3)) * (c_3 * c_4 * (rep_phrase_5 * rep_phrase_2 - rep_phrase_4 * np.sinh(tau * rep_phrase_2) * c_5) - + rep_phrase_5 * rep_phrase_2 * c_5 * c_6) + term_5 = (1 / np.sinh(rep_phrase_3)) * (c_3 * c_4 * (rep_exp_2 * rep_phrase_2 - rep_exp_1 * np.sinh(tau * rep_phrase_2) * c_5) + + rep_exp_2 * rep_phrase_2 * c_5 * c_6) # csch = 1/sinh @@ -292,16 +327,16 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): denominator = 2 * c_1 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator - term_1 = 2 * np.exp(tau * c_2) * rep_phrase_1 * c_4 * c_5 * (c_2 + 0.5 * np.sqrt(disc) * np.tanh(rep_phrase_2)) + term_1 = 2 * rep_exp_1 * rep_phrase_1 * c_4 * c_5 * (c_2 + 0.5 * np.sqrt(disc) * np.tanh(rep_phrase_2)) - term_2 = 2 * np.exp(tau * c_2) * rep_phrase_1 - 2 * np.exp(tau * c_5) * (1 / np.cosh(rep_phrase_2)) + term_2 = 2 * rep_exp_1 * rep_phrase_1 - 2 * rep_exp_2 * (1 / np.cosh(rep_phrase_2)) # sech = 1 / cosh - term_3 = np.exp(tau * c_5) * (1 / np.cosh(rep_phrase_2)) - 2 * np.exp(tau * c_2) * rep_phrase_1 + term_3 = rep_exp_2 * (1 / np.cosh(rep_phrase_2)) - 2 * rep_exp_1 * rep_phrase_1 - term_4 = np.exp(tau * c_2) * np.sqrt(disc) * rep_phrase_1 * np.tanh(rep_phrase_2) + term_4 = rep_exp_1 * np.sqrt(disc) * rep_phrase_1 * np.tanh(rep_phrase_2) - term_5 = 2 * np.exp(tau * c_2) * rep_phrase_1 - np.exp(tau * c_5) * (1 / np.cosh(rep_phrase_2)) + term_5 = -term_3 B = np.exp(-tau * c_2) * (term_1 diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index ddfd821f..dd467fe6 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -90,7 +90,10 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): alpha_t, beta_t = self._alpha_beta_calc(tau) - h = None + h = (1 / (1 - self.gamma)) * (beta_t + 2 * np.multiply(x, alpha_t) + - self.k * (x - self.theta) / self.eta ** 2 + + self.rho * self.theta / self.eta + 0.5) + return h def _alpha_beta_calc(self, tau): From 630e5ca638c54c085f03a5259424b490278a8416 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 17 Mar 2021 00:26:46 +0530 Subject: [PATCH 043/103] Added spread calculation to Jurek Class. --- .../ou_model_jurek.py | 51 +++++++++++++------ .../ou_model_mudchanatongsuk.py | 2 +- 2 files changed, 36 insertions(+), 17 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index f8307375..d134dc54 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -12,6 +12,10 @@ import numpy as np import pandas as pd +import matplotlib.pyplot as plt + +from arbitragelab.cointegration_approach.johansen import JohansenPortfolio +from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio class StochasticControlJurek: def __init__(self): @@ -33,30 +37,43 @@ def __init__(self): self.gamma = None self.beta = None + def _calc_total_return_indices(self, data): + returns_df = data.pct_change() + returns_df = returns_df.replace([np.inf, -np.inf], np.nan).ffill().dropna() + + total_return_indices = data.copy() + total_return_indices.iloc[0, :] = 1 + total_return_indices.iloc[1:, :] = pd.DataFrame.cumprod(1 + returns_df, axis=0) + + return total_return_indices + + def fit(self, data: pd.DataFrame): self.time_array = np.arange(0, len(data)) / self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] - returns_df = data.pct_change() - returns_df = returns_df.replace([np.inf, -np.inf], np.nan).ffill().dropna() + total_return_indices = self._calc_total_return_indices(data) - total_return_indices = data.copy() - total_return_indices.iloc[0, :] = 1 - total_return_indices.iloc[1:, :] = pd.DataFrame.cumprod(1 + returns_df, axis=0) + eg_portfolio = EngleGrangerPortfolio() + eg_portfolio.fit(total_return_indices, add_constant=True) + eg_adf_statistics = eg_portfolio.adf_statistics + eg_cointegration_vectors = eg_portfolio.cointegration_vectors - # df = data.iloc[:round(len(data) * 0.1), :].mean(axis=0) - # mispricing_percent = df[self.ticker_B] / df[self.ticker_A] - # print(mispricing_percent) - # total_return_indices[self.ticker_A] *= mispricing_percent + if eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc['95%', 0]: + raise Exception("ADF statistic test failure.") - #TODO : Need to figure out weights for return indices for spread calcuation. - # Use Engle cointergration in arbitragelab to calculate weights. + self.eg_scaled_vectors = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() - self.spread = total_return_indices[self.ticker_A] - total_return_indices[self.ticker_B] + self.spread = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) + self.spread.plot() + plt.show() self._estimate_params() + print(self.k) + # TODO : Test the null hypothesis of no mean reversion using estimated k by running a Monte Carlo bootstrap experiment. + # For details look at para 3 in Section IV A of the paper. def _estimate_params(self): @@ -102,10 +119,12 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, self.gamma = gamma self.beta = beta t = np.arange(0, len(data)) / self.delta_t - tau = t[:-1] - t + tau = t[-1] - t + + total_return_indices = self._calc_total_return_indices(data) - W = np.zeros(len(t)) #TODO : Need to figure out how to calculate W - S = np.zeros(len(t)) #TODO : Calculate this spread after the spread calc in fit is finalized. + W = np.ones(len(t)) # Wealth is normalized to one. #TODO : Is this the correct way? + S = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) #TODO : Do we use trained linear weights here ? N = None # The optimal weights equation is the same for both types of utility functions. @@ -128,7 +147,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2) + (2 * A * S + B) / self.gamma) * W - return N + return N / W # We return the optimal allocation of spread asset scaled by wealth. def _AB_calc_1(self, tau): diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index dd467fe6..9e5ebd5d 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -85,7 +85,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): self.gamma = gamma t = np.arange(0, len(data)) / self.delta_t - tau = t[:-1] - t + tau = t[-1] - t x = np.log(data.iloc[:, 0]) - np.log(data.iloc[:, 1]) alpha_t, beta_t = self._alpha_beta_calc(tau) From 594c1d88608cd93d0215d7a268c1c848e150b712 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 17 Mar 2021 03:47:05 +0530 Subject: [PATCH 044/103] Minor fixes to code. --- .../stochastic_control_approach/ou_model_jurek.py | 10 +++++++--- .../ou_model_mudchanatongsuk.py | 4 ++-- 2 files changed, 9 insertions(+), 5 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index d134dc54..1607d88e 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -51,7 +51,7 @@ def _calc_total_return_indices(self, data): def fit(self, data: pd.DataFrame): - self.time_array = np.arange(0, len(data)) / self.delta_t + self.time_array = np.arange(0, len(data)) * self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] total_return_indices = self._calc_total_return_indices(data) @@ -62,6 +62,7 @@ def fit(self, data: pd.DataFrame): eg_cointegration_vectors = eg_portfolio.cointegration_vectors if eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc['95%', 0]: + print(eg_adf_statistics) raise Exception("ADF statistic test failure.") self.eg_scaled_vectors = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() @@ -72,6 +73,9 @@ def fit(self, data: pd.DataFrame): self._estimate_params() print(self.k) + print(self.sigma) + print(self.mu) + # TODO : Test the null hypothesis of no mean reversion using estimated k by running a Monte Carlo bootstrap experiment. # For details look at para 3 in Section IV A of the paper. @@ -85,7 +89,7 @@ def _estimate_params(self): self.k = (-1 / self.delta_t) * np.log(np.multiply(self.spread[1:] - self.mu, self.spread[:-1] - self.mu).sum() / np.power(self.spread[1:] - self.mu, 2).sum()) - sigma_calc_sum = np.power(self.spread[1:] - self.mu - np.exp(-self.k * self.delta_t) * (self.spread[:-1] - self.mu) + sigma_calc_sum = np.power((self.spread[1:] - self.mu - np.exp(-self.k * self.delta_t) * (self.spread[:-1] - self.mu)) / np.exp(-self.k * self.delta_t), 2).sum() self.sigma = np.sqrt(2 * self.k * sigma_calc_sum / ((np.exp(2 * self.k * self.delta_t) - 1) * (N - 2))) @@ -118,7 +122,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, self.r = r self.gamma = gamma self.beta = beta - t = np.arange(0, len(data)) / self.delta_t + t = np.arange(0, len(data)) * self.delta_t tau = t[-1] - t total_return_indices = self._calc_total_return_indices(data) diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 9e5ebd5d..2a909a8a 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -38,7 +38,7 @@ def fit(self, data: pd.DataFrame): #data = data.ffill() #TODO : Might need to normalize input, estimate params is not running properly. - self.time_array = np.arange(0, len(data)) / self.delta_t + self.time_array = np.arange(0, len(data)) * self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] self.S = np.log(data.loc[:, self.ticker_B]) self.spread = np.log(data.loc[:, self.ticker_A]) - self.S @@ -84,7 +84,7 @@ def _estimate_params(self): def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): self.gamma = gamma - t = np.arange(0, len(data)) / self.delta_t + t = np.arange(0, len(data)) * self.delta_t tau = t[-1] - t x = np.log(data.iloc[:, 0]) - np.log(data.iloc[:, 1]) From bee7ca55557f6955b5e85c9be76fe30c2c7eda9b Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 17 Mar 2021 17:39:39 +0530 Subject: [PATCH 045/103] Added draft implementation of MC simulation for testing estimators in Jurek. Added incomplete implementation of log likelihood function for second paper. --- .../ou_model_jurek.py | 46 ++++++++++++++----- .../ou_model_mudchanatongsuk.py | 24 ++++++++++ 2 files changed, 58 insertions(+), 12 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 1607d88e..81efcea0 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -71,28 +71,50 @@ def fit(self, data: pd.DataFrame): self.spread.plot() plt.show() - self._estimate_params() + # TODO : This implementation of spread is incorrect. + + params = self._estimate_params(self.spread) + self.mu, self.k, self.sigma = params + + print(self.mu) print(self.k) print(self.sigma) - print(self.mu) - # TODO : Test the null hypothesis of no mean reversion using estimated k by running a Monte Carlo bootstrap experiment. - # For details look at para 3 in Section IV A of the paper. + self._check_estimations() + + + def _estimate_params(self, spread): + + N = len(spread) + mu = spread.mean() - def _estimate_params(self): + k = (-1 / self.delta_t) * np.log(np.multiply(spread[1:] - mu, spread[:-1] - mu).sum() + / np.power(spread[1:] - mu, 2).sum()) - N = len(self.spread) + sigma_calc_sum = np.power((spread[1:] - mu - np.exp(-k * self.delta_t) * (spread[:-1] - mu)) + / np.exp(-k * self.delta_t), 2).sum() - self.mu = self.spread.mean() + sigma = np.sqrt(2 * k * sigma_calc_sum / ((np.exp(2 * k * self.delta_t) - 1) * (N - 2))) - self.k = (-1 / self.delta_t) * np.log(np.multiply(self.spread[1:] - self.mu, self.spread[:-1] - self.mu).sum() - / np.power(self.spread[1:] - self.mu, 2).sum()) + return mu, k, sigma - sigma_calc_sum = np.power((self.spread[1:] - self.mu - np.exp(-self.k * self.delta_t) * (self.spread[:-1] - self.mu)) - / np.exp(-self.k * self.delta_t), 2).sum() - self.sigma = np.sqrt(2 * self.k * sigma_calc_sum / ((np.exp(2 * self.k * self.delta_t) - 1) * (N - 2))) + def _check_estimations(self): + """ + Testing against null of random walk for rate of mean reversion k. + """ + + num_paths = 100000 + + output_params = np.zeros((num_paths, 3)) + for i in range(num_paths): + white_noise_process = self.sigma * np.random.randn(len(self.spread)) + self.mu + output_params[i, :] = self._estimate_params(white_noise_process) + + plt.hist(output_params[:, 1], bins=20) + plt.show() + #TODO : This is incomplete. def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, r = 0.05, gamma = 1): diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 2a909a8a..e16a54a3 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -122,3 +122,27 @@ def _beta_calc(self, sqrt_gamma, exp_calc): self.gamma * (self.eta ** 2 + 2*self.rho*self.sigma*self.eta + 2*self.k*self.theta) * (1 - exp_calc) return left_calc * right_calc + + + # @staticmethod + # def _compute_log_likelihood(params, *args): + # """ + # Computes the average Log Likelihood. (p.13) + # + # :param params: (tuple) A tuple of three elements representing theta, mu and sigma_squared. + # :param args: (tuple) All other values that to be passed to self._compute_log_likelihood() + # :return: (float) The average log likelihood from given parameters. + # """ + # + # # Setting given parameters + # sigma, mu, k ,theta, eta, rho = params + # X,S, dt = args + # n = len(X) + # + # y = np.array([X, S].T) + # + # matrix = np.zeros((2,2)) + # matrix[0][0] = (eta ** 2) * (1 - np.exp(-2 * k * dt)) / (2 * k) + # matrix[0][1] = + # + # return -log_likelihood From 1855b398e2d883ad8ba54fc1bed336cb98495306 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 18 Mar 2021 00:19:56 +0530 Subject: [PATCH 046/103] Added draft implementation of log likelihood function for second paper. --- .../ou_model_mudchanatongsuk.py | 88 ++++++++++++++----- 1 file changed, 65 insertions(+), 23 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index e16a54a3..62a9af84 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -10,8 +10,10 @@ `__ """ +import math import numpy as np import pandas as pd +import scipy.optimize as so class StochasticControlMudchanatongsuk: def __init__(self): @@ -43,7 +45,8 @@ def fit(self, data: pd.DataFrame): self.S = np.log(data.loc[:, self.ticker_B]) self.spread = np.log(data.loc[:, self.ticker_A]) - self.S - self._estimate_params() + #self._estimate_params() + print(self._estimate_params_log_likelihood()) def _estimate_params(self): @@ -124,25 +127,64 @@ def _beta_calc(self, sqrt_gamma, exp_calc): return left_calc * right_calc - # @staticmethod - # def _compute_log_likelihood(params, *args): - # """ - # Computes the average Log Likelihood. (p.13) - # - # :param params: (tuple) A tuple of three elements representing theta, mu and sigma_squared. - # :param args: (tuple) All other values that to be passed to self._compute_log_likelihood() - # :return: (float) The average log likelihood from given parameters. - # """ - # - # # Setting given parameters - # sigma, mu, k ,theta, eta, rho = params - # X,S, dt = args - # n = len(X) - # - # y = np.array([X, S].T) - # - # matrix = np.zeros((2,2)) - # matrix[0][0] = (eta ** 2) * (1 - np.exp(-2 * k * dt)) / (2 * k) - # matrix[0][1] = - # - # return -log_likelihood + def _estimate_params_log_likelihood(self): + """ + """ + + # Setting bounds + # sigma, mu, k, theta, eta, rho + bounds = ((1e-5, None), (None, None), (1e-5, None), (None, None), (1e-5, None), (-1, 1)) + + theta_init = np.mean(self.spread) + + # Initial guesses for sigma, mu, k, theta, eta, rho + initial_guess = np.array((1, 0, 1, theta_init, 1, 0.5)) + + result = so.minimize(self._compute_log_likelihood, initial_guess, + args=(self.spread, self.S, self.delta_t), bounds=bounds) + + # Unpacking optimal values + sigma, mu, k, theta, eta, rho = result.x + + # Undo negation + max_log_likelihood = -result.fun + + return sigma, mu, k, theta, eta, rho, max_log_likelihood + + + + @staticmethod + def _compute_log_likelihood(params, *args): + """ + """ + + # Setting given parameters + sigma, mu, k ,theta, eta, rho = params + X,S, dt = args + + y = np.array([X, S]) + + matrix = np.zeros((2,2)) + matrix[0, 0] = (eta ** 2) * (1 - np.exp(-2 * k * dt)) / (2 * k) + matrix[0, 1] = rho * eta * sigma * (1 - np.exp(k * dt)) / k + matrix[1, 0] = matrix[0 ,1] + matrix[1, 1] = rho ** 2 * dt + + X = X[:-1] + S = S[:-1] + y = y[:, :-1] + + E_y = np.zeros((2, len(X))) + E_y[0, :] = X * np.exp(-k * dt) + theta * (1 - np.exp(-k * dt)) + E_y[1, :] = S + (mu - 0.5 * sigma ** 2) * dt + + vec = y - E_y + f_y_denm = (2 * math.pi * np.sqrt(np.linalg.det(matrix))) + + f_y = np.exp(-0.5 * np.einsum('ij,ij->j', vec, np.linalg.inv(matrix) @ vec)) / f_y_denm + + print(f_y) + # TODO : incorrect, need to fix. + log_likelihood = np.log(f_y).sum() + + return -log_likelihood From 0a9447e2ef18bf65dd7d0fbc7e773063f60e62f7 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 18 Mar 2021 16:03:32 +0530 Subject: [PATCH 047/103] Fixed log likelihood implementation for second paper. --- .../ou_model_mudchanatongsuk.py | 34 ++++++++++++++----- 1 file changed, 25 insertions(+), 9 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 62a9af84..0de64257 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -46,9 +46,15 @@ def fit(self, data: pd.DataFrame): self.spread = np.log(data.loc[:, self.ticker_A]) - self.S #self._estimate_params() - print(self._estimate_params_log_likelihood()) + params = self._estimate_params_log_likelihood() + print(params) + self.sigma, self.mu, self.k,self.theta, self.eta, self.rho = params[:-1] + def _estimate_params(self): + """ + Closed Form Estimators of params. + """ N = len(self.spread) - 1 @@ -84,6 +90,7 @@ def _estimate_params(self): self.rho = self.k * C * np.sqrt(V_squared * S_squared) / (self.eta * self.sigma * (1 - p)) + def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): self.gamma = gamma @@ -99,6 +106,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): return h + def _alpha_beta_calc(self, tau): sqrt_gamma = np.sqrt(1 - self.gamma) @@ -109,6 +117,7 @@ def _alpha_beta_calc(self, tau): return alpha_t, beta_t + def _alpha_calc(self, sqrt_gamma, exp_calc): left_calc = self.k * (1 - sqrt_gamma) / (2 * (self.eta ** 2)) @@ -117,6 +126,7 @@ def _alpha_calc(self, sqrt_gamma, exp_calc): return left_calc * (1 + right_calc) + def _beta_calc(self, sqrt_gamma, exp_calc): left_calc = 1/(2 * (self.eta ** 2) * ((1 - sqrt_gamma) - (1 + sqrt_gamma)*exp_calc)) @@ -129,11 +139,12 @@ def _beta_calc(self, sqrt_gamma, exp_calc): def _estimate_params_log_likelihood(self): """ + Estimates parameters of model based on log likelihood maximization. """ # Setting bounds # sigma, mu, k, theta, eta, rho - bounds = ((1e-5, None), (None, None), (1e-5, None), (None, None), (1e-5, None), (-1, 1)) + bounds = ((1e-5, None), (None, None), (1e-5, None), (None, None), (1e-5, None), (-1 + 1e-5, 1 - 1e-5)) theta_init = np.mean(self.spread) @@ -141,7 +152,7 @@ def _estimate_params_log_likelihood(self): initial_guess = np.array((1, 0, 1, theta_init, 1, 0.5)) result = so.minimize(self._compute_log_likelihood, initial_guess, - args=(self.spread, self.S, self.delta_t), bounds=bounds) + args=(self.spread, self.S, self.delta_t), bounds=bounds, options={'maxiter': 100000}) # Unpacking optimal values sigma, mu, k, theta, eta, rho = result.x @@ -156,6 +167,7 @@ def _estimate_params_log_likelihood(self): @staticmethod def _compute_log_likelihood(params, *args): """ + Helper function computes log likelihood function for a set of params. """ # Setting given parameters @@ -168,23 +180,27 @@ def _compute_log_likelihood(params, *args): matrix[0, 0] = (eta ** 2) * (1 - np.exp(-2 * k * dt)) / (2 * k) matrix[0, 1] = rho * eta * sigma * (1 - np.exp(k * dt)) / k matrix[1, 0] = matrix[0 ,1] - matrix[1, 1] = rho ** 2 * dt + matrix[1, 1] = sigma ** 2 * dt X = X[:-1] S = S[:-1] - y = y[:, :-1] + y = y[:, 1:] E_y = np.zeros((2, len(X))) E_y[0, :] = X * np.exp(-k * dt) + theta * (1 - np.exp(-k * dt)) E_y[1, :] = S + (mu - 0.5 * sigma ** 2) * dt vec = y - E_y - f_y_denm = (2 * math.pi * np.sqrt(np.linalg.det(matrix))) - f_y = np.exp(-0.5 * np.einsum('ij,ij->j', vec, np.linalg.inv(matrix) @ vec)) / f_y_denm + with np.errstate(all='raise'): # This was done due to np.nan's in final result. + try: + f_y_denm = (2 * math.pi * np.sqrt(np.linalg.det(matrix))) + + f_y = np.exp(-0.5 * np.einsum('ij,ij->j', vec, np.linalg.inv(matrix) @ vec)) / f_y_denm + except FloatingPointError as r: + return 0 + - print(f_y) - # TODO : incorrect, need to fix. log_likelihood = np.log(f_y).sum() return -log_likelihood From 94964836d40bbef268062270cf6e58ef4d5d8e6e Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 18 Mar 2021 22:24:52 +0530 Subject: [PATCH 048/103] Made changes according to review, Added test files. --- .../ou_model_jurek.py | 52 ++++++++++++------- .../ou_model_mudchanatongsuk.py | 8 +-- tests/test_ou_model_jurek.py | 17 ++++++ tests/test_ou_model_mudchanatongsuk.py | 17 ++++++ 4 files changed, 71 insertions(+), 23 deletions(-) create mode 100644 tests/test_ou_model_jurek.py create mode 100644 tests/test_ou_model_mudchanatongsuk.py diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 81efcea0..4712d90a 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -14,7 +14,6 @@ import pandas as pd import matplotlib.pyplot as plt -from arbitragelab.cointegration_approach.johansen import JohansenPortfolio from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio class StochasticControlJurek: @@ -25,8 +24,8 @@ def __init__(self): self.ticker_B = None self.spread = None self.time_array = None + self.delta_t = None - self.delta_t = 1 / 251 #TODO : Is this value correct for this paper? # Estimated params from training data. self.sigma = None self.mu = None @@ -37,7 +36,12 @@ def __init__(self): self.gamma = None self.beta = None - def _calc_total_return_indices(self, data): + @staticmethod + def _calc_total_return_indices(data): + """ + The total return indices calculation follows Section IV A in Jurek (2007). + """ + returns_df = data.pct_change() returns_df = returns_df.replace([np.inf, -np.inf], np.nan).ffill().dropna() @@ -48,9 +52,12 @@ def _calc_total_return_indices(self, data): return total_return_indices + def fit(self, data: pd.DataFrame, delta_t = 1 / 252, significance_level = 0.95): + """ + The spread construction follows Section IV A in Jurek (2007). + """ - def fit(self, data: pd.DataFrame): - + self.delta_t = delta_t self.time_array = np.arange(0, len(data)) * self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] @@ -61,7 +68,7 @@ def fit(self, data: pd.DataFrame): eg_adf_statistics = eg_portfolio.adf_statistics eg_cointegration_vectors = eg_portfolio.cointegration_vectors - if eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc['95%', 0]: + if eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc[f'{int(significance_level * 100)}%', 0]: print(eg_adf_statistics) raise Exception("ADF statistic test failure.") @@ -71,7 +78,8 @@ def fit(self, data: pd.DataFrame): self.spread.plot() plt.show() - # TODO : This implementation of spread is incorrect. + # TODO : This implementation of spread might be incorrect. + # The values of estimators calculated do not match what is expected. params = self._estimate_params(self.spread) self.mu, self.k, self.sigma = params @@ -84,6 +92,9 @@ def fit(self, data: pd.DataFrame): def _estimate_params(self, spread): + """ + These formulas for the estimators are given in Appendix E of Jurek (2007). + """ N = len(spread) @@ -149,8 +160,8 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, total_return_indices = self._calc_total_return_indices(data) - W = np.ones(len(t)) # Wealth is normalized to one. #TODO : Is this the correct way? - S = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) #TODO : Do we use trained linear weights here ? + W = np.ones(len(t)) # Wealth is normalized to one. + S = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) N = None # The optimal weights equation is the same for both types of utility functions. @@ -171,7 +182,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, elif utility_type == 2: A, B = self._AB_calc_2(tau) - N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2) + (2 * A * S + B) / self.gamma) * W + N = ((self.k * (self.mu - S) - self.r * S) / (self.gamma * self.sigma ** 2) + (2 * A * S + B) / self.gamma) * W return N / W # We return the optimal allocation of spread asset scaled by wealth. @@ -206,13 +217,14 @@ def _A_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): #Note : A<=0 and decreasing in tau for gamma > 1, and vice versa for gamma < 1. A = None - if 0 < self.gamma < gamma_0: + error_margin = 1e-4 + if 0 < self.gamma < gamma_0 - error_margin: A = -c_2 / c_1 + (np.sqrt(-disc) / (2 * c_1)) * np.tan(np.sqrt(-disc) * tau / 2 + np.arctan(2 * c_2 / np.sqrt(-disc))) - elif self.gamma == gamma_0: + elif gamma_0 - error_margin <= self.gamma <= gamma_0 + error_margin: A = -(c_2 / c_1) * (1 + 1 / (c_2 * tau - 1)) - elif gamma_0 < self.gamma < 1: + elif gamma_0 + error_margin < self.gamma < 1: # coth = 1/tanh and arccoth(x) = arctanh(1/x) # For reference : https://www.efunda.com/math/hyperbolic/hyperbolic.cfm @@ -233,7 +245,8 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): c_5 = -((self.k + self.r) / self.sigma ** 2) * ((1 - self.gamma) / self.gamma) * self.k * self.mu B = None - if 0 < self.gamma < gamma_0: + error_margin = 1e-4 + if 0 < self.gamma < gamma_0 - error_margin: phi_1 = np.sqrt(-disc) * (np.cos(np.sqrt(-disc) * tau / 2) - 1) + 2 * c_2 * np.sin(np.sqrt(-disc) * tau / 2) phi_2 = np.arctanh(np.tan(0.25 * (np.sqrt(-disc) * tau - 2 * np.arctan(2 * c_2 / np.sqrt(-disc))))) + \ @@ -242,10 +255,10 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): B = c_4 * phi_1 / (c_1 * np.sqrt(-disc)) + (4 * phi_2 / np.sqrt(-disc)) * (c_5 - c_4 / c_1) * \ np.cos(np.sqrt(-disc) * tau / 2 - np.arctan(c_2 / np.sqrt(-disc))) - elif self.gamma == gamma_0: + elif gamma_0 - error_margin <= self.gamma <= gamma_0 + error_margin: B = (c_1 * c_5 * (c_2 * tau - 2) - (c_2 ** 2) * c_4) * tau / (2 * c_1 * (c_2 * tau - 1)) - elif self.gamma > gamma_0: + elif self.gamma > gamma_0 + error_margin: B = (4 * (c_2 * c_5 - c_3 * c_4 + (c_3 * c_4 - c_2 * c_5) * np.cosh(np.sqrt(disc) * tau / 2)) + 2 * c_5 * np.sqrt(disc) * np.sinh(np.sqrt(disc) * tau / 2)) \ / (disc * np.cosh(np.sqrt(disc) * tau / 2) - 2 * c_2 * np.sqrt(disc) * np.sinh(np.sqrt(disc) * tau / 2)) @@ -293,11 +306,12 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): c_6 = self.k * (self.k + self.r) * (self.gamma - 1) * self.mu / (self.gamma * self.sigma ** 2) B = None + error_margin = 1e-4 rep_exp_1 = np.exp(tau * c_2) rep_exp_2 = np.exp(tau * c_5) - if 0 < self.gamma < gamma_0: + if 0 < self.gamma < gamma_0 - error_margin: rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) rep_phrase_2 = np.sqrt(c_1 * c_3) / rep_phrase_1 @@ -323,7 +337,7 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): -c_3 * term_5 * c_4)) / denominator - elif self.gamma == gamma_0: + elif gamma_0 - error_margin <= self.gamma <= gamma_0 + error_margin: denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 @@ -339,7 +353,7 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): B = (-term_1 + term_2 - term_3 + term_4) / denominator - elif gamma_0 < self.gamma < 1: + elif gamma_0 + error_margin < self.gamma < 1: rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 0de64257..b785b53f 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -37,15 +37,15 @@ def __init__(self): def fit(self, data: pd.DataFrame): # Preprocessing - #data = data.ffill() - #TODO : Might need to normalize input, estimate params is not running properly. + data = data.ffill() self.time_array = np.arange(0, len(data)) * self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] self.S = np.log(data.loc[:, self.ticker_B]) self.spread = np.log(data.loc[:, self.ticker_A]) - self.S - #self._estimate_params() + #self._estimate_params() #TODO : V_squared estimator is returning a negative value which is incorrect. Need to check why? + params = self._estimate_params_log_likelihood() print(params) self.sigma, self.mu, self.k,self.theta, self.eta, self.rho = params[:-1] @@ -192,7 +192,7 @@ def _compute_log_likelihood(params, *args): vec = y - E_y - with np.errstate(all='raise'): # This was done due to np.nan's in final result. + with np.errstate(all='raise'): # This was done due to np.nan's outputted in final result of scipy minimize. try: f_y_denm = (2 * math.pi * np.sqrt(np.linalg.det(matrix))) diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py new file mode 100644 index 00000000..27ae8e18 --- /dev/null +++ b/tests/test_ou_model_jurek.py @@ -0,0 +1,17 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html + +""" +Test functions for the Jurek OU model in the Stochastic Control Approach module. +""" + +import unittest +import numpy as np +import pandas as pd + +from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek + + +class TestOUModelJurek(unittest.TestCase): + pass \ No newline at end of file diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py new file mode 100644 index 00000000..1e282172 --- /dev/null +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -0,0 +1,17 @@ +# Copyright 2019, Hudson and Thames Quantitative Research +# All rights reserved +# Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html + +""" +Test functions for the Mudchanatongsuk OU model in the Stochastic Control Approach module. +""" + +import unittest +import numpy as np +import pandas as pd + +from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import StochasticControlMudchanatongsuk + + +class TestOUModelMudchanatongsuk(unittest.TestCase): + pass \ No newline at end of file From 9cd83904206e04160a6dc37fc4bcad0d02d31d48 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 19 Mar 2021 00:10:02 +0530 Subject: [PATCH 049/103] Added draft implementation of test cases. Made slight changes to time_array calculation. --- .../ou_model_jurek.py | 6 +-- .../ou_model_mudchanatongsuk.py | 10 ++++- tests/test_ou_model_jurek.py | 33 +++++++++++++++- tests/test_ou_model_mudchanatongsuk.py | 39 ++++++++++++++++++- 4 files changed, 82 insertions(+), 6 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 4712d90a..c8c20245 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -58,10 +58,10 @@ def fit(self, data: pd.DataFrame, delta_t = 1 / 252, significance_level = 0.95): """ self.delta_t = delta_t - self.time_array = np.arange(0, len(data)) * self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] total_return_indices = self._calc_total_return_indices(data) + self.time_array = np.arange(0, len(total_return_indices)) * self.delta_t eg_portfolio = EngleGrangerPortfolio() eg_portfolio.fit(total_return_indices, add_constant=True) @@ -155,10 +155,10 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, self.r = r self.gamma = gamma self.beta = beta - t = np.arange(0, len(data)) * self.delta_t - tau = t[-1] - t total_return_indices = self._calc_total_return_indices(data) + t = np.arange(0, len(total_return_indices)) * self.delta_t + tau = t[-1] - t W = np.ones(len(t)) # Wealth is normalized to one. S = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index b785b53f..ef5e8f26 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -34,10 +34,15 @@ def __init__(self): self.gamma = None + @staticmethod + def _data_preprocessing(data): + + return data.ffill() + def fit(self, data: pd.DataFrame): # Preprocessing - data = data.ffill() + data = self._data_preprocessing(data) self.time_array = np.arange(0, len(data)) * self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] @@ -93,6 +98,9 @@ def _estimate_params(self): def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): + # Preprocessing + data = self._data_preprocessing(data) + self.gamma = gamma t = np.arange(0, len(data)) * self.delta_t tau = t[-1] - t diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index 27ae8e18..f66e20c9 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -7,6 +7,7 @@ """ import unittest +import os import numpy as np import pandas as pd @@ -14,4 +15,34 @@ class TestOUModelJurek(unittest.TestCase): - pass \ No newline at end of file + + @classmethod + def setUpClass(cls) -> None: + np.random.seed(0) + + project_path = os.path.dirname(__file__) + cls.path = project_path + '/test_data/gld_gdx_data.csv' + data = pd.read_csv(cls.path) + data = data.set_index('Date') + + cls.dataframe = data[['GLD', 'GDX']] + + def test_fit(self): + sc = StochasticControlJurek() + + sc.fit(self.dataframe, 1/252, 0.95) + + np.testing.assert_array_equal(sc.spread, np.zeros(len(sc.time_array))) + self.assertAlmostEqual(sc.mu, 0, delta=1e-4) + self.assertAlmostEqual(sc.k, 0, delta=1e-4) + self.assertAlmostEqual(sc.sigma, 0, delta=1e-4) + + def test_optimal_weights(self): + + sc = StochasticControlJurek() + + sc.fit(self.dataframe, 1/252, 0.95) + + weights = sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) + + np.testing.assert_array_equal(weights, np.zeros(len(sc.time_array))) diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index 1e282172..a2e455c2 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -7,6 +7,7 @@ """ import unittest +import os import numpy as np import pandas as pd @@ -14,4 +15,40 @@ class TestOUModelMudchanatongsuk(unittest.TestCase): - pass \ No newline at end of file + + @classmethod + def setUpClass(cls) -> None: + + np.random.seed(0) + + project_path = os.path.dirname(__file__) + cls.path = project_path + '/test_data/gld_gdx_data.csv' + data = pd.read_csv(cls.path) + data = data.set_index('Date') + + cls.dataframe = data[['GLD', 'GDX']] + + cls.sc = StochasticControlMudchanatongsuk() + + def test_fit(self): + sc = StochasticControlMudchanatongsuk() + + sc.fit(self.dataframe) + + np.testing.assert_array_equal(sc.spread, np.zeros(len(sc.time_array))) + self.assertAlmostEqual(sc.sigma, 0, delta=1e-4) + self.assertAlmostEqual(sc.mu, 0, delta=1e-4) + self.assertAlmostEqual(sc.k, 0, delta=1e-4) + self.assertAlmostEqual(sc.theta, 0, delta=1e-4) + self.assertAlmostEqual(sc.eta, 0, delta=1e-4) + self.assertAlmostEqual(sc.rho, 0, delta=1e-4) + + + def test_optimal_weights(self): + sc = StochasticControlMudchanatongsuk() + + sc.fit(self.dataframe) + + weights = sc.optimal_portfolio_weights(self.dataframe, gamma = 10) + + np.testing.assert_array_equal(weights, np.zeros(len(sc.time_array))) From 1d47dd260784da380a18a2b39716d1004af3560e Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 19 Mar 2021 03:14:30 +0530 Subject: [PATCH 050/103] Added some docstrings and inline comments. --- .../ou_model_jurek.py | 120 ++++++++++++------ 1 file changed, 84 insertions(+), 36 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index c8c20245..c18eda00 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -16,32 +16,51 @@ from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio + class StochasticControlJurek: + """ + This class derives the optimal dynamic strategy for arbitrageurs with a finite horizon + and non-myopic preferences facing a mean-reverting arbitrage opportunity (e.g. an equity pairs trade). + + To capture the presence of horizon and divergence risk, we model the dynamics of the mispricing + using a mean-reverting OU process. Under this process, although the mispricing is guaranteed + to be eliminated at some future date, the timing of convergence, as well as the maximum magnitude + of the mispricing prior to convergence, are uncertain. With this assumption, we are able to derive + the arbitrageur's optimal dynamic portfolio policy for a set of general, non-myopic preference + specifications, including CRRA utility defined over wealth at a finite horizon and Epstein-Zin + utility defined over intermediate cash flows (e.g. fees). + """ + def __init__(self): - #Training Data. - self.ticker_A = None - self.ticker_B = None - self.spread = None - self.time_array = None - self.delta_t = None + #Characteristics of Training Data. + self.ticker_A = None # Ticker Symbol of first stock. + self.ticker_B = None # Ticker Symbol of second stock. + self.spread = None # Constructed spread from training data. + self.time_array = None # Time indices of training data. + self.delta_t = None # Time difference between each index in data, calculated in years. # Estimated params from training data. - self.sigma = None - self.mu = None - self.k = None + self.sigma = None # Standard deviation of spread. + self.mu = None # Long run mean of spread. + self.k = None # Rate of mean reversion. # Params inputted by user. - self.r = None - self.gamma = None - self.beta = None + self.r = None # Rate of returns. + self.gamma = None # Coefficient of relative risk aversion. + self.beta = None # Rate of time preference. + @staticmethod - def _calc_total_return_indices(data): + def _calc_total_return_indices(data : pd.DataFrame) -> pd.DataFrame: """ - The total return indices calculation follows Section IV A in Jurek (2007). + This method calculates the total return indices from pricing data. + This calculation follows Section IV A in Jurek (2007). + + :param data: (pd.DataFrame) Contains price series of both stocks in spread. """ + #Calculating the daily returns. returns_df = data.pct_change() returns_df = returns_df.replace([np.inf, -np.inf], np.nan).ffill().dropna() @@ -52,26 +71,39 @@ def _calc_total_return_indices(data): return total_return_indices - def fit(self, data: pd.DataFrame, delta_t = 1 / 252, significance_level = 0.95): + def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: float = 0.95): """ - The spread construction follows Section IV A in Jurek (2007). + This method uses inputted training data to calculate the spread and + estimate the parameters of the corresponding OU process. + + The spread construction implementation follows Section IV A in Jurek (2007). + + :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param delta_t: (float) Time difference between each index of data, calculated in years. + :param significance_level: (float) This significance level is used in the ADF statistic test. + Value can be one of the following: (0.90, 0.95, 0.99). """ + # Setting instance attributes. self.delta_t = delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] + #Calculating the total return indices from pricing data. total_return_indices = self._calc_total_return_indices(data) self.time_array = np.arange(0, len(total_return_indices)) * self.delta_t + # As mentioned in the paper, the vector of linear weights are calculated using co-integrating regression. eg_portfolio = EngleGrangerPortfolio() - eg_portfolio.fit(total_return_indices, add_constant=True) - eg_adf_statistics = eg_portfolio.adf_statistics - eg_cointegration_vectors = eg_portfolio.cointegration_vectors + eg_portfolio.fit(total_return_indices, add_constant=True) # Fitting the total return indices. + eg_adf_statistics = eg_portfolio.adf_statistics # Stores the results of the ADF statistic test. + eg_cointegration_vectors = eg_portfolio.cointegration_vectors # Stores the calculated weights for the pair o stocks in the spread. if eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc[f'{int(significance_level * 100)}%', 0]: + # Making sure that the data passes the ADF statistic test. print(eg_adf_statistics) raise Exception("ADF statistic test failure.") + # Scaling the weights such that they sum to 1. self.eg_scaled_vectors = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() self.spread = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) @@ -91,21 +123,27 @@ def fit(self, data: pd.DataFrame, delta_t = 1 / 252, significance_level = 0.95): self._check_estimations() - def _estimate_params(self, spread): + def _estimate_params(self, spread: pd.DataFrame): """ + This method implements the closed form solutions for estimators of the model parameters. These formulas for the estimators are given in Appendix E of Jurek (2007). + + :param: (pd.DataFrame) Price series of the constructed spread. """ N = len(spread) + # Mean estimator. mu = spread.mean() + # Estimator for rate of mean reversion. k = (-1 / self.delta_t) * np.log(np.multiply(spread[1:] - mu, spread[:-1] - mu).sum() / np.power(spread[1:] - mu, 2).sum()) sigma_calc_sum = np.power((spread[1:] - mu - np.exp(-k * self.delta_t) * (spread[:-1] - mu)) / np.exp(-k * self.delta_t), 2).sum() + #Estimator for standard deviation. sigma = np.sqrt(2 * k * sigma_calc_sum / ((np.exp(2 * k * self.delta_t) - 1) * (N - 2))) return mu, k, sigma @@ -128,45 +166,55 @@ def _check_estimations(self): #TODO : This is incomplete. - def optimal_portfolio_weights(self, data: pd.DataFrame, beta, utility_type = 1, r = 0.05, gamma = 1): + def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, gamma: float = 1, beta: float = 0.1, r: float = 0.05): """ - Implementation of Theorem 1 and Theorem 2 in Jurek (2007). - utility_type = 1 implies agent with utility of terminal wealth. - gamma = 1 implies log utility investor. - gamma != 1 implies general CRRA investor. + This method implements the optimal portfolio strategy for two types of investors with varying utility functions. - utility_type = 2 implies agent whose utility is defined over intermediate consumption - with agent’s preferences described by Epstein-Zin recursive utility with psi(elasticity of intertemporal substitution) = 1. - gamma = 1 reduces to standard log utility. - gamma ! = 1, gamma > 1 implies more risk averse investors, whereas gamma < 1 implies more risk tolerance. + The first type of investor is represented by utility_type = 1. + This agent has constant relative risk aversion preferences(CRRA investor) with utility defined over terminal wealth. + For this type of investor, gamma = 1 implies log utility investor, and + gamma != 1 implies general CRRA investor. - What is beta? - 1)subjective rate of time preference. + The second type of investor is represented by utility_type = 2. + This agent has utility defined over intermediate consumption, + with agent’s preferences described by Epstein-Zin recursive utility with psi(elasticity of intertemporal substitution) = 1. + For this type of investor, gamma = 1 reduces to standard log utility investor, and + gamma > 1 implies more risk averse investors, + whereas gamma < 1 implies more risk tolerance in comparison to investor with log utility. - 2)beta signifies the constant fraction of total wealth an investor chooses to consume. This is analogous to a hedge fund investor + What is beta? + Beta signifies the constant fraction of total wealth an investor chooses to consume. This is analogous to a hedge fund investor who cares both about terminal wealth in some risk-averse way and consumes a constant fraction, β, of assets under management (the management fee). + For utility_type = 2, C(Consumption) = beta * W. - For utility_type = 2, C(Consumption) = beta * W + :param data: Contains price series of both stocks in spread. + :param utility_type: Flag signifies type of investor preferences. + :param gamma: coefficient of relative risk aversion. + :param beta: Subjective rate of time preference. (Only required for utility_type = 2). + :param r: Rate of Returns. """ + # Setting instance attributes. self.r = r self.gamma = gamma self.beta = beta + #Calculating the total return indices from pricing data. total_return_indices = self._calc_total_return_indices(data) t = np.arange(0, len(total_return_indices)) * self.delta_t - tau = t[-1] - t + tau = t[-1] - t # Stores time remaining till closure. (In years) - W = np.ones(len(t)) # Wealth is normalized to one. + W = np.ones(len(t)) # Wealth is normalized to one. + # Calculating the spread with weights calculated from training data. S = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) N = None # The optimal weights equation is the same for both types of utility functions. # For gamma = 1, the outputs weights are identical for both types of utility functions, - # whereas for gamma != 1, the calculation of A and B functions are different. + # whereas for gamma != 1, the calculation of A and B functions in the equation are different. if self.gamma == 1: N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2)) * W From f56385c2566571f886040c00aec958e9101474b1 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 19 Mar 2021 12:14:35 +0530 Subject: [PATCH 051/103] Minor code changes to convert spread to numpy array. --- .../ou_model_jurek.py | 23 +++++++++++++------ .../ou_model_mudchanatongsuk.py | 3 +++ 2 files changed, 19 insertions(+), 7 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index c18eda00..afd82db0 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -17,6 +17,7 @@ from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio + class StochasticControlJurek: """ This class derives the optimal dynamic strategy for arbitrageurs with a finite horizon @@ -113,6 +114,10 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: # TODO : This implementation of spread might be incorrect. # The values of estimators calculated do not match what is expected. + + self.spread = self.spread.to_numpy() # TODO : This conversion seems to have changed the estimated values. Not sure why? + + params = self._estimate_params(self.spread) self.mu, self.k, self.sigma = params @@ -190,11 +195,11 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g of assets under management (the management fee). For utility_type = 2, C(Consumption) = beta * W. - :param data: Contains price series of both stocks in spread. - :param utility_type: Flag signifies type of investor preferences. - :param gamma: coefficient of relative risk aversion. - :param beta: Subjective rate of time preference. (Only required for utility_type = 2). - :param r: Rate of Returns. + :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param utility_type: (int) Flag signifies type of investor preferences. + :param gamma: (float) coefficient of relative risk aversion. + :param beta: (float) Subjective rate of time preference. (Only required for utility_type = 2). + :param r: (float) Rate of Returns. """ # Setting instance attributes. @@ -211,6 +216,8 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g # Calculating the spread with weights calculated from training data. S = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) + S = S.to_numpy() # TODO : This conversion in fit seems to have changed the estimated values. + N = None # The optimal weights equation is the same for both types of utility functions. # For gamma = 1, the outputs weights are identical for both types of utility functions, @@ -237,8 +244,10 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g def _AB_calc_1(self, tau): """ - For utility_type = 1. - Follows Appendix A.2 in the paper. + This helper function computes the A and B functions for investors with utility_type = 1. + The implementation follows Appendix A.2 in the paper. + + :param: tau """ c_1 = 2 * self.sigma ** 2 / self.gamma diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index ef5e8f26..ad6d77ae 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -49,6 +49,8 @@ def fit(self, data: pd.DataFrame): self.S = np.log(data.loc[:, self.ticker_B]) self.spread = np.log(data.loc[:, self.ticker_A]) - self.S + self.spread = self.spread.to_numpy() # Converting from pd.Series to numpy array. + self.S = self.S.to_numpy() # Converting from pd.Series to numpy array. #self._estimate_params() #TODO : V_squared estimator is returning a negative value which is incorrect. Need to check why? params = self._estimate_params_log_likelihood() @@ -105,6 +107,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): t = np.arange(0, len(data)) * self.delta_t tau = t[-1] - t x = np.log(data.iloc[:, 0]) - np.log(data.iloc[:, 1]) + x = x.to_numpy() # Converting from pd.Series to numpy array. alpha_t, beta_t = self._alpha_beta_calc(tau) From a90c5720ca152d9d1a6813adda52a9ea83f3a116 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 19 Mar 2021 16:42:34 +0530 Subject: [PATCH 052/103] Completed documentation of code in Jurek class. --- .../ou_model_jurek.py | 151 ++++++++++++++---- 1 file changed, 119 insertions(+), 32 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index afd82db0..d2cedbf7 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -17,7 +17,6 @@ from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio - class StochasticControlJurek: """ This class derives the optimal dynamic strategy for arbitrageurs with a finite horizon @@ -128,12 +127,12 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: self._check_estimations() - def _estimate_params(self, spread: pd.DataFrame): + def _estimate_params(self, spread: np.array): """ This method implements the closed form solutions for estimators of the model parameters. These formulas for the estimators are given in Appendix E of Jurek (2007). - :param: (pd.DataFrame) Price series of the constructed spread. + :param: (np.array) Price series of the constructed spread. """ N = len(spread) @@ -247,38 +246,57 @@ def _AB_calc_1(self, tau): This helper function computes the A and B functions for investors with utility_type = 1. The implementation follows Appendix A.2 in the paper. - :param: tau + :param tau: (np.array) Array with time till completion in years. """ + # Calculating value of variable c_1 in Appendix A.2.1. c_1 = 2 * self.sigma ** 2 / self.gamma + # Calculating value of variable c_2 in Appendix A.2.1. c_2 = -(self.k / self.gamma + self.r * (1 - self.gamma) / self.gamma) + # Calculating value of variable c_3 in Appendix A.2.1. c_3 = 0.5 * ((1 - self.gamma) / self.gamma) * (((self.k + self.r) / self.sigma) ** 2) + # Calculating value of discriminant in Appendix A.2.1. disc = 4 * (self.k ** 2 - self.r ** 2 * (1 - self.gamma)) / self.gamma - #Note : discriminant is always positive for gamma > 1. + # Note: discriminant is always positive for gamma > 1. + # Calculating value of variable gamma_0 in Appendix A.2.1. gamma_0 = 1 - (self.k / self.r) ** 2 - #Note : gamma_0 is not always > 0. + # Note: gamma_0 is not always > 0. - A = self._A_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) - B = self._B_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) + A = self._A_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function A. + B = self._B_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function B. return A, B def _A_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): + """ + This method calculates the value of function A as described in the paper for investor with utility_type = 1. + The implementation follows Appendix A.2.1 in the paper. - #Note : A<=0 and decreasing in tau for gamma > 1, and vice versa for gamma < 1. + Value of function A <= 0 and decreasing in tau for gamma > 1, and vice versa for gamma < 1. + + :param tau: (np.array) Array with time till completion in years. + :param c_1: (float) Value of variable c_1 in Appendix A.2.1. + :param c_2: (float) Value of variable c_2 in Appendix A.2.1. + :param c_3: (float) Value of variable c_3 in Appendix A.2.1. + :param disc: (float) Value of discriminant in Appendix A.2.1. + :param gamma_0: (float) Value of variable gamma_0 in Appendix A.2.1. + """ A = None - error_margin = 1e-4 + error_margin = 1e-4 # Error margin around gamma_0. + if 0 < self.gamma < gamma_0 - error_margin: + A = -c_2 / c_1 + (np.sqrt(-disc) / (2 * c_1)) * np.tan(np.sqrt(-disc) * tau / 2 + np.arctan(2 * c_2 / np.sqrt(-disc))) elif gamma_0 - error_margin <= self.gamma <= gamma_0 + error_margin: + A = -(c_2 / c_1) * (1 + 1 / (c_2 * tau - 1)) elif gamma_0 + error_margin < self.gamma < 1: @@ -288,24 +306,42 @@ def _A_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): A = -c_2 / c_1 + (np.sqrt(disc) / (2 * c_1)) * (1 / np.tanh(-np.sqrt(disc) * tau / 2 + np.arctanh(np.sqrt(disc) / (2 * c_2)))) elif self.gamma > 1: + A = -c_2 / c_1 + (np.sqrt(disc) / (2 * c_1)) * np.tanh(-np.sqrt(disc) * tau / 2 + np.arctanh(2 * c_2 / np.sqrt(disc))) return A def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): + """ + This method calculates the value of function B as described in the paper for investor with utility_type = 1. + The implementation follows Appendix A.2.2 in the paper. - #Note : When self.mu = 0, c_4 and c_5 become zero and consequently B becomes zero. + When self.mu = 0, c_4 and c_5 become zero and consequently B becomes zero. + + :param tau: (np.array) Array with time till completion in years. + :param c_1: (float) Value of variable c_1 in Appendix A.2.1. + :param c_2: (float) Value of variable c_2 in Appendix A.2.1. + :param c_3: (float) Value of variable c_3 in Appendix A.2.1. + :param disc: (float) Value of discriminant in Appendix A.2.1. + :param gamma_0: (float) Value of variable gamma_0 in Appendix A.2.1. + """ + # Calculating value of variable c_4 in Appendix A.2.2. c_4 = 2 * self.k * self.mu / self.gamma + # Calculating value of variable c_5 in Appendix A.2.2. c_5 = -((self.k + self.r) / self.sigma ** 2) * ((1 - self.gamma) / self.gamma) * self.k * self.mu B = None - error_margin = 1e-4 + error_margin = 1e-4 # Error margin around gamma_0. + if 0 < self.gamma < gamma_0 - error_margin: + + # Calculating value of function phi_1 in Appendix A.2.2. phi_1 = np.sqrt(-disc) * (np.cos(np.sqrt(-disc) * tau / 2) - 1) + 2 * c_2 * np.sin(np.sqrt(-disc) * tau / 2) + # Calculating value of function phi_2 in Appendix A.2.2. phi_2 = np.arctanh(np.tan(0.25 * (np.sqrt(-disc) * tau - 2 * np.arctan(2 * c_2 / np.sqrt(-disc))))) + \ np.arctanh(np.tan(0.5 * np.arctan(2 * c_2 / np.sqrt(-disc)))) @@ -313,9 +349,11 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): np.cos(np.sqrt(-disc) * tau / 2 - np.arctan(c_2 / np.sqrt(-disc))) elif gamma_0 - error_margin <= self.gamma <= gamma_0 + error_margin: + B = (c_1 * c_5 * (c_2 * tau - 2) - (c_2 ** 2) * c_4) * tau / (2 * c_1 * (c_2 * tau - 1)) elif self.gamma > gamma_0 + error_margin: + B = (4 * (c_2 * c_5 - c_3 * c_4 + (c_3 * c_4 - c_2 * c_5) * np.cosh(np.sqrt(disc) * tau / 2)) + 2 * c_5 * np.sqrt(disc) * np.sinh(np.sqrt(disc) * tau / 2)) \ / (disc * np.cosh(np.sqrt(disc) * tau / 2) - 2 * c_2 * np.sqrt(disc) * np.sinh(np.sqrt(disc) * tau / 2)) @@ -325,56 +363,94 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): def _AB_calc_2(self, tau): """ - For utility_type = 2. - Follows appendix B.1 in the paper. + This helper function computes the A and B functions for investors with utility_type = 2. + The implementation follows Appendix B.1 in the paper. + + :param tau: (np.array) Array with time till completion in years. """ + # Calculating value of variable c_1 in Appendix B.1.1. c_1 = 2 * self.sigma ** 2 / self.gamma + # Calculating value of variable c_2 in Appendix B.1.1. c_2 = (self.gamma * (2 * self.r - self.beta) - 2 * (self.k + self.r)) / (2 * self.gamma) + # Calculating value of variable c_3 in Appendix B.1.1. c_3 = ((self.k + self.r) ** 2) * (1 - self.gamma) / (2 * self.gamma * (self.sigma ** 2)) + # Calculating value of discriminant in Appendix B.1.1. disc = ((2 * self.k + self.beta) ** 2 + (self.gamma - 1) * ((-2 * self.r + self.beta) ** 2)) / self.gamma + # Calculating value of variable gamma_0 in Appendix B.1.1. gamma_0 = 4 * (self.k + self.r) * (self.r - self.beta - self.k) / ((2 * self.r - self.beta) ** 2) - A = self._A_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) - B = self._B_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) + A = self._A_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function A. + B = self._B_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function B. return A, B def _A_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): + """ + This method calculates the value of function A as described in the paper for investor with utility_type = 2. + The implementation follows Appendix B.1.1 in the paper. + + The formulas for calculating function A given in Appendix B.1.1 are the same as those in Appendix A.2.1, + with the values of variables differing. + + :param tau: (np.array) Array with time till completion in years. + :param c_1: (float) Value of variable c_1 in Appendix B.1.1. + :param c_2: (float) Value of variable c_2 in Appendix B.1.1. + :param c_3: (float) Value of variable c_3 in Appendix B.1.1. + :param disc: (float) Value of discriminant in Appendix B.1.1. + :param gamma_0: (float) Value of variable gamma_0 in Appendix B.1.1. + """ # Same calculation as for general CRRA Investor. return self._A_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): + """ + This method calculates the value of function B as described in the paper for investor with utility_type = 2. + The implementation follows Appendix B.1.2 in the paper. + + When self.mu = 0, c_4 and c_6 become zero and consequently B becomes zero. - # Note : When self.mu = 0, c_4 and c_6 become zero and consequently B becomes zero. + :param tau: (np.array) Array with time till completion in years. + :param c_1: (float) Value of variable c_1 in Appendix B.1.1. + :param c_2: (float) Value of variable c_2 in Appendix B.1.1. + :param c_3: (float) Value of variable c_3 in Appendix B.1.1. + :param disc: (float) Value of discriminant in Appendix B.1.1. + :param gamma_0: (float) Value of variable gamma_0 in Appendix B.1.1. + """ + # Calculating value of variable c_4 in Appendix B.1.2. c_4 = 2 * self.k * self.mu / self.gamma + # Calculating value of variable c_5 in Appendix B.1.2. c_5 = -(self.k + self.r * (1 - self.gamma) + self.beta * self.gamma) / (2 * self.gamma) + # Calculating value of variable c_6 in Appendix B.1.2. c_6 = self.k * (self.k + self.r) * (self.gamma - 1) * self.mu / (self.gamma * self.sigma ** 2) B = None - error_margin = 1e-4 + error_margin = 1e-4 # Error margin around gamma_0. - rep_exp_1 = np.exp(tau * c_2) - rep_exp_2 = np.exp(tau * c_5) + rep_exp_1 = np.exp(tau * c_2) # Repeating Exponential Form with variable c_2. + rep_exp_2 = np.exp(tau * c_5) # Repeating Exponential Form with variable c_5. if 0 < self.gamma < gamma_0 - error_margin: + # Implementation of Case I in Appendix B.1.2. - rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) - rep_phrase_2 = np.sqrt(c_1 * c_3) / rep_phrase_1 - rep_phrase_3 = rep_phrase_1 * tau + np.arctan(c_2 / rep_phrase_1) + rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) # Repeating Phrase 1. + rep_phrase_2 = np.sqrt(c_1 * c_3) / rep_phrase_1 # Repeating Phrase 2. + rep_phrase_3 = rep_phrase_1 * tau + np.arctan(c_2 / rep_phrase_1) # Repeating Phrase 3. - denominator = c_1 * rep_phrase_2 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) + denominator = c_1 * rep_phrase_2 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. + + # The final equation for B is split into 5 terms. term_1 = rep_exp_1 * rep_phrase_2 * c_4 * c_5 * (c_2 - rep_phrase_1 * np.tan(rep_phrase_3)) @@ -395,8 +471,11 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): elif gamma_0 - error_margin <= self.gamma <= gamma_0 + error_margin: + # Implementation of Case II in Appendix B.1.2. + + denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 # Denominator in final equation. - denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 + # The final equation for B is split into 4 terms. term_1 = rep_exp_1 * tau * c_4 * c_2 ** 3 @@ -410,14 +489,18 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): B = (-term_1 + term_2 - term_3 + term_4) / denominator + elif gamma_0 + error_margin < self.gamma < 1: + # Implementation of Case III in Appendix B.1.2. - rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) - rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) - rep_phrase_3 = np.arctanh(rep_phrase_2 / c_2) - tau * rep_phrase_2 + rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) # Repeated Phrase 1. + rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) # Repeated Phrase 2. + rep_phrase_3 = np.arctanh(rep_phrase_2 / c_2) - tau * rep_phrase_2 # Repeated Phrase 3. # arccoth(x) = arctanh(1/x) - denominator = c_2 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) + denominator = c_2 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. + + # The final equation for B is split into 5 terms. term_1 = rep_exp_1 * rep_phrase_1 * c_6 * c_2 ** 2 @@ -436,12 +519,16 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): B = np.exp(-tau * c_2) * (term_1 - (term_2 + (rep_phrase_2 * term_3 + term_4) * c_6) * c_2 + term_5) / denominator + elif self.gamma > 1: + # Implementation of Case IV in Appendix B.1.2. + + rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1. + rep_phrase_2 = 0.5 * np.sqrt(disc) * tau - np.arctanh(2 * c_2 / np.sqrt(disc)) # Repeated Phrase 2. - rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1 - rep_phrase_2 = 0.5 * np.sqrt(disc) * tau - np.arctanh(2 * c_2 / np.sqrt(disc)) # Repeated Phrase 2 + denominator = 2 * c_1 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. - denominator = 2 * c_1 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator + # The final equation for B is split into 5 terms. term_1 = 2 * rep_exp_1 * rep_phrase_1 * c_4 * c_5 * (c_2 + 0.5 * np.sqrt(disc) * np.tanh(rep_phrase_2)) From 407288f31237a5e5d9cdedc1732ed8dfe04d5f1b Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Sat, 20 Mar 2021 14:43:12 +0530 Subject: [PATCH 053/103] Added docstrings. --- .../ou_model_jurek.py | 8 +-- .../ou_model_mudchanatongsuk.py | 58 ++++++++++++++----- 2 files changed, 48 insertions(+), 18 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index d2cedbf7..d971e10b 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -33,9 +33,9 @@ class StochasticControlJurek: def __init__(self): - #Characteristics of Training Data. - self.ticker_A = None # Ticker Symbol of first stock. - self.ticker_B = None # Ticker Symbol of second stock. + # Characteristics of Training Data. + self.ticker_A = None # Ticker Symbol of first stock. + self.ticker_B = None # Ticker Symbol of second stock. self.spread = None # Constructed spread from training data. self.time_array = None # Time indices of training data. self.delta_t = None # Time difference between each index in data, calculated in years. @@ -47,7 +47,7 @@ def __init__(self): # Params inputted by user. self.r = None # Rate of returns. - self.gamma = None # Coefficient of relative risk aversion. + self.gamma = None # Coefficient of relative risk aversion. self.beta = None # Rate of time preference. diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index ad6d77ae..1bfea946 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -15,37 +15,68 @@ import pandas as pd import scipy.optimize as so + class StochasticControlMudchanatongsuk: + """ + This class implements a stochastic control approach to the problem of pairs trading. + + We model the log-relationship between a pair of stock prices as an OrnsteinUhlenbeck process, + and use this to formulate a portfolio optimization based stochastic control problem. + We are able to obtain the optimal solution to this control problem in closed + form via the corresponding Hamilton-Jacobi-Bellman equation. This closed form solution + is calculated under a power utility on terminal wealth. + The parameters in the model are calculated using closed form maximum-likelihood estimation formulas. + """ + def __init__(self): - self.ticker_A = None - self.ticker_B = None - self.S = None - self.spread = None - self.time_array = None + # Characteristics of Training Data. + self.ticker_A = None # Ticker Symbol of first stock. + self.ticker_B = None # Ticker Symbol of second stock. + self.S = None # Log price of stock B in spread. + self.spread = None # Constructed spread from training data. + self.time_array = None # Time indices of training data. + self.delta_t = 1 / 251 # Time difference between each index in data, calculated in years. + + # Estimated params from training data. + self.sigma = None # Standard deviation of stock B. + self.mu = None # Drift of stock B. + self.k = None # Rate of mean reversion of spread. + self.theta = None # Long run mean of spread. + self.eta = None # Standard deviation of spread. + self.rho = None # Instantaneous correlation coefficient between two standard brownian motions. - self.delta_t = 1 / 251 - self.sigma = None - self.mu = None - self.k = None - self.theta = None - self.eta = None - self.rho = None + # Params inputted by user. + self.gamma = None # Parameter of utility function (self.gamma < 1) - self.gamma = None @staticmethod def _data_preprocessing(data): + """ + Helper function for input data preprocessing. + + :param data: (pd.DataFrame) Pricing data of both stocks in spread. + """ return data.ffill() + def fit(self, data: pd.DataFrame): + """ + This method uses inputted training data to calculate the spread and + estimate the parameters of the corresponding OU process. + + The spread construction implementation follows Section II A in Mudchanatongsuk (2008). + + :param data: (pd.DataFrame) Contains price series of both stocks in spread. + """ # Preprocessing data = self._data_preprocessing(data) self.time_array = np.arange(0, len(data)) * self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] + self.S = np.log(data.loc[:, self.ticker_B]) self.spread = np.log(data.loc[:, self.ticker_A]) - self.S @@ -174,7 +205,6 @@ def _estimate_params_log_likelihood(self): return sigma, mu, k, theta, eta, rho, max_log_likelihood - @staticmethod def _compute_log_likelihood(params, *args): """ From 112b5e33b9552232bebce4276a6dc3da34c5847c Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 22 Mar 2021 14:45:44 +0530 Subject: [PATCH 054/103] Completed code documentation and made changes for pylint 10/10/. --- .../ou_model_jurek.py | 20 +++---- .../ou_model_mudchanatongsuk.py | 54 ++++++++++++++++--- 2 files changed, 57 insertions(+), 17 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index d971e10b..60017929 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -10,6 +10,7 @@ `__ """ +# pylint: disable=invalid-name, too-many-instance-attributes, too-many-locals import numpy as np import pandas as pd import matplotlib.pyplot as plt @@ -37,6 +38,7 @@ def __init__(self): self.ticker_A = None # Ticker Symbol of first stock. self.ticker_B = None # Ticker Symbol of second stock. self.spread = None # Constructed spread from training data. + self.scaled_spread_weights = None # Scaled weights for the prices in spread. self.time_array = None # Time indices of training data. self.delta_t = None # Time difference between each index in data, calculated in years. @@ -104,9 +106,9 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: raise Exception("ADF statistic test failure.") # Scaling the weights such that they sum to 1. - self.eg_scaled_vectors = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() + self.scaled_spread_weights = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() - self.spread = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) + self.spread = (total_return_indices * self.scaled_spread_weights).sum(axis=1) self.spread.plot() plt.show() @@ -213,7 +215,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g W = np.ones(len(t)) # Wealth is normalized to one. # Calculating the spread with weights calculated from training data. - S = (total_return_indices * self.eg_scaled_vectors).sum(axis=1) + S = (total_return_indices * self.scaled_spread_weights).sum(axis=1) S = S.to_numpy() # TODO : This conversion in fit seems to have changed the estimated values. @@ -267,13 +269,13 @@ def _AB_calc_1(self, tau): # Note: gamma_0 is not always > 0. - A = self._A_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function A. + A = self._A_calc_1(tau, c_1, c_2, disc, gamma_0) # Calculating value of function A. B = self._B_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function B. return A, B - def _A_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): + def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0): """ This method calculates the value of function A as described in the paper for investor with utility_type = 1. The implementation follows Appendix A.2.1 in the paper. @@ -283,7 +285,6 @@ def _A_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): :param tau: (np.array) Array with time till completion in years. :param c_1: (float) Value of variable c_1 in Appendix A.2.1. :param c_2: (float) Value of variable c_2 in Appendix A.2.1. - :param c_3: (float) Value of variable c_3 in Appendix A.2.1. :param disc: (float) Value of discriminant in Appendix A.2.1. :param gamma_0: (float) Value of variable gamma_0 in Appendix A.2.1. """ @@ -385,13 +386,13 @@ def _AB_calc_2(self, tau): gamma_0 = 4 * (self.k + self.r) * (self.r - self.beta - self.k) / ((2 * self.r - self.beta) ** 2) - A = self._A_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function A. + A = self._A_calc_2(tau, c_1, c_2, disc, gamma_0) # Calculating value of function A. B = self._B_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function B. return A, B - def _A_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): + def _A_calc_2(self, tau, c_1, c_2, disc, gamma_0): """ This method calculates the value of function A as described in the paper for investor with utility_type = 2. The implementation follows Appendix B.1.1 in the paper. @@ -402,13 +403,12 @@ def _A_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): :param tau: (np.array) Array with time till completion in years. :param c_1: (float) Value of variable c_1 in Appendix B.1.1. :param c_2: (float) Value of variable c_2 in Appendix B.1.1. - :param c_3: (float) Value of variable c_3 in Appendix B.1.1. :param disc: (float) Value of discriminant in Appendix B.1.1. :param gamma_0: (float) Value of variable gamma_0 in Appendix B.1.1. """ # Same calculation as for general CRRA Investor. - return self._A_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) + return self._A_calc_1(tau, c_1, c_2, disc, gamma_0) def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 1bfea946..35b73c23 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -10,6 +10,7 @@ `__ """ +# pylint: disable=invalid-name, too-many-instance-attributes import math import numpy as np import pandas as pd @@ -74,9 +75,11 @@ def fit(self, data: pd.DataFrame): # Preprocessing data = self._data_preprocessing(data) + # Setting instance attributes. self.time_array = np.arange(0, len(data)) * self.delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] + # Calculating the spread. self.S = np.log(data.loc[:, self.ticker_B]) self.spread = np.log(data.loc[:, self.ticker_A]) - self.S @@ -91,7 +94,8 @@ def fit(self, data: pd.DataFrame): def _estimate_params(self): """ - Closed Form Estimators of params. + This method implements the closed form solutions for estimators of the model parameters. + These formulas for the estimators are given in Appendix of Mudchanatongsuk (2007). """ N = len(self.spread) - 1 @@ -130,18 +134,31 @@ def _estimate_params(self): def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): + """ + This method calculates the final optimal portfolio weights for the calculated spread. + + The calculation of weights follows Section III in Mudchanatongsuk (2008), specifically equation 28. + + :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param gamma: (float) Parameter of utility function (gamma < 1) + """ # Preprocessing data = self._data_preprocessing(data) + # Setting instance attributes. self.gamma = gamma t = np.arange(0, len(data)) * self.delta_t tau = t[-1] - t + + # Calculating spread. x = np.log(data.iloc[:, 0]) - np.log(data.iloc[:, 1]) x = x.to_numpy() # Converting from pd.Series to numpy array. + # Calculating the alpha and beta functions. alpha_t, beta_t = self._alpha_beta_calc(tau) + # Calculating the final optimal portfolio weights. h = (1 / (1 - self.gamma)) * (beta_t + 2 * np.multiply(x, alpha_t) - self.k * (x - self.theta) / self.eta ** 2 + self.rho * self.theta / self.eta + 0.5) @@ -150,9 +167,15 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): def _alpha_beta_calc(self, tau): + """ + This helper function computes the alpha and beta functions + as given in equation 24 and 25 of Mudchanatongsuk (2008). + + :param tau: (np.array) Array with time till completion in years. + """ - sqrt_gamma = np.sqrt(1 - self.gamma) - exp_calc = np.exp(2 * self.k * tau / sqrt_gamma) + sqrt_gamma = np.sqrt(1 - self.gamma) # Repeating Calculation involving gamma. + exp_calc = np.exp(2 * self.k * tau / sqrt_gamma) # Repeating Calculation involving gamma and tau series. alpha_t = self._alpha_calc(sqrt_gamma, exp_calc) beta_t = self._beta_calc(sqrt_gamma, exp_calc) @@ -161,7 +184,14 @@ def _alpha_beta_calc(self, tau): def _alpha_calc(self, sqrt_gamma, exp_calc): + """ + This helper function computes the alpha function in equation 24. + + :param sqrt_gamma: (float) Repeating value. + :param exp_calc: (np.array) Repeating series of values. + """ + # The equation for calculation of alpha is split into two parts. left_calc = self.k * (1 - sqrt_gamma) / (2 * (self.eta ** 2)) right_calc = 2 * sqrt_gamma / (1 - sqrt_gamma - (1 + sqrt_gamma) * exp_calc) @@ -170,11 +200,18 @@ def _alpha_calc(self, sqrt_gamma, exp_calc): def _beta_calc(self, sqrt_gamma, exp_calc): + """ + This helper function computes the beta function in equation 25. + + :param sqrt_gamma: (float) Repeating value. + :param exp_calc: (np.array) Repeating series of values. + """ - left_calc = 1/(2 * (self.eta ** 2) * ((1 - sqrt_gamma) - (1 + sqrt_gamma)*exp_calc)) + # The equation for calculation of beta is split into two parts. + left_calc = 1/(2 * (self.eta ** 2) * ((1 - sqrt_gamma) - (1 + sqrt_gamma) * exp_calc)) - right_calc = self.gamma * sqrt_gamma * (self.eta ** 2 + 2*self.rho*self.sigma*self.eta) * ((1 - exp_calc) ** 2) - \ - self.gamma * (self.eta ** 2 + 2*self.rho*self.sigma*self.eta + 2*self.k*self.theta) * (1 - exp_calc) + right_calc = self.gamma * sqrt_gamma * (self.eta ** 2 + 2 * self.rho * self.sigma * self.eta) * ((1 - exp_calc) ** 2) - \ + self.gamma * (self.eta ** 2 + 2 * self.rho * self.sigma * self.eta + 2 * self.k * self.theta) * (1 - exp_calc) return left_calc * right_calc @@ -209,6 +246,9 @@ def _estimate_params_log_likelihood(self): def _compute_log_likelihood(params, *args): """ Helper function computes log likelihood function for a set of params. + This implementation follows Appendix of Mudchanatongsuk (2008). + + param params: (tuple) Contains values of set params. """ # Setting given parameters @@ -238,7 +278,7 @@ def _compute_log_likelihood(params, *args): f_y_denm = (2 * math.pi * np.sqrt(np.linalg.det(matrix))) f_y = np.exp(-0.5 * np.einsum('ij,ij->j', vec, np.linalg.inv(matrix) @ vec)) / f_y_denm - except FloatingPointError as r: + except FloatingPointError: return 0 From 8b8f6ef1c2dbcaeb59fe2b4682f57ae00aa6c88d Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 22 Mar 2021 16:31:10 +0530 Subject: [PATCH 055/103] Added implementation of Theorem 3 and 4 in Jurek paper. --- .../ou_model_jurek.py | 78 +++++++++++++++++++ 1 file changed, 78 insertions(+) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 60017929..29755a20 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -11,6 +11,7 @@ """ # pylint: disable=invalid-name, too-many-instance-attributes, too-many-locals +import cvxpy as cp import numpy as np import pandas as pd import matplotlib.pyplot as plt @@ -243,6 +244,83 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g return N / W # We return the optimal allocation of spread asset scaled by wealth. + def optimal_portfolio_weights_fund_flows(self, data: pd.DataFrame, f: float, gamma: float = 1, r: float = 0.05): + """ + Implementation of Theorem 4 in Jurek (2007). + + This method calculates the optimal portfolio allocation of an agent with + constant relative risk aversion with utility defined over terminal wealth, + (utility_type = 1) , in the presence of fund flows. + + Note: For all values of gamma, the presence of fund flows affect the general portfolio rule + only by introducing a coefficient of proportionality. + + Also note, this method is only applicable for investors with utility defined over terminal wealth. + + What is f? + + f is the coefficient of proportionality for fund flows and is the drift term in the + stochastic process equation for fund flows. (Refer Appendix C) + + :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param gamma: (float) coefficient of relative risk aversion. + :param f: (float) coefficient of proportionality (assumed to be positive). + :param r: (float) Rate of Returns. + """ + + N = self.optimal_portfolio_weights(data, utility_type=1, gamma=gamma, r=r) + + return (1 / (1 + f)) * N + + + def _stabilization_region_calc(self, S, tau, utility_type = 1): + """ + Implementation of Theorem 3 in Jurek (2007). + + :param S: (np.array) spread. + :param tau: (np.array) Array with time till completion in years. + :param utility_type: (int) Flag signifies type of investor preferences. + """ + + if self.gamma == 1: + # TODO : Is the region defined at gamma = 1? + # Calculation of A and B functions are not done in case of gamma = 1. (Need to implement Appendix A.1 and B.2). + + raise NotImplementedError("Calculation of stabilization region is not implemented for gamma = 1.") + + A = None + B = None + if utility_type == 1: + A, B = self._AB_calc_1(tau) + + elif utility_type == 2: + A, B = self._AB_calc_2(tau) + + # Calculating phi (Refer Equation 17 in Jurek (2007)). + phi = (2 * A / self.gamma) - ((self.k + self.r) / (self.gamma * self.sigma ** 2)) + # Note : phi < 0. + + term_1 = (self.k * self.mu + self.sigma ** 2 * B) / (self.gamma * self.sigma ** 2) + term_2 = np.sqrt(-phi) + + max_bound = np.zeros(len(tau)) + min_bound = np.zeros(len(tau)) + + for ind in range(len(tau)): + S = cp.Variable() + constraint = abs(phi[ind] * S + term_1[ind]) <= term_2[ind] - 1e-6 + + prob_max = cp.Problem(cp.Maximize(S), constraint) + prob_max.solve() + max_bound[ind] = prob_max.value + + prob_min = cp.Problem(cp.Minimize(S), constraint) + prob_min.solve() + min_bound[ind] = prob_min.value + + return min_bound, max_bound + + def _AB_calc_1(self, tau): """ This helper function computes the A and B functions for investors with utility_type = 1. From 3027faae3ae9e846c5a52654100ad46bb9298355 Mon Sep 17 00:00:00 2001 From: JuanKo96 Date: Tue, 23 Mar 2021 12:38:40 +0900 Subject: [PATCH 056/103] Fix some minor issues after reviewing PR --- .../basic_distance_approach.py | 45 +++++++++++++------ .../distance_approach/distance_approach.rst | 6 ++- tests/test_basic_distance_approach.py | 12 ++--- 3 files changed, 41 insertions(+), 22 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index 6ccbcbd7..4cbf1734 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -41,7 +41,8 @@ def __init__(self): devadarsh.track('DistanceStrategy') - def form_pairs(self, train_data, method='standard', industry_dict=None, num_top=5, skip_top=0, list_names=None): + def form_pairs(self, train_data, method='standard', industry_dict=None, num_top=5, skip_top=0, selection_pool=50, + list_names=None): """ Forms pairs based on input training data. @@ -79,6 +80,7 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= :param list_names: (list) List containing names of elements if Numpy array is used as input. :param method: (str) Methods to use for sorting pairs [``standard`` by default, ``variance``, ``zero_crossing``]. + :param selection_pool: (int) Number of pairs to use before sorting them with the selection method :param industry_dict: (dict) Dictionary matching ticker to industry group. """ @@ -93,17 +95,11 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= normalized = normalized.dropna(axis=0) # If industry dictionary is given, pairs are matched within the same industry group - if industry_dict: - # Finding closest pairs for each element, excluding duplicates - all_pairs = self.find_pair(normalized, industry_dict) - - else: - # Finding closest pairs for each element, excluding duplicates - all_pairs = self.find_pair(normalized) + all_pairs = self.find_pair(normalized, industry_dict) # Choosing needed pairs to construct a portfolio - self.pairs = self.sort_pairs(all_pairs, num_top, skip_top) + self.pairs = self.sort_pairs(all_pairs, selection_pool) # Calculating historical volatility of pair portfolios (diffs of normalized prices) self.train_std = self.find_volatility(normalized, self.pairs) @@ -118,17 +114,38 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= # based on the method self.selection_method(method, num_top, skip_top) + # Storing only the necessary values for pairs selected in the above + self.num_crossing = {pair: self.num_crossing[pair] for pair in self.pairs} + self.train_std = {pair: self.train_std[pair] for pair in self.pairs} + self.train_portfolio = self.train_portfolio[self.train_portfolio.columns + .intersection([str(pair) for pair in self.pairs])] + def selection_method(self, method, num_top, skip_top): """ - Select pairs based on the method. + Select pairs based on the method. This module helps sorting selected pairs for the given method + in the formation period. + + :param method: (str) Methods to use for sorting pairs [``standard`` by default, ``variance``, + ``zero_crossing``]. + :param num_top: (int) Number of top pairs to use for portfolio formation. + :param skip_top:(int) Number of first top pairs to skip. For example, use skip_top=10 + if you'd like to take num_top pairs starting from the 10th one. """ - if method not in ['standard', 'zero_crossing', 'variance']: + if method not in ['standard', 'industry', 'zero_crossing', 'variance']: # Raise an error if the given method is inappropriate. raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, " - "‘zero_crossing’, or 'variance'") + "'industry', ‘zero_crossing’, or 'variance'") + + if method == 'standard': + + self.pairs = self.pairs[skip_top:(skip_top + num_top)] - if method == 'zero_crossing': + elif method == 'industry': + + self.pairs = self.pairs[skip_top:(skip_top + num_top)] + + elif method == 'zero_crossing': # Sorting pairs from the dictionary by the number of zero crossings in a descending order sorted_pairs = sorted(self.num_crossing.items(), key=lambda x: x[1], reverse=True) @@ -141,7 +158,7 @@ def selection_method(self, method, num_top, skip_top): self.pairs = pairs_selected - elif method == 'variance': + else: # Sorting pairs from the dictionary by the size of variance in a descending order sorted_pairs = sorted(self.train_std.items(), key=lambda x: x[1], reverse=True) diff --git a/docs/source/distance_approach/distance_approach.rst b/docs/source/distance_approach/distance_approach.rst index 2cd872a6..2feb9750 100644 --- a/docs/source/distance_approach/distance_approach.rst +++ b/docs/source/distance_approach/distance_approach.rst @@ -96,9 +96,10 @@ As basic pairs formation confirms declining profitability in pairs trading, some selection criteria have emerged. Here, we describe three different methods from the basic approach in selecting pairs for trading. -First is only allowing for matching securities within the same industry group. The second is sorting +First is only allowing for matching securities within the same industry group . The second is sorting selected pairs based on the number of zero-crossings in the formation period and the third is sorting selected pairs based on the historical standard deviation where pairs with high standard deviation are selected. +These selection methods are inspired by the work by Do and Faff (2010, 2012). 1. **Pairs within the same industry group** @@ -125,7 +126,8 @@ form of the number of zero crossings. 3. **Pairs with a higher historical standard deviation** The historical standard deviation calculated in the formation period can also be a criterion to sort -selected pairs. +selected pairs. According to the work of Do and Faff(2010), as having a small SSD decreases the variance +of the spread, this approach could increase the expected profitability of the method. After pairs were matched, by sorting the pairs based on their historical standard deviation in the formation period, we can select top :math:`n` pairs that have the highest standard deviation. diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index 7a265966..626c5c58 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -62,8 +62,8 @@ def test_form_pairs(self): strategy_variance = DistanceStrategy() # Performing the pairs formation step - strategy.form_pairs(self.train_data, num_top=5, skip_top=0) - strategy_industry.form_pairs(self.train_data, method='standard', + strategy.form_pairs(self.train_data, method = 'standard', num_top=5, skip_top=0) + strategy_industry.form_pairs(self.train_data, method='industry', industry_dict=self.industry_dict, num_top=5, skip_top=0) strategy_zero_crossing.form_pairs(self.train_data, method='zero_crossing', num_top=5, skip_top=0) strategy_variance.form_pairs(self.train_data, method='variance', num_top=5, skip_top=0) @@ -86,10 +86,10 @@ def test_form_pairs(self): ('EFA', 'EWQ'), ('EPP', 'SPY')] expected_pairs_industry = [('EFA', 'EWQ'), ('EFA', 'EWU'), ('SPY', 'VPL'), ('EEM', 'EWU'), ('DIA', 'SPY')] - expected_pairs_zero_crossing = [('EPP', 'SPY'), ('EFA', 'VGK'), ('EPP', 'VPL'), - ('EWQ', 'VGK'), ('EFA', 'EWQ')] - expected_pairs_variance = [('EPP', 'SPY'), ('EPP', 'VPL'), ('EFA', 'EWQ'), - ('EWQ', 'VGK'), ('EFA', 'VGK')] + expected_pairs_zero_crossing = [('EPP', 'SPY'), ('DIA', 'EWJ'), ('EEM', 'EWJ'), + ('EEM', 'EFA'), ('EWU', 'VPL')] + expected_pairs_variance = [('IEF', 'TIP'), ('EWU', 'FXI'), ('SPY', 'VGK'), + ('EWJ', 'EWQ'), ('EEM', 'EWQ')] self.assertCountEqual(strategy.pairs, expected_pairs) self.assertCountEqual(strategy_industry.pairs, expected_pairs_industry) From 699b19f26e43da4334d6e535efa1a16e9f489a86 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 23 Mar 2021 14:31:03 +0530 Subject: [PATCH 057/103] Minor Fixes for Theorem 3. --- .../stochastic_control_approach/ou_model_jurek.py | 11 +++++++++-- 1 file changed, 9 insertions(+), 2 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 29755a20..bdfaaaa4 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -220,6 +220,13 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g S = S.to_numpy() # TODO : This conversion in fit seems to have changed the estimated values. + min_bound, max_bound = self._stabilization_region_calc(S, tau, utility_type) + + plt.plot(S) + plt.plot(min_bound) + plt.plot(max_bound) + plt.show() + N = None # The optimal weights equation is the same for both types of utility functions. # For gamma = 1, the outputs weights are identical for both types of utility functions, @@ -300,7 +307,7 @@ def _stabilization_region_calc(self, S, tau, utility_type = 1): phi = (2 * A / self.gamma) - ((self.k + self.r) / (self.gamma * self.sigma ** 2)) # Note : phi < 0. - term_1 = (self.k * self.mu + self.sigma ** 2 * B) / (self.gamma * self.sigma ** 2) + term_1 = (self.k * self.mu + (self.sigma ** 2) * B) / (self.gamma * self.sigma ** 2) term_2 = np.sqrt(-phi) max_bound = np.zeros(len(tau)) @@ -308,7 +315,7 @@ def _stabilization_region_calc(self, S, tau, utility_type = 1): for ind in range(len(tau)): S = cp.Variable() - constraint = abs(phi[ind] * S + term_1[ind]) <= term_2[ind] - 1e-6 + constraint = [cp.abs(phi[ind] * S + term_1[ind]) <= term_2[ind] - 1e-6] prob_max = cp.Problem(cp.Maximize(S), constraint) prob_max.solve() From e2eb1b6456a17c38ffdca3fb644535ad6bb81deb Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 23 Mar 2021 16:14:45 +0530 Subject: [PATCH 058/103] [Debug] Debugging changes for V_squared issue. --- .../ou_model_mudchanatongsuk.py | 29 ++++++++++++++----- 1 file changed, 22 insertions(+), 7 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 35b73c23..56ca1a39 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -85,10 +85,10 @@ def fit(self, data: pd.DataFrame): self.spread = self.spread.to_numpy() # Converting from pd.Series to numpy array. self.S = self.S.to_numpy() # Converting from pd.Series to numpy array. - #self._estimate_params() #TODO : V_squared estimator is returning a negative value which is incorrect. Need to check why? + self._estimate_params() params = self._estimate_params_log_likelihood() - print(params) + print(f"Params from likelihood : {params[:-1]}") self.sigma, self.mu, self.k,self.theta, self.eta, self.rho = params[:-1] @@ -108,17 +108,18 @@ def _estimate_params(self): p = (1 / (N * np.power(self.spread[:-1], 2).sum() - self.spread[:-1].sum() ** 2)) * \ (N * np.multiply(self.spread[1:], self.spread[:-1]).sum() - (self.spread[N] - self.spread[0]) * np.sum(self.spread[:-1]) - self.spread[:-1].sum() ** 2) + # TODO : This calculation of p is incorrect. Calculation of q is correct. + + p = np.exp(-0.18565618 * self.delta_t) # Correct value of p calculated from likelihood params. + print(p) q = (self.spread[N] - self.spread[0] + (1 - p) * self.spread[:-1].sum()) / N V_squared = (1 / N) * (self.spread[N] ** 2 - self.spread[0] ** 2 + (1 + p ** 2) * np.power(self.spread[:-1], 2).sum() - 2 * p * np.multiply(self.spread[1:], self.spread[:-1]).sum() - N * q) + # TODO : This calculation of V_squared is incorrect. - - C = (1/(N * np.sqrt(V_squared * S_squared))) * (np.multiply(self.spread[1:], np.diff(self.S)).sum() - - p * np.multiply(self.spread[:-1], np.diff(self.S)).sum() - - m * (self.spread[N] - self.spread[0]) - - m * (1 - p) * self.spread[:-1].sum()) + print(V_squared) self.sigma = np.sqrt(S_squared / self.delta_t) @@ -128,10 +129,24 @@ def _estimate_params(self): self.theta = q / (1 - p) + V_squared = (0.3038416 ** 2) * (1 - p ** 2) / (2 * self.k) # Correct value of V_squared calculated from likelihood params. + + print(V_squared) + + + C = (1/(N * np.sqrt(V_squared * S_squared))) * (np.multiply(self.spread[1:], np.diff(self.S)).sum() + - p * np.multiply(self.spread[:-1], np.diff(self.S)).sum() + - m * (self.spread[N] - self.spread[0]) + - m * (1 - p) * self.spread[:-1].sum()) + + + self.eta = np.sqrt(2 * self.k * V_squared / (1 - p ** 2)) self.rho = self.k * C * np.sqrt(V_squared * S_squared) / (self.eta * self.sigma * (1 - p)) + print(f"Params from closed form : {(self.sigma, self.mu, self.k, self.theta, self.eta, self.rho)}") + def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): """ From fa4374ca6bab85870446084c04bd6e8f1b1c854e Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 23 Mar 2021 19:17:07 +0100 Subject: [PATCH 059/103] Minor adjustments to Basic Distance Strategy --- .../basic_distance_approach.py | 18 +++++++----------- tests/test_basic_distance_approach.py | 4 ++-- 2 files changed, 9 insertions(+), 13 deletions(-) diff --git a/arbitragelab/distance_approach/basic_distance_approach.py b/arbitragelab/distance_approach/basic_distance_approach.py index 4cbf1734..bf7d36af 100644 --- a/arbitragelab/distance_approach/basic_distance_approach.py +++ b/arbitragelab/distance_approach/basic_distance_approach.py @@ -80,7 +80,7 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= :param list_names: (list) List containing names of elements if Numpy array is used as input. :param method: (str) Methods to use for sorting pairs [``standard`` by default, ``variance``, ``zero_crossing``]. - :param selection_pool: (int) Number of pairs to use before sorting them with the selection method + :param selection_pool: (int) Number of pairs to use before sorting them with the selection method. :param industry_dict: (dict) Dictionary matching ticker to industry group. """ @@ -95,7 +95,6 @@ def form_pairs(self, train_data, method='standard', industry_dict=None, num_top= normalized = normalized.dropna(axis=0) # If industry dictionary is given, pairs are matched within the same industry group - all_pairs = self.find_pair(normalized, industry_dict) # Choosing needed pairs to construct a portfolio @@ -132,19 +131,15 @@ def selection_method(self, method, num_top, skip_top): if you'd like to take num_top pairs starting from the 10th one. """ - if method not in ['standard', 'industry', 'zero_crossing', 'variance']: + if method not in ['standard', 'zero_crossing', 'variance']: # Raise an error if the given method is inappropriate. raise Exception("Please give an appropriate method for sorting pairs between ‘standard’, " - "'industry', ‘zero_crossing’, or 'variance'") + "‘zero_crossing’, or 'variance'") if method == 'standard': self.pairs = self.pairs[skip_top:(skip_top + num_top)] - elif method == 'industry': - - self.pairs = self.pairs[skip_top:(skip_top + num_top)] - elif method == 'zero_crossing': # Sorting pairs from the dictionary by the number of zero crossings in a descending order @@ -270,11 +265,12 @@ def get_pairs(self): def get_num_crossing(self): """ - Outputs pairs that were created in the pairs formation step with its number of zero crossing + Outputs pairs that were created in the pairs formation step with its number of zero crossing. - :return: (dictionary) Dictionary with keys as pairs and values as the number of zero + :return: (dict) Dictionary with keys as pairs and values as the number of zero crossings for pairs. """ + return self.num_crossing def count_number_crossing(self): @@ -285,7 +281,7 @@ def count_number_crossing(self): future convergence, this method calculates the number of times the normalized spread crosses the value zero which measures the frequency of divergence and convergence between two securities. - :return: (dictionary) Dictionary with keys as pairs and values as the number of zero + :return: (dict) Dictionary with keys as pairs and values as the number of zero crossings for pairs. """ diff --git a/tests/test_basic_distance_approach.py b/tests/test_basic_distance_approach.py index 626c5c58..6dddc9ad 100644 --- a/tests/test_basic_distance_approach.py +++ b/tests/test_basic_distance_approach.py @@ -63,7 +63,7 @@ def test_form_pairs(self): # Performing the pairs formation step strategy.form_pairs(self.train_data, method = 'standard', num_top=5, skip_top=0) - strategy_industry.form_pairs(self.train_data, method='industry', + strategy_industry.form_pairs(self.train_data, method='standard', industry_dict=self.industry_dict, num_top=5, skip_top=0) strategy_zero_crossing.form_pairs(self.train_data, method='zero_crossing', num_top=5, skip_top=0) strategy_variance.form_pairs(self.train_data, method='variance', num_top=5, skip_top=0) @@ -249,4 +249,4 @@ def test_exceptions(self): # When trying to get pairs with inappropriate method with self.assertRaises(Exception): - strategy.selection_method(method='wrong input',num_top=5,skip_top=0) + strategy.selection_method(method='wrong input', num_top=5, skip_top=0) From dd95f369f3aff0acc7c1fec01c69fa12d66ee23b Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 23 Mar 2021 19:17:35 +0100 Subject: [PATCH 060/103] Updated changelog to Basic Distance Strategy --- docs/source/changelog.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/source/changelog.rst b/docs/source/changelog.rst index 1f1c402e..9697afec 100644 --- a/docs/source/changelog.rst +++ b/docs/source/changelog.rst @@ -12,6 +12,8 @@ Changelog .. For Help: https://releases.readthedocs.io/en/latest/index.html +* :feature:`42` Options to sort pairs by zero-crossings, variance, same industry group added to the Basic Distance Strategy. +* :support:`42` Updated Basic Distance Strategy documentation. * :feature:`40` Vine Copula Partner Selection Approaches added to the Copula Approach Module. * :support:`40` Vine Copula Partner Selection Approaches documentation. * :support:`38` Removed TensorFlow from requirements and adjusted installation guide. From 21ca601e883bad07ce7b2b1094e12363eb921d0d Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 24 Mar 2021 13:33:43 +0530 Subject: [PATCH 061/103] Changed Exceptions to Warnings in Jurek class. --- .../ou_model_jurek.py | 29 +++++++++---------- 1 file changed, 13 insertions(+), 16 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index bdfaaaa4..41b8e922 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -11,6 +11,7 @@ """ # pylint: disable=invalid-name, too-many-instance-attributes, too-many-locals +import warnings import cvxpy as cp import numpy as np import pandas as pd @@ -87,6 +88,9 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: Value can be one of the following: (0.90, 0.95, 0.99). """ + if len(data) < (10 / delta_t): + warnings.warn("Please make sure length of training data is greater than 10 years.") + # Setting instance attributes. self.delta_t = delta_t self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] @@ -104,7 +108,7 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: if eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc[f'{int(significance_level * 100)}%', 0]: # Making sure that the data passes the ADF statistic test. print(eg_adf_statistics) - raise Exception("ADF statistic test failure.") + warnings.warn("ADF statistic test failure.") # Scaling the weights such that they sum to 1. self.scaled_spread_weights = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() @@ -113,13 +117,8 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: self.spread.plot() plt.show() - # TODO : This implementation of spread might be incorrect. - # The values of estimators calculated do not match what is expected. - - self.spread = self.spread.to_numpy() # TODO : This conversion seems to have changed the estimated values. Not sure why? - params = self._estimate_params(self.spread) self.mu, self.k, self.sigma = params @@ -220,12 +219,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g S = S.to_numpy() # TODO : This conversion in fit seems to have changed the estimated values. - min_bound, max_bound = self._stabilization_region_calc(S, tau, utility_type) - - plt.plot(S) - plt.plot(min_bound) - plt.plot(max_bound) - plt.show() + self._stabilization_region_calc(S, tau, utility_type) N = None # The optimal weights equation is the same for both types of utility functions. @@ -290,10 +284,10 @@ def _stabilization_region_calc(self, S, tau, utility_type = 1): """ if self.gamma == 1: - # TODO : Is the region defined at gamma = 1? - # Calculation of A and B functions are not done in case of gamma = 1. (Need to implement Appendix A.1 and B.2). + # Calculation of A and B functions are not done in case of gamma = 1. (Refer Appendix A.1 and B.2). - raise NotImplementedError("Calculation of stabilization region is not implemented for gamma = 1.") + warnings.warn("Calculation of stabilization region is not implemented for gamma = 1.") + return A = None B = None @@ -325,7 +319,10 @@ def _stabilization_region_calc(self, S, tau, utility_type = 1): prob_min.solve() min_bound[ind] = prob_min.value - return min_bound, max_bound + plt.plot(S) + plt.plot(min_bound) + plt.plot(max_bound) + plt.show() def _AB_calc_1(self, tau): From ca06c71fe297af9102214dddc7f63b508824589e Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 24 Mar 2021 16:46:01 +0530 Subject: [PATCH 062/103] Adding Sphinx Documentation. --- docs/source/index.rst | 2 + .../ou_model_jurek.rst | 102 ++++++++++++++++++ .../ou_model_mudchanatongsuk.rst | 6 ++ 3 files changed, 110 insertions(+) create mode 100644 docs/source/stochastic_control_approach/ou_model_jurek.rst create mode 100644 docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst diff --git a/docs/source/index.rst b/docs/source/index.rst index f9e4cc7d..bea5dafd 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -113,6 +113,8 @@ This project is licensed under an all rights reserved licence. :hidden: stochastic_control_approach/introduction + stochastic_control_approach/ou_model_jurek + stochastic_control_approach/ou_model_mudchanatongsuk .. toctree:: :maxdepth: 2 diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst new file mode 100644 index 00000000..f0a53b6d --- /dev/null +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -0,0 +1,102 @@ +.. _stochastic_control_approach_strategies-ou_model_jurek: + +.. note:: + The following implementations and documentation closely following work: + + `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. `__. + + +============== +OU Model Jurek +============== + +Introduction +############ + +In this module, we derive the optimal dynamic strategy for arbitrageurs with a finite horizon and +non-myopic preferences facing a mean-reverting arbitrage opportunity (e.g. an equity pairs +trade). + +The law of one price asserts that - in a frictionless market - securities with identical payoffs +must trade at identical prices. If this were not the case, arbitrageurs could generate a riskless +profit by supplying (demanding) the expensive (cheap) asset until the mispricing was eliminated. +Of course, real world markets are not frictionless, and the prices of securities with identical payoffs +may significantly diverge for extended periods of time. Arbitrageurs can earn potentially attractive +profits by taking offsetting positions in these relatively mispriced securities, but a worsening of the +mispricing can result in sizable capital losses. + +Unlike textbook arbitrages, which generate riskless profits and require no capital commitments, +exploiting real-world mispricings requires the assumption of some combination of horizon and divergence risk. +These two risks represent the uncertainty about whether the mispricing will converge before the positions +must be closed (or profits reported) and the possibility of a worsening in the mispricing prior to its elimination. + +While a complete treatment of optimal arbitrage and price formation requires a general equilibrium framework, +this paper takes on the more modest goal of examining the arbitrageur's strategy in +partial equilibrium. + +Modelling +######### + +To capture the presence of horizon and divergence risk, we model the dynamics of the mispricing +using a mean-reverting stochastic process. Under this process, although the mispricing is guaranteed +to be eliminated at some future date, the timing of convergence, as well as the maximum magnitude +of the mispricing prior to convergence, are uncertain. With this assumption, we are able to derive +the arbitrageur's optimal dynamic portfolio policy for a set of general, non-myopic preference +specifications, including CRRA utility defined over wealth at a finite horizon and Epstein-Zin +utility defined over intermediate cash flows (e.g. fees). This allows us to analytically examine the +role of intertemporal hedging demands in arbitrage activities and represents a novel contribution +relative to the commonly assumed log utility specification, under which hedging demands are absent. + +We find that, in the presence of horizon and divergence risk, there is a critical level of the mispricing +beyond which further divergence in the mispricing precipitates a reduction in the allocation. +Although a divergence in the mispricing results in an improvement in the instantaneous investment +opportunity set and should induce added participation by rational arbitrageurs, this effect can be +more than offset by the combination of the loss in wealth and the nearing of the evaluation date, +which reduce the arbitrageur's effective risk-bearing capacity. The complex tradeoff between these +two effects leads to the creation of a time-varying boundary, outside of which continued divergence +of the mispricing induces rational arbitrageurs to cut their losses and decrease their allocations to +the mispricing. + +The central assumption of our model is that the arbitrage opportunity is described by an +Ornstein-Uhlenbeck process (henceforth OU). The OU process captures the two key features of a +real-world mispricing: the convergence times are uncertain and the mispricing can diverge arbitrarily far +from its mean prior to convergence. + +The optimal trading strategies we derive are self-financing and can be interpreted as the optimal +trading rules for a fund which is not subject to withdrawals but also cannot raise additional assets +(i.e. a closed-end fund). The dynamics of the optimal allocation to the arbitrage opportunity are +driven by two factors: the necessity of maintaining wealth (equity) above zero and the proximity +of the arbitrageur's terminal evaluation date, which affects his appetite for risk. + + +Investor Preferences +******************** + +We consider two alternative preferences structures for the arbitrageur in our continuous-time +model. In the first, we assume that the agent has constant relative risk aversion and maximizes +the discounted utility of terminal wealth. The arbitrageur's value function at time :math:`t` - denoted by +:math:`V_t` - takes the form: + +.. math:: + + V_{t}=\sup E_{t}\left[e^{-\beta(T-t)} \frac{W_{T}^{1-\gamma}}{1-\gamma}\right] + +The second preference structure we consider is the recursive utility of Epstein and Zin (1989, 1991), +which allows the elasticity of intertemporal substitution and the coefficient of relative risk aversion +to vary independently. Under this preference specification, the value function of the arbitrageur is +given by: + +.. math:: + + V_{t}=\sup E_{t}\left[\int_{t}^{T} f\left(C_{s}, J_{s}\right) d s\right] + +where :math:`f\left(C_{s}, J_{s}\right)` is the normalized aggregator for the continuous-time Epstein-Zin utility function: + +.. math:: + + f\left(C_{t}, J_{t}\right)=\beta(1-\gamma) \cdot J_{t} \cdot\left[\log C_{t}-\frac{1}{1-\gamma} \log \left((1-\gamma) J_{t}\right)\right] + + +Here we consider the special case of a unit elasticity of intertemporal substitution (:math:`\psi = 1`). + + diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst new file mode 100644 index 00000000..48a8879b --- /dev/null +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -0,0 +1,6 @@ +.. _stochastic_control_approach_strategies-ou_model_mudchanatongsuk: + + +======================== +OU Model Mudchanatongsuk +======================== From d9a0a8e56dd4213243cf8161d3ebab52d140431b Mon Sep 17 00:00:00 2001 From: PanPip Date: Wed, 24 Mar 2021 13:23:58 +0100 Subject: [PATCH 063/103] Updated Basic Distance Strategy sphinx docs --- .../source/distance_approach/distance_approach.rst | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/docs/source/distance_approach/distance_approach.rst b/docs/source/distance_approach/distance_approach.rst index 2feb9750..4c54d443 100644 --- a/docs/source/distance_approach/distance_approach.rst +++ b/docs/source/distance_approach/distance_approach.rst @@ -115,11 +115,11 @@ gives a dictionary of industry group as an input. 2. **Pairs with a higher number of zero-crossings** -The number of zero crossings in the formation period does have some usefulness in predicting the future -convergence according to the work of Do and Faff (2010). +The number of zero crossings in the formation period has a positive relation to the future spread +convergence according to the work by Do and Faff (2010). After pairs were matched either within the same industry group or every industry, the top :math:`n` pairs -that had the highest number of zero crossings during the 12-month formation period are admitted to the +that had the highest number of zero crossings during the formation period are admitted to the portfolio we select. This method incorporates the time-series dimension of the historical data in the form of the number of zero crossings. @@ -129,8 +129,8 @@ The historical standard deviation calculated in the formation period can also be selected pairs. According to the work of Do and Faff(2010), as having a small SSD decreases the variance of the spread, this approach could increase the expected profitability of the method. -After pairs were matched, by sorting the pairs based on their historical standard deviation in the -formation period, we can select top :math:`n` pairs that have the highest standard deviation. +After pairs were matched, we can sort them based on their historical standard deviation in the formation period +to select top :math:`n` pairs with the highest variance of the spread. Implementation ************** @@ -290,8 +290,11 @@ The following research notebook can be used to better understand the distance ap * `Basic Distance Approach`_ +* `Basic Distance Approach Comparison`_ + .. _`Basic Distance Approach`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Distance%20Approach/basic_distance_approach.ipynb +.. _`Basic Distance Approach Comparison`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Distance%20Approach/basic_distance_approach_comparison.ipynb References ########## @@ -300,4 +303,3 @@ References * `Do, B., and Faff, R. (2012). Are pairs trading profits robust to trading costs? Journal of Financial Research, 35(2):261–287. `_ * `Gatev, E., Goetzmann, W.N. and Rouwenhorst, K.G., 2006. Pairs trading: Performance of a relative-value arbitrage rule. The Review of Financial Studies, 19(3), pp.797-827. `_ * `Krauss, C., 2017. Statistical arbitrage pairs trading strategies: Review and outlook. Journal of Economic Surveys, 31(2), pp.513-545. `_ - From aed65f44402231497e858965b63d260125e1a293 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 24 Mar 2021 23:21:32 +0530 Subject: [PATCH 064/103] Minor changes to Jurek Class. --- .../stochastic_control_approach/ou_model_jurek.py | 13 +++++++------ .../stochastic_control_approach/ou_model_jurek.rst | 2 +- 2 files changed, 8 insertions(+), 7 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 41b8e922..e6fc306a 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -75,7 +75,7 @@ def _calc_total_return_indices(data : pd.DataFrame) -> pd.DataFrame: return total_return_indices - def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: float = 0.95): + def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = False, significance_level: float = 0.95): """ This method uses inputted training data to calculate the spread and estimate the parameters of the corresponding OU process. @@ -84,6 +84,7 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: :param data: (pd.DataFrame) Contains price series of both stocks in spread. :param delta_t: (float) Time difference between each index of data, calculated in years. + :param adf_test: (bool) Flag which defines whether the adf statistic test should be conducted. :param significance_level: (float) This significance level is used in the ADF statistic test. Value can be one of the following: (0.90, 0.95, 0.99). """ @@ -105,7 +106,7 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, significance_level: eg_adf_statistics = eg_portfolio.adf_statistics # Stores the results of the ADF statistic test. eg_cointegration_vectors = eg_portfolio.cointegration_vectors # Stores the calculated weights for the pair o stocks in the spread. - if eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc[f'{int(significance_level * 100)}%', 0]: + if adf_test is True and eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc[f'{int(significance_level * 100)}%', 0]: # Making sure that the data passes the ADF statistic test. print(eg_adf_statistics) warnings.warn("ADF statistic test failure.") @@ -308,14 +309,14 @@ def _stabilization_region_calc(self, S, tau, utility_type = 1): min_bound = np.zeros(len(tau)) for ind in range(len(tau)): - S = cp.Variable() - constraint = [cp.abs(phi[ind] * S + term_1[ind]) <= term_2[ind] - 1e-6] + s = cp.Variable() + constraint = [cp.abs(phi[ind] * s + term_1[ind]) <= term_2[ind] - 1e-6] - prob_max = cp.Problem(cp.Maximize(S), constraint) + prob_max = cp.Problem(cp.Maximize(s), constraint) prob_max.solve() max_bound[ind] = prob_max.value - prob_min = cp.Problem(cp.Minimize(S), constraint) + prob_min = cp.Problem(cp.Minimize(s), constraint) prob_min.solve() min_bound[ind] = prob_min.value diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index f0a53b6d..931183ed 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -3,7 +3,7 @@ .. note:: The following implementations and documentation closely following work: - `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. `__. + `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. `__ ============== From de46dd9c97cd75bc0bd121882f73f73d8aad05d2 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 25 Mar 2021 21:25:32 +0530 Subject: [PATCH 065/103] Adding sphinx documentation for Jurek Class. --- .../ou_model_jurek.rst | 187 ++++++++++++++++++ 1 file changed, 187 insertions(+) diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 931183ed..d4210584 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -99,4 +99,191 @@ where :math:`f\left(C_{s}, J_{s}\right)` is the normalized aggregator for the co Here we consider the special case of a unit elasticity of intertemporal substitution (:math:`\psi = 1`). +.. note:: + + In this paper, the choice of preference structures is driven by economic intuition regarding the incentives + of real-life arbitrageurs. In particular, it can be assumed that the arbitrageur + is a proprietary trading desk or delegated money manager with a fixed investment horizon. It + seems likely that such investors would only be interested in the distribution of wealth at a finite + horizon, e.g. at the end of the fiscal year, rather than the value of a long-dated consumption + stream. + + However, the decision to model arbitrageurs as finite-horizon CRRA investors neglects + the role of management fees, which are often collected by arbitrageurs. To capture this feature, + we also consider the Epstein-Zin model specialized to the case of a unit elasticity of inter-temporal + substitution. In this case the agent's consumption to wealth ratio is constant, + which we exploit as a model of a flat management fee, collected (and consumed) as a continuous + stream rather than as a lump-sum payment. + + +Spread Construction +******************* + +To construct the spread for the portfolio, firstly we calculate the total return index for each asset :math:`i` in the spread. + +.. math:: + P_{i, t}=\left(\frac{1}{P_{i, 1}}\right) \cdot\left(P_{i, 1} \cdot \prod_{j=1}^{t-1}\left(1+R_{i, j+1}\right)\right) + +The price spread is then constructed by taking a linear combination of the total return indices. +These weights are estimated by using a co-integrating regression technique such as Engle Granger. + + +Optimal Portfolio Strategy +************************** + +The portfolio consists of a riskless asset and the mean reverting spread. We denote +the prices of the two assets by :math:`B_t` and :math:`S_t`, respectively. Their dynamics are given by, + +.. math:: + + \begin{aligned} + d B_{t} &=r B_{t} d t \\ + d S_{t} &=\kappa\left(\bar{S}-S_{t}\right) d t+\sigma d Z + \end{aligned} + +.. note:: + + We assume that there are no margin constraints, no transaction costs and a frictionless, continuous-time setting. + +The evolution of wealth which determines the budget constraints is written as, + +.. math:: + + d W_{t}=N_{t} d S_{t}+M_{t} d B_{t}-C_{t} 1\left[C_{t}>0\right] d t + +where :math:`N_t` denotes the number of units of spread and :math:`M_t` denotes the number of riskless assets. + +For the terminal wealth problem, the optimal portfolio allocation is given by: + +.. math:: + + N(W, S, \tau)=\left\{\begin{array}{cc} + \left(\frac{\kappa(\bar{S}-S)-r S}{\sigma^{2}}\right) W & \gamma=1 \\ + \left(\frac{\kappa(\bar{S}-S)-r S}{\gamma \sigma^{2}}+\frac{2 A(\tau) S+B(\tau)}{\gamma}\right) W & \gamma \neq 1 + \end{array}\right. + +The functions :math:`A(\tau)` and :math:`B(\tau)` depend on the time remaining to the horizon and the parameters of the underlying model. + +For the intermediate consumption problem, the optimal portfolio allocation has the same form as the corresponding equation for terminal wealth problem. + +Obviously, the functional form of the coefficient functions :math:`A(\tau)` and :math:`B(\tau)` are different. + + +Stabilization Region +******************** + +In this section, We are interested in determining the direction in which an arbitrageur trades in response +to a shock to the value of the spread asset. If an arbitrageur increases his position in the spread asset +in response to an adverse shock, his trading is likely to have a stabilizing effect on the mispricing, +contributing to its elimination in equilibrium. Conversely, if the arbitrageur decreases his position +in response to the adverse shock, his trading will tend to exacerbate the mispricing. + +Sometimes arbitrageurs do not arbitrage. For instance, if the mispricing is sufficiently wide, a divergence +in the mispricing can result in the decline of the total allocation, as the wealth effect dominates +the improvement in the investment opportunity set. To characterize the conditions under which arbitrageurs cease +to trade against the mispricing, we derive precise, analytical conditions for the time-varying envelope within which +arbitrageurs trade against the mispricing. + +In the general case when :math:`\bar{S} \neq 0` the range of values of :math:`S` +for which the arbitrageur's response to an adverse shock is stabilizing - i.e. the agent trades against +the spread, increasing his position as the spread widens - is determined by a time-varying envelope +determined by both :math:`A(\tau)` and :math:`B(\tau)`. The boundary of the stabilization region is determined by the +following inequality: + +.. math:: + + \left| \phi(\tau) S+\frac{\kappa \bar{S}+\sigma^{2} B(\tau)}{\gamma \sigma^{2}}\right |<\sqrt{-\phi(\tau)} + +where, + +.. math:: + + \phi(\tau) = \left(\frac{2 A(\tau)}{\gamma}-\frac{\kappa+r}{\gamma \sigma^{2}}\right) + +As long as the spread is within the stabilization region, the improvement in investment opportunities +from a divergence of the spread away from its long-run mean outweighs the negative +wealth effect and the arbitrageur increases his position, :math:`N`, in the mean-reverting asset. When +the spread is outside of the stabilization region, the wealth effect dominates, leading the agent to +curb his position despite an improvement in investment opportunities. + + +Fund Flows +********** + +This section deals with the inclusion of fund flows. Delegated managers are not only exposed to the +financial fluctuations of asset prices but also to their client's desires to contribute or withdraw funds. +Paradoxically, clients are most likely to withdraw funds after performance has been poor +(i.e. spreads have been widening) and investment opportunities are the best. + +In the presence of fund flows the evolution of wealth under management will depend not only +on performance, denoted by :math:`\Pi_t`, but also on fund flows, :math:`F_t`.We therefore have: + +.. math:: + + \begin{aligned} + d \Pi &=\tilde{N} d S+(W-\tilde{N} S) r d t \\ + d F &=f d \Pi+\sigma_{f} W d Z_{f} \\ + d W &=d \Pi+d F=(1+f) d \Pi+\sigma_{f} W d Z_{f} + \end{aligned} + +where :math:`\tilde{N}` is the optimal policy rule chosen by a fund manager facing fund flows of the type described +above, and :math:`E[d Z_{f} dZ] = 0`. The fund flow magnifies the effect of performance on wealth +under management, with each dollar in performance generating a fund flow of :math:`f` dollars. + + +The optimal portfolio allocation of an agent with constant relative risk aversion with utility +defined over terminal wealth, in the presence of fund flows is given by: + +.. math:: + + \tilde{N}(S, \tau)=\left(\frac{1}{1+f}\right) \cdot N(S, \tau) + +where :math:`N(S, \tau)` is the optimal policy function in the problem without fund flows +and :math:`f` denotes the proportionality coefficient. + +The intuition behind this elegant solution is simple. The performance-chasing component of +fund flows increases the volatility of wealth by a factor of :math:`(1 + f)`, causing a manager who anticipates +this flow to commensurately decrease the amount of risk taken on by the underlying strategy. + + +How to use this submodule +######################### + + +Step 1: Model fitting +********************* + + +Implementation +============== + +.. automodule:: arbitragelab.stochastic_control_approach.ou_model_jurek + +.. autoclass:: StochasticControlJurek + :members: __init__ + +.. automethod:: StochasticControlJurek.fit + + +Step 2: Getting the Optimal Portfolio Weights +********************************************* + + +Implementation +============== + +.. automethod:: StochasticControlJurek.optimal_portfolio_weights + + +Example +####### + + +Research Notebook +################# + + + +References +########## From 45de28a0327091ff36809f6ac6c93fc97307d080 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 26 Mar 2021 15:19:43 +0530 Subject: [PATCH 066/103] Adding sphinx documentation for second Class. --- .../ou_model_mudchanatongsuk.py | 2 +- .../ou_model_jurek.rst | 3 +- .../ou_model_mudchanatongsuk.rst | 131 ++++++++++++++++++ 3 files changed, 134 insertions(+), 2 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 56ca1a39..1c65d38d 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -5,8 +5,8 @@ Module implements the optimal pairs trading strategy using Stochastic Control Approach. This module is a realization of the methodology in the following paper: + `Mudchanatongsuk, S., Primbs, J.A. and Wong, W., 2008, June. Optimal pairs trading: A stochastic control approach. - In 2008 American control conference (pp. 1035-1039). IEEE. `__ """ diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index d4210584..d10b12c5 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -3,7 +3,8 @@ .. note:: The following implementations and documentation closely following work: - `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. `__ + `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. + `__ ============== diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index 48a8879b..e7524534 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -1,6 +1,137 @@ .. _stochastic_control_approach_strategies-ou_model_mudchanatongsuk: +.. note:: + The following implementations and documentation closely following work: + + `Mudchanatongsuk, S., Primbs, J.A. and Wong, W., 2008, June. Optimal pairs trading: A stochastic control approach. + `__ + + ======================== OU Model Mudchanatongsuk ======================== + +Introduction +############ + +In this module, we implement a stochastic control based approach to the problem of pairs trading. +The paper models the log-relationship between a pair of stock prices as an Ornstein-Uhlenbeck process +and use this to formulate a portfolio optimization based stochastic control problem. +This problem is constructed in such a way that one may either +trade based on the spread (by buying and selling equal amounts of the stocks in the pair) or +place money in a risk free asset. Then the optimal solution to this control problem +is obtained in closed form via the corresponding Hamilton-Jacobi-Bellman equation under a power utility on terminal wealth. + +Modelling +######### + +Let :math:`A(t)` and :math:`B(t)` denote respectively the prices of the +pair of stocks :math:`A` and :math:`B` at time :math:`t`. We assume that stock :math:`B` +follows a geometric Brownian motion, + +.. math:: + + d B(t)=\mu B(t) d t+\sigma B(t) d Z(t) + +where :math:`\mu` is the drift, :math:`\sigma` is the volatility, and :math:`Z(t)` is a standard +Brownian motion. + +Let :math:`X(t)` denote the spread of the two stocks at time :math:`t`, +defined as + +.. math:: + + X(t) = \ln(A(t)) − \ln(B(t)) + +We assume that the spread follows an Ornstein-Uhlenbeck process + +.. math:: + + d X(t)=k(\theta-X(t)) d t+\eta d W(t) + +where :math:`k` is the rate of reversion, :math:`\eta` is the standard deviation and +:math:`\theta` is the long-term equilibrium level to which the spread reverts. + +:math:`\rho` denotes the instantaneous correlation coefficient between :math:`Z(t)` and :math:`W(t)`. + +Let :math:`V(t)` be the value of a self-financing pairs-trading portfolio and +let :math:`h(t)` and :math:`-h(t)` denote respectively the +portfolio weights for stocks :math:`A` and :math:`B` at time :math:`t`. + + +The wealth dynamics of the portfolio value is given by, + +.. math:: + d V(t)= V(t)\left\{\left[h(t)\left(k(\theta-X(t))+\frac{1}{2} \eta^{2}+\rho \sigma \eta\right)+ + r\right] d t+\eta d W(t)\right\} + + + +Given below is the formulation of the portfolio optimization pair-trading problem +as a stochastic optimal control problem. We assume that an investor’s preference +can be represented by the utility function :math:`U(x) = \frac{1}{\gamma} x^\gamma` +with :math:`x ≥ 0` and :math:`\gamma < 1`. In this formulation, our objective is to maximize expected utility at +the final time :math:`T`. Thus, we seek to solve + + +.. math:: + \begin{aligned} + \sup _{h(t)} \quad & E\left[\frac{1}{\gamma}(V(T))^{\gamma}\right] \\[0.8em] + \text { subject to: } \quad & V(0)=v_{0}, \quad X(0)=x_{0} \\[0.5em] + d X(t)=& k(\theta-X(t)) d t+\eta d W(t) \\ + d V(t)=& V(t)((h(t)(k(\theta-X(t))+\frac{1}{2} \eta^{2}\\ + &+\rho \sigma \eta)+r) d t+\eta d W(t)) + \end{aligned} + +Finally, the optimal weights are given by, + +.. math:: + h^{*}(t, x)=\frac{1}{1-\gamma}\left[\beta(t)+2 x \alpha(t)-\frac{k(x-\theta)}{\eta^{2}}+ + \frac{\rho \sigma}{\eta}+\frac{1}{2}\right] + + + +How to use this submodule +######################### + + +Step 1: Model fitting +********************* + + +Implementation +============== + +.. automodule:: arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk + +.. autoclass:: StochasticControlMudchanatongsuk + :members: __init__ + +.. automethod:: StochasticControlMudchanatongsuk.fit + + +Step 2: Getting the Optimal Portfolio Weights +********************************************* + + +Implementation +============== + +.. automethod:: StochasticControlMudchanatongsuk.optimal_portfolio_weights + + +Example +####### + + +Research Notebook +################# + + + +References +########## + + + From 30360a9aea4a61ce9ab604e79cce2a1463f5b154 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 26 Mar 2021 16:44:15 +0530 Subject: [PATCH 067/103] Minor additions to sphinx docs. --- .../ou_model_jurek.rst | 17 +++++++++++++++++ .../ou_model_mudchanatongsuk.rst | 13 ++++++++++++- 2 files changed, 29 insertions(+), 1 deletion(-) diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index d10b12c5..74d13fd0 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -250,10 +250,17 @@ this flow to commensurately decrease the amount of risk taken on by the underlyi How to use this submodule ######################### +This submodule contains two public methods. One for estimating the parameters of the model using training data, +and the second method is for calculating the final optimal portfolio weights using evaluation data. Step 1: Model fitting ********************* +We input the training data to the fit method which calculates the spread +and the closed form estimators of the parameters of the model. + +We can also specify the time period between steps(delta_t) in the data +and whether we want to run the ADF statistic test to evaluate the spread. Implementation ============== @@ -269,6 +276,11 @@ Implementation Step 2: Getting the Optimal Portfolio Weights ********************************************* +In this step we input the evaluation data and specify the type of investor we are looking for. +We also need to specify the utility function parameter :math:`\gamma` and the risk free rate of return :math:`r`. + +If we choose the investor with intermediate consumption, we also need to specify the parameter :math:`\beta`. + Implementation ============== @@ -283,8 +295,13 @@ Example Research Notebook ################# +The following research notebook can be used to better understand the approach described above. + +* `Dynamic Portfolio Selection in Arbitrage`_ +.. _`Dynamic Portfolio Selection in Arbitrage`: References ########## +* `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. `__ diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index e7524534..8a2d2fc5 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -95,10 +95,14 @@ Finally, the optimal weights are given by, How to use this submodule ######################### +This submodule contains two public methods. One for estimating the parameters of the model using training data, +and the second method is for calculating the final optimal portfolio weights using evaluation data. Step 1: Model fitting ********************* +We input the training data to the fit method which calculates the spread +and the estimators of the parameters of the model. Implementation ============== @@ -114,6 +118,7 @@ Implementation Step 2: Getting the Optimal Portfolio Weights ********************************************* +In this step we input the evaluation data and specify the utility function parameter :math:`\gamma`. Implementation ============== @@ -128,10 +133,16 @@ Example Research Notebook ################# +The following research notebook can be used to better understand the approach described above. + +* `Optimal Pairs Trading A Stochastic Control Approach`_ + +.. _`Optimal Pairs Trading A Stochastic Control Approach`: + References ########## - +* `Mudchanatongsuk, S., Primbs, J.A. and Wong, W., 2008, June. Optimal pairs trading: A stochastic control approach. `__ From 889baa4c3d9f78166db0376c8f545b26684958fd Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 30 Mar 2021 16:58:54 +0530 Subject: [PATCH 068/103] Added functions to view model params and added Example section to docs. --- .../ou_model_jurek.py | 34 ++++++-- .../ou_model_mudchanatongsuk.py | 36 ++++++++- .../ou_model_jurek.rst | 81 ++++++++++++++----- .../ou_model_mudchanatongsuk.rst | 48 +++++++++-- 4 files changed, 168 insertions(+), 31 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index e6fc306a..4a816ca8 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -123,11 +123,7 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = Fal params = self._estimate_params(self.spread) self.mu, self.k, self.sigma = params - print(self.mu) - print(self.k) - print(self.sigma) - - self._check_estimations() + #self._check_estimations() def _estimate_params(self, spread: np.array): @@ -633,3 +629,31 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): return B + + @staticmethod + def _calc_half_life(k: float) -> float: + """ + Function returns half life of mean reverting spread from rate of mean reversion. + """ + + return np.log(2) / k # Half life of shocks. + + + def describe(self) -> pd.Series: + """ + Method returns values of instance attributes calculated from training data. + """ + + if self.sigma is None: + raise Exception("Please run the fit method before calling describe.") + + index = ['Ticker of first stock', 'Ticker of second stock', 'Scaled Spread weights', + 'long-term mean', 'rate of mean reversion', 'standard deviation', 'half-life'] + + data = [self.ticker_A, self.ticker_B, np.round(self.scaled_spread_weights.values, 3), + self.mu, self.k, self.sigma, self._calc_half_life(self.k)] + + # Combine data and indexes into the pandas Series + output = pd.Series(data=data, index=index) + + return output diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 1c65d38d..1c18810c 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -85,10 +85,10 @@ def fit(self, data: pd.DataFrame): self.spread = self.spread.to_numpy() # Converting from pd.Series to numpy array. self.S = self.S.to_numpy() # Converting from pd.Series to numpy array. - self._estimate_params() + #self._estimate_params() params = self._estimate_params_log_likelihood() - print(f"Params from likelihood : {params[:-1]}") + #print(f"Params from likelihood : {params[:-1]}") self.sigma, self.mu, self.k,self.theta, self.eta, self.rho = params[:-1] @@ -300,3 +300,35 @@ def _compute_log_likelihood(params, *args): log_likelihood = np.log(f_y).sum() return -log_likelihood + + + @staticmethod + def _calc_half_life(k: float) -> float: + """ + Function returns half life of mean reverting spread from rate of mean reversion. + """ + + return np.log(2) / k # Half life of shocks. + + + def describe(self) -> pd.Series: + """ + Method returns values of instance attributes calculated from training data. + """ + + if self.sigma is None: + raise Exception("Please run the fit method before calling describe.") + + index = ['Ticker of first stock', 'Ticker of second stock', + 'long-term mean of spread', 'rate of mean reversion of spread', 'standard deviation of spread', 'half-life of spread', + 'Drift of stock B', 'standard deviation of stock B'] + + data = [self.ticker_A, self.ticker_B, + self.theta, self.k, self.eta, self._calc_half_life(self.k), + self.mu, self.sigma] + + # Combine data and indexes into the pandas Series + output = pd.Series(data=data, index=index) + + return output + diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 74d13fd0..61fbf460 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -3,8 +3,7 @@ .. note:: The following implementations and documentation closely following work: - `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. - `__ + `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. `__ ============== @@ -14,7 +13,7 @@ OU Model Jurek Introduction ############ -In this module, we derive the optimal dynamic strategy for arbitrageurs with a finite horizon and +In the paper corresponding to this module, the authors derive the optimal dynamic strategy for arbitrageurs with a finite horizon and non-myopic preferences facing a mean-reverting arbitrage opportunity (e.g. an equity pairs trade). @@ -38,17 +37,17 @@ partial equilibrium. Modelling ######### -To capture the presence of horizon and divergence risk, we model the dynamics of the mispricing +To capture the presence of horizon and divergence risk, the authors model the dynamics of the mispricing using a mean-reverting stochastic process. Under this process, although the mispricing is guaranteed to be eliminated at some future date, the timing of convergence, as well as the maximum magnitude -of the mispricing prior to convergence, are uncertain. With this assumption, we are able to derive +of the mispricing prior to convergence, are uncertain. With this assumption, the authors are able to derive the arbitrageur's optimal dynamic portfolio policy for a set of general, non-myopic preference specifications, including CRRA utility defined over wealth at a finite horizon and Epstein-Zin utility defined over intermediate cash flows (e.g. fees). This allows us to analytically examine the role of intertemporal hedging demands in arbitrage activities and represents a novel contribution relative to the commonly assumed log utility specification, under which hedging demands are absent. -We find that, in the presence of horizon and divergence risk, there is a critical level of the mispricing +It was observed that, in the presence of horizon and divergence risk, there is a critical level of the mispricing beyond which further divergence in the mispricing precipitates a reduction in the allocation. Although a divergence in the mispricing results in an improvement in the instantaneous investment opportunity set and should induce added participation by rational arbitrageurs, this effect can be @@ -63,7 +62,7 @@ Ornstein-Uhlenbeck process (henceforth OU). The OU process captures the two key real-world mispricing: the convergence times are uncertain and the mispricing can diverge arbitrarily far from its mean prior to convergence. -The optimal trading strategies we derive are self-financing and can be interpreted as the optimal +The optimal trading strategies derived are self-financing and can be interpreted as the optimal trading rules for a fund which is not subject to withdrawals but also cannot raise additional assets (i.e. a closed-end fund). The dynamics of the optimal allocation to the arbitrage opportunity are driven by two factors: the necessity of maintaining wealth (equity) above zero and the proximity @@ -73,8 +72,8 @@ of the arbitrageur's terminal evaluation date, which affects his appetite for ri Investor Preferences ******************** -We consider two alternative preferences structures for the arbitrageur in our continuous-time -model. In the first, we assume that the agent has constant relative risk aversion and maximizes +The authors considerd two alternative preferences structures for the arbitrageur in our continuous-time +model. In the first, the authors assumed that the agent has constant relative risk aversion and maximizes the discounted utility of terminal wealth. The arbitrageur's value function at time :math:`t` - denoted by :math:`V_t` - takes the form: @@ -82,7 +81,7 @@ the discounted utility of terminal wealth. The arbitrageur's value function at t V_{t}=\sup E_{t}\left[e^{-\beta(T-t)} \frac{W_{T}^{1-\gamma}}{1-\gamma}\right] -The second preference structure we consider is the recursive utility of Epstein and Zin (1989, 1991), +The second preference structure they considered is the recursive utility of Epstein and Zin (1989, 1991), which allows the elasticity of intertemporal substitution and the coefficient of relative risk aversion to vary independently. Under this preference specification, the value function of the arbitrageur is given by: @@ -98,7 +97,7 @@ where :math:`f\left(C_{s}, J_{s}\right)` is the normalized aggregator for the co f\left(C_{t}, J_{t}\right)=\beta(1-\gamma) \cdot J_{t} \cdot\left[\log C_{t}-\frac{1}{1-\gamma} \log \left((1-\gamma) J_{t}\right)\right] -Here we consider the special case of a unit elasticity of intertemporal substitution (:math:`\psi = 1`). +Here the authors considered the special case of a unit elasticity of intertemporal substitution (:math:`\psi = 1`). .. note:: @@ -111,16 +110,16 @@ Here we consider the special case of a unit elasticity of intertemporal substitu However, the decision to model arbitrageurs as finite-horizon CRRA investors neglects the role of management fees, which are often collected by arbitrageurs. To capture this feature, - we also consider the Epstein-Zin model specialized to the case of a unit elasticity of inter-temporal + the authors also consider the Epstein-Zin model specialized to the case of a unit elasticity of inter-temporal substitution. In this case the agent's consumption to wealth ratio is constant, - which we exploit as a model of a flat management fee, collected (and consumed) as a continuous + which can be exploited as a model of a flat management fee, collected (and consumed) as a continuous stream rather than as a lump-sum payment. Spread Construction ******************* -To construct the spread for the portfolio, firstly we calculate the total return index for each asset :math:`i` in the spread. +To construct the spread for the portfolio, firstly the authors calculated the total return index for each asset :math:`i` in the spread. .. math:: P_{i, t}=\left(\frac{1}{P_{i, 1}}\right) \cdot\left(P_{i, 1} \cdot \prod_{j=1}^{t-1}\left(1+R_{i, j+1}\right)\right) @@ -132,7 +131,7 @@ These weights are estimated by using a co-integrating regression technique such Optimal Portfolio Strategy ************************** -The portfolio consists of a riskless asset and the mean reverting spread. We denote +The portfolio consists of a riskless asset and the mean reverting spread. The authors denote the prices of the two assets by :math:`B_t` and :math:`S_t`, respectively. Their dynamics are given by, .. math:: @@ -144,7 +143,7 @@ the prices of the two assets by :math:`B_t` and :math:`S_t`, respectively. Their .. note:: - We assume that there are no margin constraints, no transaction costs and a frictionless, continuous-time setting. + The authors assumed that there are no margin constraints, no transaction costs and there is a frictionless, continuous-time setting. The evolution of wealth which determines the budget constraints is written as, @@ -173,7 +172,7 @@ Obviously, the functional form of the coefficient functions :math:`A(\tau)` and Stabilization Region ******************** -In this section, We are interested in determining the direction in which an arbitrageur trades in response +In this section, the authors are interested in determining the direction in which an arbitrageur trades in response to a shock to the value of the spread asset. If an arbitrageur increases his position in the spread asset in response to an adverse shock, his trading is likely to have a stabilizing effect on the mispricing, contributing to its elimination in equilibrium. Conversely, if the arbitrageur decreases his position @@ -182,7 +181,7 @@ in response to the adverse shock, his trading will tend to exacerbate the mispri Sometimes arbitrageurs do not arbitrage. For instance, if the mispricing is sufficiently wide, a divergence in the mispricing can result in the decline of the total allocation, as the wealth effect dominates the improvement in the investment opportunity set. To characterize the conditions under which arbitrageurs cease -to trade against the mispricing, we derive precise, analytical conditions for the time-varying envelope within which +to trade against the mispricing, the authors derived precise, analytical conditions for the time-varying envelope within which arbitrageurs trade against the mispricing. In the general case when :math:`\bar{S} \neq 0` the range of values of :math:`S` @@ -217,7 +216,7 @@ Paradoxically, clients are most likely to withdraw funds after performance has b (i.e. spreads have been widening) and investment opportunities are the best. In the presence of fund flows the evolution of wealth under management will depend not only -on performance, denoted by :math:`\Pi_t`, but also on fund flows, :math:`F_t`.We therefore have: +on performance, denoted by :math:`\Pi_t`, but also on fund flows, :math:`F_t`.Consequently: .. math:: @@ -262,17 +261,26 @@ and the closed form estimators of the parameters of the model. We can also specify the time period between steps(delta_t) in the data and whether we want to run the ADF statistic test to evaluate the spread. + Implementation ============== .. automodule:: arbitragelab.stochastic_control_approach.ou_model_jurek + .. autoclass:: StochasticControlJurek :members: __init__ + .. automethod:: StochasticControlJurek.fit +.. tip:: + To view the estimated model parameters from training data, call the ``describe`` function. + + .. automethod:: StochasticControlJurek.describe + + Step 2: Getting the Optimal Portfolio Weights ********************************************* @@ -291,6 +299,41 @@ Implementation Example ####### +We use GLD and GDX tickers from Yahoo Finance as the dataset for this example. + +.. code-block:: + + data1 = yf.download("GLD GDX", start="2009-03-25", end="2019-03-25") + data2 = yf.download("GLD GDX", start="2019-03-27", end="2020-03-27") + + data_train_dataframe = data1["Adj Close"][["GLD", "GDX"]] + data_test_dataframe = data2["Adj Close"][["GLD", "GDX"]] + +.. Note:: + To get good results for the estimated parameters, using atleast 10 years of training data is recommended. + +In the following code block, we are initializing the class and firstly, +we use the fit method to generate the parameters of the model. +Then, we call ``describe`` to view the estimated parameters. +Finally, we use the out-of-sample test data to calculate the optimal portfolio weights using the fitted model. + +.. code-block:: + + from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek + + sc = StochasticControlJurek() + + sc.fit(data_train_dataframe) + + print(sc.describe()) + + plt.plot(sc.optimal_portfolio_weights(data_test_dataframe, beta = 0.01, gamma = 0.5, utility_type=1)) + plt.show() + + +.. Note:: + For utility_type = 2 and low values of :math:`\gamma (< 1)`, the model becomes unstable with respect to the value of :math:`k`. + Research Notebook ################# diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index 8a2d2fc5..0422d6dd 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -15,7 +15,7 @@ OU Model Mudchanatongsuk Introduction ############ -In this module, we implement a stochastic control based approach to the problem of pairs trading. +In the paper corresponding to this module, the authors implement a stochastic control based approach to the problem of pairs trading. The paper models the log-relationship between a pair of stock prices as an Ornstein-Uhlenbeck process and use this to formulate a portfolio optimization based stochastic control problem. This problem is constructed in such a way that one may either @@ -27,7 +27,7 @@ Modelling ######### Let :math:`A(t)` and :math:`B(t)` denote respectively the prices of the -pair of stocks :math:`A` and :math:`B` at time :math:`t`. We assume that stock :math:`B` +pair of stocks :math:`A` and :math:`B` at time :math:`t`. The authors assume that stock :math:`B` follows a geometric Brownian motion, .. math:: @@ -44,7 +44,7 @@ defined as X(t) = \ln(A(t)) − \ln(B(t)) -We assume that the spread follows an Ornstein-Uhlenbeck process +The authors assume that the spread follows an Ornstein-Uhlenbeck process .. math:: @@ -69,10 +69,10 @@ The wealth dynamics of the portfolio value is given by, Given below is the formulation of the portfolio optimization pair-trading problem -as a stochastic optimal control problem. We assume that an investor’s preference +as a stochastic optimal control problem. The authors assume that an investor’s preference can be represented by the utility function :math:`U(x) = \frac{1}{\gamma} x^\gamma` with :math:`x ≥ 0` and :math:`\gamma < 1`. In this formulation, our objective is to maximize expected utility at -the final time :math:`T`. Thus, we seek to solve +the final time :math:`T`. Thus, the authors seek to solve .. math:: @@ -107,14 +107,23 @@ and the estimators of the parameters of the model. Implementation ============== + .. automodule:: arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk + .. autoclass:: StochasticControlMudchanatongsuk :members: __init__ + .. automethod:: StochasticControlMudchanatongsuk.fit +.. tip:: + To view the estimated model parameters from training data, call the ``describe`` function. + + .. automethod:: StochasticControlMudchanatongsuk.describe + + Step 2: Getting the Optimal Portfolio Weights ********************************************* @@ -129,6 +138,35 @@ Implementation Example ####### +We use GLD and GDX tickers from Yahoo Finance as the dataset for this example. + +.. code-block:: + + data1 = yf.download("GLD GDX", start="2012-03-25", end="2016-01-09") + data2 = yf.download("GLD GDX", start="2016-02-21", end="2020-08-15") + + data_train_dataframe = data1["Adj Close"][["GLD", "GDX"]] + data_test_dataframe = data2["Adj Close"][["GLD", "GDX"]] + + +In the following code block, we are initializing the class and firstly, +we use the fit method to generate the parameters of the model. +Then, we call ``describe`` to view the estimated parameters. +Finally, we use the out-of-sample test data to calculate the optimal portfolio weights using the fitted model. + +.. code-block:: + + from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import StochasticControlMudchanatongsuk + + sc = StochasticControlMudchanatongsuk() + + sc.fit(data_train_dataframe) + + print(sc.describe()) + + plt.plot(sc.optimal_portfolio_weights(data_test_dataframe)) + plt.show() + Research Notebook ################# From a6c9ae28e769141c51f63e52e12e41a3e748d44b Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 30 Mar 2021 23:21:43 +0530 Subject: [PATCH 069/103] Added test cases, made changes to Jurek class method structure. Made stabilization region calc method public. Minor changes to docs. --- .../ou_model_jurek.py | 78 ++++--- .../ou_model_mudchanatongsuk.py | 112 +++++----- .../ou_model_jurek.rst | 35 +++- .../ou_model_mudchanatongsuk.rst | 4 + tests/test_ou_model_jurek.py | 195 +++++++++++++++++- tests/test_ou_model_mudchanatongsuk.py | 77 ++++++- 6 files changed, 394 insertions(+), 107 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 4a816ca8..843c8043 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -15,7 +15,6 @@ import cvxpy as cp import numpy as np import pandas as pd -import matplotlib.pyplot as plt from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio @@ -115,8 +114,6 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = Fal self.scaled_spread_weights = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() self.spread = (total_return_indices * self.scaled_spread_weights).sum(axis=1) - self.spread.plot() - plt.show() self.spread = self.spread.to_numpy() # TODO : This conversion seems to have changed the estimated values. Not sure why? @@ -152,21 +149,41 @@ def _estimate_params(self, spread: np.array): return mu, k, sigma - def _check_estimations(self): + # def _check_estimations(self): + # """ + # Testing against null of random walk for rate of mean reversion k. + # """ + # + # num_paths = 100000 + # + # output_params = np.zeros((num_paths, 3)) + # for i in range(num_paths): + # white_noise_process = self.sigma * np.random.randn(len(self.spread)) + self.mu + # output_params[i, :] = self._estimate_params(white_noise_process) + # + # plt.hist(output_params[:, 1], bins=20) + # plt.show() + # #TODO : This is incomplete. + + + def _spread_calc(self, data: pd.DataFrame): """ - Testing against null of random walk for rate of mean reversion k. + This method calculates the spread on test data using the scaled weights from training data. + + :param data: (pd.DataFrame) Contains price series of both stocks in spread. """ - num_paths = 100000 + #Calculating the total return indices from pricing data. + total_return_indices = self._calc_total_return_indices(data) + t = np.arange(0, len(total_return_indices)) * self.delta_t + tau = t[-1] - t # Stores time remaining till closure. (In years) - output_params = np.zeros((num_paths, 3)) - for i in range(num_paths): - white_noise_process = self.sigma * np.random.randn(len(self.spread)) + self.mu - output_params[i, :] = self._estimate_params(white_noise_process) + # Calculating the spread with weights calculated from training data. + S = (total_return_indices * self.scaled_spread_weights).sum(axis=1) - plt.hist(output_params[:, 1], bins=20) - plt.show() - #TODO : This is incomplete. + S = S.to_numpy() # TODO : This conversion in fit seems to have changed the estimated values. + + return tau, S def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, gamma: float = 1, beta: float = 0.1, r: float = 0.05): @@ -205,18 +222,9 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g self.gamma = gamma self.beta = beta - #Calculating the total return indices from pricing data. - total_return_indices = self._calc_total_return_indices(data) - t = np.arange(0, len(total_return_indices)) * self.delta_t - tau = t[-1] - t # Stores time remaining till closure. (In years) - - W = np.ones(len(t)) # Wealth is normalized to one. - # Calculating the spread with weights calculated from training data. - S = (total_return_indices * self.scaled_spread_weights).sum(axis=1) - - S = S.to_numpy() # TODO : This conversion in fit seems to have changed the estimated values. + tau, S = self._spread_calc(data) - self._stabilization_region_calc(S, tau, utility_type) + W = np.ones(len(tau)) # Wealth is normalized to one. N = None # The optimal weights equation is the same for both types of utility functions. @@ -271,20 +279,29 @@ def optimal_portfolio_weights_fund_flows(self, data: pd.DataFrame, f: float, gam return (1 / (1 + f)) * N - def _stabilization_region_calc(self, S, tau, utility_type = 1): + def stabilization_region_calc(self, data: pd.DataFrame, utility_type: int = 1, gamma: float = 1, beta: float = 0.1, r: float = 0.05): """ Implementation of Theorem 3 in Jurek (2007). - :param S: (np.array) spread. - :param tau: (np.array) Array with time till completion in years. + :param data: (pd.DataFrame) Contains price series of both stocks in spread. :param utility_type: (int) Flag signifies type of investor preferences. + :param gamma: (float) coefficient of relative risk aversion. + :param beta: (float) Subjective rate of time preference. (Only required for utility_type = 2). + :param r: (float) Rate of Returns. """ + # Setting instance attributes. + self.r = r + self.gamma = gamma + self.beta = beta + + tau, S = self._spread_calc(data) + if self.gamma == 1: # Calculation of A and B functions are not done in case of gamma = 1. (Refer Appendix A.1 and B.2). warnings.warn("Calculation of stabilization region is not implemented for gamma = 1.") - return + return None A = None B = None @@ -316,10 +333,7 @@ def _stabilization_region_calc(self, S, tau, utility_type = 1): prob_min.solve() min_bound[ind] = prob_min.value - plt.plot(S) - plt.plot(min_bound) - plt.plot(max_bound) - plt.show() + return S, min_bound, max_bound def _AB_calc_1(self, tau): diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 1c18810c..671d988e 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -92,60 +92,60 @@ def fit(self, data: pd.DataFrame): self.sigma, self.mu, self.k,self.theta, self.eta, self.rho = params[:-1] - def _estimate_params(self): - """ - This method implements the closed form solutions for estimators of the model parameters. - These formulas for the estimators are given in Appendix of Mudchanatongsuk (2007). - """ - - N = len(self.spread) - 1 - - m = (self.S[N] - self.S[0]) / N - - S_squared = (np.power(np.diff(self.S), 2).sum() - 2 * m * (self.S[N] - self.S[0]) + N*m*m) / N - - - p = (1 / (N * np.power(self.spread[:-1], 2).sum() - self.spread[:-1].sum() ** 2)) * \ - (N * np.multiply(self.spread[1:], self.spread[:-1]).sum() - - (self.spread[N] - self.spread[0]) * np.sum(self.spread[:-1]) - self.spread[:-1].sum() ** 2) - # TODO : This calculation of p is incorrect. Calculation of q is correct. - - p = np.exp(-0.18565618 * self.delta_t) # Correct value of p calculated from likelihood params. - print(p) - - q = (self.spread[N] - self.spread[0] + (1 - p) * self.spread[:-1].sum()) / N - - V_squared = (1 / N) * (self.spread[N] ** 2 - self.spread[0] ** 2 + (1 + p ** 2) * np.power(self.spread[:-1], 2).sum() - - 2 * p * np.multiply(self.spread[1:], self.spread[:-1]).sum() - N * q) - # TODO : This calculation of V_squared is incorrect. - - print(V_squared) - - self.sigma = np.sqrt(S_squared / self.delta_t) - - self.mu = (m / self.delta_t) + (0.5 * (self.sigma ** 2)) - - self.k = - np.log(p) / self.delta_t - - self.theta = q / (1 - p) - - V_squared = (0.3038416 ** 2) * (1 - p ** 2) / (2 * self.k) # Correct value of V_squared calculated from likelihood params. - - print(V_squared) - - - C = (1/(N * np.sqrt(V_squared * S_squared))) * (np.multiply(self.spread[1:], np.diff(self.S)).sum() - - p * np.multiply(self.spread[:-1], np.diff(self.S)).sum() - - m * (self.spread[N] - self.spread[0]) - - m * (1 - p) * self.spread[:-1].sum()) - - - - self.eta = np.sqrt(2 * self.k * V_squared / (1 - p ** 2)) - - self.rho = self.k * C * np.sqrt(V_squared * S_squared) / (self.eta * self.sigma * (1 - p)) - - print(f"Params from closed form : {(self.sigma, self.mu, self.k, self.theta, self.eta, self.rho)}") + # def _estimate_params(self): + # """ + # This method implements the closed form solutions for estimators of the model parameters. + # These formulas for the estimators are given in Appendix of Mudchanatongsuk (2007). + # """ + # + # N = len(self.spread) - 1 + # + # m = (self.S[N] - self.S[0]) / N + # + # S_squared = (np.power(np.diff(self.S), 2).sum() - 2 * m * (self.S[N] - self.S[0]) + N*m*m) / N + # + # + # p = (1 / (N * np.power(self.spread[:-1], 2).sum() - self.spread[:-1].sum() ** 2)) * \ + # (N * np.multiply(self.spread[1:], self.spread[:-1]).sum() - + # (self.spread[N] - self.spread[0]) * np.sum(self.spread[:-1]) - self.spread[:-1].sum() ** 2) + # # TODO : This calculation of p is incorrect. Calculation of q is correct. + # + # p = np.exp(-0.18565618 * self.delta_t) # Correct value of p calculated from likelihood params. + # print(p) + # + # q = (self.spread[N] - self.spread[0] + (1 - p) * self.spread[:-1].sum()) / N + # + # V_squared = (1 / N) * (self.spread[N] ** 2 - self.spread[0] ** 2 + (1 + p ** 2) * np.power(self.spread[:-1], 2).sum() + # - 2 * p * np.multiply(self.spread[1:], self.spread[:-1]).sum() - N * q) + # # TODO : This calculation of V_squared is incorrect. + # + # print(V_squared) + # + # self.sigma = np.sqrt(S_squared / self.delta_t) + # + # self.mu = (m / self.delta_t) + (0.5 * (self.sigma ** 2)) + # + # self.k = - np.log(p) / self.delta_t + # + # self.theta = q / (1 - p) + # + # V_squared = (0.3038416 ** 2) * (1 - p ** 2) / (2 * self.k) # Correct value of V_squared calculated from likelihood params. + # + # print(V_squared) + # + # + # C = (1/(N * np.sqrt(V_squared * S_squared))) * (np.multiply(self.spread[1:], np.diff(self.S)).sum() + # - p * np.multiply(self.spread[:-1], np.diff(self.S)).sum() + # - m * (self.spread[N] - self.spread[0]) + # - m * (1 - p) * self.spread[:-1].sum()) + # + # + # + # self.eta = np.sqrt(2 * self.k * V_squared / (1 - p ** 2)) + # + # self.rho = self.k * C * np.sqrt(V_squared * S_squared) / (self.eta * self.sigma * (1 - p)) + # + # print(f"Params from closed form : {(self.sigma, self.mu, self.k, self.theta, self.eta, self.rho)}") def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): @@ -158,6 +158,9 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): :param gamma: (float) Parameter of utility function (gamma < 1) """ + if gamma >= 1: + raise Exception("Please make sure value of gamma is less than 1.") + # Preprocessing data = self._data_preprocessing(data) @@ -331,4 +334,3 @@ def describe(self) -> pd.Series: output = pd.Series(data=data, index=index) return output - diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 61fbf460..71dc5509 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -295,6 +295,27 @@ Implementation .. automethod:: StochasticControlJurek.optimal_portfolio_weights +Step 3: Stabilization Region +**************************** + +In this optional step, we can calculate the boundaries of the stabilization region for the spread calculated from the data. + +Implementation +============== + +.. automethod:: StochasticControlJurek.stabilization_region_calc + + +Step 4: Optimal Portfolio Weights with Fund Flows +************************************************* + +In this optional step, we calculate the optimal portfolio weights with the inclusion of fund flows for the CRRA investor. + +Implementation +============== + +.. automethod:: StochasticControlJurek.optimal_portfolio_weights_fund_flows + Example ####### @@ -312,7 +333,10 @@ We use GLD and GDX tickers from Yahoo Finance as the dataset for this example. .. Note:: To get good results for the estimated parameters, using atleast 10 years of training data is recommended. -In the following code block, we are initializing the class and firstly, +Example 1 +********* + +In the following code block, after initializing the class firstly, we use the fit method to generate the parameters of the model. Then, we call ``describe`` to view the estimated parameters. Finally, we use the out-of-sample test data to calculate the optimal portfolio weights using the fitted model. @@ -334,6 +358,15 @@ Finally, we use the out-of-sample test data to calculate the optimal portfolio w .. Note:: For utility_type = 2 and low values of :math:`\gamma (< 1)`, the model becomes unstable with respect to the value of :math:`k`. +Example 2 +********* + +For stabilization region + +Example 3 +********* + +For fund flows Research Notebook ################# diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index 0422d6dd..62b4cb19 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -129,6 +129,10 @@ Step 2: Getting the Optimal Portfolio Weights In this step we input the evaluation data and specify the utility function parameter :math:`\gamma`. +.. note:: + As noted in the paper, please make sure the value of gamma is less than 1. + + Implementation ============== diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index f66e20c9..ddd76eef 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -5,7 +5,7 @@ """ Test functions for the Jurek OU model in the Stochastic Control Approach module. """ - +import warnings import unittest import os import numpy as np @@ -30,19 +30,196 @@ def setUpClass(cls) -> None: def test_fit(self): sc = StochasticControlJurek() - sc.fit(self.dataframe, 1/252, 0.95) + with warnings.catch_warnings(): + warnings.simplefilter("ignore", UserWarning) + sc.fit(self.dataframe, delta_t=1/252, adf_test=True, significance_level=0.95) + + spread_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, + 0.5440914321753456, 0.5471230270552558, 0.5566709779363245, 0.5532053519529174, + 0.5516073438832347, 0.5489831227316044, 0.5466971132268911, 0.5434512050224662, + 0.5453702735903314, 0.5424140575831877, 0.5450224920172433, 0.5421415318431051, + 0.5399089411892184, 0.5417342658455901, 0.5440976512434289, 0.5467950767477552, + 0.5515669810213595, 0.5561602409477461, 0.557182448471494, 0.5561335579963324, + 0.5566339956831441, 0.5521263613656556, 0.5390771353290404, 0.5433116196626523, + 0.5423901587923536, 0.5310046126730086, 0.5299496560807411, 0.5299140307516241, + 0.5290870021197289, 0.5280183485753618, 0.5386137486358292, 0.5410873897027797, + 0.5387603530740576, 0.5352495487153268, 0.5374129802697099, 0.5448692920210395, + 0.5400420169347888, 0.5404828705175425, 0.5359861307007192, 0.5284024338590281, + 0.5358697412015444, 0.5371643904164909, 0.5331592612797672, 0.5377038488055406, + 0.5372396478215287, 0.5312962591087894, 0.5211917143212158, 0.5190644803181462, + 0.5251666364813955, 0.5239848905417022, 0.5203248327883234, 0.5243929266377997, + 0.5191150765020052, 0.5220658221349787, 0.5176793463326727, 0.516863975659782, + 0.5175054097681386, 0.5117401246636695, 0.5122159389305105, 0.5177991465134326, + 0.513038871315079, 0.5098731313766349, 0.5085175023043633, 0.5040433641772756, + 0.5039290495180081, 0.5002238140944849, 0.4947870896437365, 0.49780569727511526, + 0.5020354188220554, 0.5023496206998971, 0.5054215932061087] + + np.testing.assert_array_equal(sc.spread, spread_value) + + self.assertAlmostEqual(sc.mu, 0.532823, delta=1e-4) + self.assertAlmostEqual(sc.k, 10.2728, delta=1e-4) + self.assertAlmostEqual(sc.sigma, 0.0743999, delta=1e-4) + + + def test_describe(self): + sc = StochasticControlJurek() + + with self.assertRaises(Exception): + sc.describe() + + with warnings.catch_warnings(): + warnings.simplefilter("ignore", UserWarning) + sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + + index = ['Ticker of first stock', 'Ticker of second stock', 'Scaled Spread weights', + 'long-term mean', 'rate of mean reversion', 'standard deviation', 'half-life'] + + data = ['GLD', 'GDX', [0.779, -0.221], 0.532823, 10.2728, 0.0743999, 0.067474] + + pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc.describe(), check_exact=False, atol=1e-4) - np.testing.assert_array_equal(sc.spread, np.zeros(len(sc.time_array))) - self.assertAlmostEqual(sc.mu, 0, delta=1e-4) - self.assertAlmostEqual(sc.k, 0, delta=1e-4) - self.assertAlmostEqual(sc.sigma, 0, delta=1e-4) def test_optimal_weights(self): sc = StochasticControlJurek() - sc.fit(self.dataframe, 1/252, 0.95) + with warnings.catch_warnings(): + warnings.simplefilter("ignore", UserWarning) + sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + + weights = sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + + weights_value = [-73.45194149467186, -66.92279595239394, -65.15408289280388, -35.43777877275913, + -34.545817687919545, -42.535359317812855, -67.68919459098552, -58.56650579922123, + -54.36327112091763, -47.45713298534966, -41.44201490315255, -32.89844175560287, + -37.96096743214949, -30.18088183878759, -37.060772390128506, -29.479402457404348, + -23.60620567684073, -28.42505229728819, -34.66288294932173, -41.78249330166799, + -54.37101206797773, -66.49171390891671, -69.2030397247047, -66.45661770001615, + -67.79578295793033, -55.93171185761935, -21.540238878824916, -32.726868430709885, + -30.316954989694864, -0.2964470572123097, 2.4712176283324236, 2.548417241307483, + 4.714693033871299, 7.519785928719447, -20.497495188429824, -27.06729132591058, + -20.947832834193054, -11.69200027231988, -17.452717588039015, -37.247605794787766, + -24.5030045585155, -25.72274610257665, -13.832747281667135, 6.28649720491654, + -13.620032093482212, -17.124887100964134, -6.494784173912921, -18.6978042520508, + -17.529819813294633, -1.6519685678067688, 25.4931602870002, 31.25446478754843, + 14.784765120158685, 17.99308095126069, 27.98439238126017, 16.914096722374268, + 31.452327361923672, 23.40469539338531, 35.68396003464806, 38.1450485471757, + 36.56085532095218, 53.20482218153802, 52.27927773305257, 36.570939606379525, + 50.92261233207725, 60.964273675008954, 65.91794540384299, 80.72165214689629, + 82.56422216475477, 96.13482957606092, 116.22091468441988, 109.1943316005652, + 97.8535878146283, 100.10622031248108, 92.57663162301588] - weights = sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) + np.testing.assert_array_equal(weights, weights_value) + + # TODO: Add checks for other cases of gamma and utility type for 100% code coverage. + # What about gamma = 0.5 and utility_type=2? + + + def test_stabilization_region(self): + + sc = StochasticControlJurek() + + with warnings.catch_warnings(): + warnings.simplefilter("ignore", UserWarning) + sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + + S, min_bound, max_bound = sc.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + + S_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, + 0.5440914321753456, 0.5471230270552558, 0.5566709779363245, 0.5532053519529174, + 0.5516073438832347, 0.5489831227316044, 0.5466971132268911, 0.5434512050224662, + 0.5453702735903314, 0.5424140575831877, 0.5450224920172433, 0.5421415318431051, + 0.5399089411892184, 0.5417342658455901, 0.5440976512434289, 0.5467950767477552, + 0.5515669810213595, 0.5561602409477461, 0.557182448471494, 0.5561335579963324, + 0.5566339956831441, 0.5521263613656556, 0.5390771353290404, 0.5433116196626523, + 0.5423901587923536, 0.5310046126730086, 0.5299496560807411, 0.5299140307516241, + 0.5290870021197289, 0.5280183485753618, 0.5386137486358292, 0.5410873897027797, + 0.5387603530740576, 0.5352495487153268, 0.5374129802697099, 0.5448692920210395, + 0.5400420169347888, 0.5404828705175425, 0.5359861307007192, 0.5284024338590281, + 0.5358697412015444, 0.5371643904164909, 0.5331592612797672, 0.5377038488055406, + 0.5372396478215287, 0.5312962591087894, 0.5211917143212158, 0.5190644803181462, + 0.5251666364813955, 0.5239848905417022, 0.5203248327883234, 0.5243929266377997, + 0.5191150765020052, 0.5220658221349787, 0.5176793463326727, 0.516863975659782, + 0.5175054097681386, 0.5117401246636695, 0.5122159389305105, 0.5177991465134326, + 0.513038871315079, 0.5098731313766349, 0.5085175023043633, 0.5040433641772756, + 0.5039290495180081, 0.5002238140944849, 0.4947870896437365, 0.49780569727511526, + 0.5020354188220554, 0.5023496206998971, 0.5054215932061087] + + min_bound_value = [0.5114954740261215, 0.511494304659523, 0.5114930719447892, 0.511491772862663, + 0.5114904043053522, 0.5114889630823879, 0.5114874459281928, 0.5114858495116325, + 0.5114841704478517, 0.5114824053127447, 0.5114805506604544, 0.5114786030443454, + 0.5114765590419567, 0.5114744152845064, 0.5114721684915997, 0.5114698155118698, + 0.5114673533703791, 0.5114647793237237, 0.5114620909238913, 0.5114592860920708, + 0.5114563632037615, 0.5114533211866995, 0.5114501596333154, 0.511446878929659, + 0.5114434804029621, 0.5114399664902919, 0.5114363409310583, 0.5114326089864681, + 0.5114287776894266, 0.5114248561288008, 0.5114208557724526, 0.5114167908339828, + 0.511412678688732, 0.5114085403452506, 0.5114044009791965, 0.5114002905374362, + 0.5113962444210516, 0.5113923042569426, 0.5113885187688384, 0.511384944759741, + 0.5113816482191418, 0.511378705569804, 0.511376205070451, 0.511374248392369, + 0.5113729523897055, 0.5113724510851133, 0.5113728890138528, 0.5113744592285356, + 0.5113773528151565, 0.511381797500334, 0.5113880522315185, 0.5113964110175347, + 0.5114072071883844, 0.5114208181088091, 0.5114376703799909, 0.5114582455627015, + 0.5114830864528888, 0.5115128039368494, 0.5115480844474176, 0.5115896980347043, + 0.5116385070545585, 0.5116954754648763, 0.5117616787042263, 0.5118383141092488, + 0.5119267118078763, 0.512028346006258, 0.512144846571341, 0.5122780108031038, + 0.5124298152978717, 0.5126024278381169, 0.5127982193212931, 0.5130197758849269, + 0.5132699116333537, 0.5135516827763962, 0.5138684046323441] + + max_bound_value = [0.5504663932787668, 0.5504650623703748, 0.5504636483725223, 0.5504621458535578, + 0.550460548998529, 0.5504588515790302, 0.5504570469203628, 0.5504551278657476, + 0.5504530867372842, 0.5504509152933343, 0.5504486046819679, 0.5504461453900639, + 0.5504435271876233, 0.5504407390667989, 0.5504377691750882, 0.5504346047420877, + 0.5504312319991208, 0.5504276360910032, 0.5504238009790952, 0.5504197093347314, + 0.5504153424219909, 0.5504106799686727, 0.5504057000242086, 0.5504003788031157, + 0.5503946905124223, 0.5503886071613505, 0.5503820983513332, 0.550375131044248, + 0.5503676693065147, 0.5503596740264586, 0.5503511026020539, 0.5503419085958711, + 0.5503320413537078, 0.5503214455830255, 0.5503100608869134, 0.550297821248873, + 0.5502846544632468, 0.5502704815056058, 0.5502552158368782, 0.5502387626344095, + 0.5502210179425316, 0.5502018677345667, 0.5501811868775095, 0.5501588379899172, + 0.5501346701828164, 0.5501085176726986, 0.550080198254951, 0.5500495116253599, + 0.5500162375366732, 0.5499801337766138, 0.5499409339532445, 0.5498983539501722, + 0.5498520537857988, 0.5498016879649662, 0.5497468668698894, 0.5496871622327966, + 0.5496221034636182, 0.5495511736884243, 0.5494738054880556, 0.5493893763277539, + 0.5492972036697708, 0.5491965397614428, 0.5490865660904667, 0.5489663874959719, + 0.5488350259169966, 0.5486914137468271, 0.5485343867390974, 0.5483626763748868, + 0.5481749015425326, 0.5479695592938455, 0.5477450143079432, 0.547499486496596, + 0.5472310358926771, 0.5469375435302057, 0.5466166863794518] + + + np.testing.assert_array_equal(S, S_value) + np.testing.assert_array_equal(min_bound, min_bound_value) + np.testing.assert_array_equal(max_bound, max_bound_value) + + + def test_optimal_weights_fund_flows(self): + + sc = StochasticControlJurek() - np.testing.assert_array_equal(weights, np.zeros(len(sc.time_array))) + with warnings.catch_warnings(): + warnings.simplefilter("ignore", UserWarning) + sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + + weights = sc.optimal_portfolio_weights_fund_flows(self.dataframe, f=0.2, gamma = 0.5) + + weights_value = [-61.209951245559886, -55.768996626994955, -54.29506907733657, -29.53148231063261, + -28.788181406599623, -35.446132764844045, -56.407662159154604, -48.80542149935103, + -45.30272593409803, -39.54761082112472, -34.53501241929379, -27.41536812966906, + -31.63413952679124, -25.15073486565633, -30.883976991773757, -24.566168714503625, + -19.671838064033942, -23.68754358107349, -28.88573579110144, -34.81874441805666, + -45.30917672331478, -55.40976159076393, -57.66919977058725, -55.38051475001346, + -56.49648579827527, -46.60975988134946, -17.950199065687432, -27.272390358924905, + -25.264129158079054, -0.2470392143435914, 2.059348023610353, 2.1236810344229027, + 3.928910861559416, 6.266488273932873, -17.081245990358187, -22.556076104925484, + -17.456527361827547, -9.743333560266567, -14.543931323365847, -31.039671495656474, + -20.419170465429584, -21.43562175214721, -11.52728940138928, 5.238747670763784, + -11.350026744568511, -14.270739250803446, -5.412320144927434, -15.581503543375668, + -14.608183177745529, -1.3766404731723074, 21.244300239166837, 26.045387322957026, + 12.320637600132239, 14.994234126050577, 23.320326984383478, 14.095080601978557, + 26.21027280160306, 19.503912827821093, 29.736633362206717, 31.787540455979748, + 30.467379434126816, 44.33735181794835, 43.56606477754381, 30.475783005316273, + 42.435510276731044, 50.803561395840795, 54.93162116986916, 67.2680434557469, + 68.80351847062897, 80.11235798005077, 96.85076223701657, 90.99527633380434, + 81.54465651219026, 83.4218502604009, 77.14719301917991] + + + np.testing.assert_array_equal(weights, weights_value) diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index a2e455c2..544dfce6 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -30,18 +30,52 @@ def setUpClass(cls) -> None: cls.sc = StochasticControlMudchanatongsuk() + def test_fit(self): sc = StochasticControlMudchanatongsuk() sc.fit(self.dataframe) - np.testing.assert_array_equal(sc.spread, np.zeros(len(sc.time_array))) - self.assertAlmostEqual(sc.sigma, 0, delta=1e-4) - self.assertAlmostEqual(sc.mu, 0, delta=1e-4) - self.assertAlmostEqual(sc.k, 0, delta=1e-4) - self.assertAlmostEqual(sc.theta, 0, delta=1e-4) - self.assertAlmostEqual(sc.eta, 0, delta=1e-4) - self.assertAlmostEqual(sc.rho, 0, delta=1e-4) + spread_value = [2.0887923929288523, 2.1094166241052568, 2.142854916105869, 2.0874899841437258, 2.063640345328846, + 2.0746168560671223, 2.1097829292924457, 2.1073878043606307, 2.1186930608205428, 2.114695107155425, + 2.103095768137663, 2.1215705039862782, 2.124685352890708, 2.1157789172191848, 2.1269984320130346, + 2.120925503747776, 2.0763581413867684, 2.0595664254555057, 2.0523098321895366, 2.0797748079356957, + 2.1197252327440586, 2.131219793094243, 2.082081096325099, 2.0929293564196105, 2.1285514677643356, + 2.117750899307466, 2.0830138676604886, 2.106107155811972, 2.0496029865939436, 2.0050226960285182, + 1.9786263643353657, 1.9816431811190234, 1.9894204445041153, 1.9514558194020695, 1.9853812497671273, + 1.9846230785716679, 1.939022254160427, 1.9350347152497411, 1.9579985647080247, 1.996822168058443, + 1.963797288878891, 1.9847212944236645, 1.9674718306977712, 1.941258381912097, 1.971988526032174, + 1.9723574683305594, 1.973661841888858, 2.013718843187712, 2.0205219195979014, 2.0100021771087766, + 2.0004053530573787, 2.012571119972438, 2.0470873187820344, 2.0774352146534167, 2.053195021245263, + 2.0774606535295734, 2.06082098723021, 2.0742880142111084, 2.060417339214223, 2.0530928294396382, + 2.0890217923893957, 2.059036586082702, 2.035044438470959, 2.072153226841589, 2.069307015169184, + 2.0383888802559467, 2.043152450272762, 2.0504190679184715, 2.034227852538867, 2.0090985697450647, + 2.019908369440301, 2.009667357261374, 1.9797365648180438, 2.01008349909157, 2.0202245834522397] + + np.testing.assert_array_equal(sc.spread, spread_value) + self.assertAlmostEqual(sc.sigma, 0.503695, delta=1e-4) + self.assertAlmostEqual(sc.mu, 0.114877, delta=1e-4) + self.assertAlmostEqual(sc.k, 3.99205, delta=1e-4) + self.assertAlmostEqual(sc.theta, 1.98816, delta=1e-4) + self.assertAlmostEqual(sc.eta, 0.404292, delta=1e-4) + self.assertAlmostEqual(sc.rho, 0.96202, delta=1e-4) + + + def test_describe(self): + sc = StochasticControlMudchanatongsuk() + + with self.assertRaises(Exception): + sc.describe() + + sc.fit(self.dataframe) + + index = ['Ticker of first stock', 'Ticker of second stock', + 'long-term mean of spread', 'rate of mean reversion of spread', 'standard deviation of spread', 'half-life of spread', + 'Drift of stock B', 'standard deviation of stock B'] + + data = ['GLD', 'GDX', 1.98816, 3.99205, 0.404292, 0.173632, 0.114877, 0.503695] + + pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc.describe(), check_exact=False, atol=1e-4) def test_optimal_weights(self): @@ -49,6 +83,29 @@ def test_optimal_weights(self): sc.fit(self.dataframe) - weights = sc.optimal_portfolio_weights(self.dataframe, gamma = 10) - - np.testing.assert_array_equal(weights, np.zeros(len(sc.time_array))) + with self.assertRaises(Exception): + sc.optimal_portfolio_weights(self.dataframe, gamma = 10) + + weights = sc.optimal_portfolio_weights(self.dataframe, gamma = -10) + + weights_value = [0.6807970425341383, 0.5788270189292528, 0.4237456386361687, 0.6450834372737371, + 0.7318800196910422, 0.6725665016257416, 0.5137455982771261, 0.5117099817524071, + 0.4536787173239446, 0.4587916338411348, 0.4947409799799004, 0.40935585749175935, + 0.38656582779882165, 0.4119577215551326, 0.3576746243419241, 0.37205756995215905, + 0.5364494177553357, 0.5912391763672612, 0.6087201255096889, 0.4933662450056616, + 0.3322708500364613, 0.2807566340156271, 0.45706866084645936, 0.40803843763022246, + 0.2683653938434968, 0.3009241934120373, 0.4202148927130246, 0.32903803274992643, + 0.5246204647066117, 0.6749545941905897, 0.7588892323365495, 0.7385587466201069, + 0.7020478426104525, 0.8238791404743722, 0.6979215228988004, 0.6917047438277323, + 0.8365209290118862, 0.8401240368143309, 0.754516641656195, 0.6183636050618108, + 0.7182449688122026, 0.6425285645177642, 0.6901494231876113, 0.7653424279618145, + 0.6605525316290899, 0.652089070778512, 0.6409423355789974, 0.5118482097864904, + 0.4857268994701272, 0.5119999415779317, 0.5350930783653811, 0.49397895578467543, + 0.3888903487219631, 0.29800762140526377, 0.3642822152122685, 0.29285532211506354, + 0.33686879455357427, 0.2971957603672995, 0.3329060663478341, 0.35032173033381425, + 0.2523906371601354, 0.3301480022615564, 0.390645486517426, 0.29293440407814975, + 0.29903173795128984, 0.3754395278348421, 0.36179056247411795, 0.34247802333072985, + 0.3803355129092354, 0.43858981861753515, 0.4110154830924428, 0.43302883383533586, + 0.4995100506045553, 0.42845097673506394, 0.40433684605306186] + + np.testing.assert_array_equal(weights, weights_value) From 78b7a79fba863b99a0b9dd546d5231c2ed8c63c6 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 31 Mar 2021 15:40:26 +0530 Subject: [PATCH 070/103] Added plots and code examples to Jurek docs. --- 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specify the parameter :math:`\beta`. +.. figure:: images/optimal_weights.png + :scale: 100 % + :align: center + :figclass: align-center + + Implementation ============== @@ -306,6 +312,12 @@ Implementation .. automethod:: StochasticControlJurek.stabilization_region_calc +.. figure:: images/stabilization_bound.png + :scale: 100 % + :align: center + :figclass: align-center + + Step 4: Optimal Portfolio Weights with Fund Flows ************************************************* @@ -317,7 +329,13 @@ Implementation .. automethod:: StochasticControlJurek.optimal_portfolio_weights_fund_flows -Example +.. figure:: images/optimal_weights_fund_flows.png + :scale: 100 % + :align: center + :figclass: align-center + + +Examples ####### We use GLD and GDX tickers from Yahoo Finance as the dataset for this example. @@ -361,12 +379,54 @@ Finally, we use the out-of-sample test data to calculate the optimal portfolio w Example 2 ********* -For stabilization region +In the following code block, after initializing the class firstly, +we use the fit method to generate the parameters of the model. +Then, we call ``describe`` to view the estimated parameters. +Finally, on the out-of-sample test data we calculate the stabilization region for the spread calculated from test data. + +.. code-block:: + + from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek + + sc = StochasticControlJurek() + + sc.fit(data_train_dataframe) + + print(sc.describe()) + + S, min_bound, max_bound = sc.stabilization_region_calc(data_test_dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + + plt.plot(S, label='Spread') + plt.plot(min_bound, color='red', linestyle='dashed') + plt.plot(max_bound, color='red', linestyle='dashed') + plt.legend() + plt.show() + + Example 3 ********* -For fund flows +In the following code block, after initializing the class firstly, +we use the fit method to generate the parameters of the model. +Then, we call ``describe`` to view the estimated parameters. +Finally, we use the out-of-sample test data to calculate the optimal portfolio weights with fund flows +using the fitted model. + +.. code-block:: + + from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek + + sc = StochasticControlJurek() + + sc.fit(data_train_dataframe) + + print(sc.describe()) + + plt.plot(sc.optimal_portfolio_weights_fund_flows(data_test_dataframe, f=0.05, gamma = 0.5)) + plt.show() + + Research Notebook ################# From 84373616b3779a78a9d9d15206eed8e32f30dc94 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 31 Mar 2021 17:29:16 +0530 Subject: [PATCH 071/103] Added test cases for code coverage and added a test dataset. --- .../ou_model_jurek.py | 16 +- tests/test_data/shell-rdp-close_USD.csv | 4521 +++++++++++++++++ tests/test_ou_model_jurek.py | 28 + 3 files changed, 4563 insertions(+), 2 deletions(-) create mode 100644 tests/test_data/shell-rdp-close_USD.csv diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 843c8043..f8160085 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -217,6 +217,12 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g :param r: (float) Rate of Returns. """ + if gamma <= 0: + raise Exception("The value of gamma should be positive.") + + if utility_type not in [1, 2]: + raise Exception("Please make sure utility_type is either 1 or 2.") + # Setting instance attributes. self.r = r self.gamma = gamma @@ -242,7 +248,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g if utility_type == 1: A, B = self._AB_calc_1(tau) - elif utility_type == 2: + else: A, B = self._AB_calc_2(tau) N = ((self.k * (self.mu - S) - self.r * S) / (self.gamma * self.sigma ** 2) + (2 * A * S + B) / self.gamma) * W @@ -290,6 +296,12 @@ def stabilization_region_calc(self, data: pd.DataFrame, utility_type: int = 1, g :param r: (float) Rate of Returns. """ + if gamma <= 0: + raise Exception("The value of gamma should be positive.") + + if utility_type not in [1, 2]: + raise Exception("Please make sure utility_type is either 1 or 2.") + # Setting instance attributes. self.r = r self.gamma = gamma @@ -308,7 +320,7 @@ def stabilization_region_calc(self, data: pd.DataFrame, utility_type: int = 1, g if utility_type == 1: A, B = self._AB_calc_1(tau) - elif utility_type == 2: + else: A, B = self._AB_calc_2(tau) # Calculating phi (Refer Equation 17 in Jurek (2007)). diff --git a/tests/test_data/shell-rdp-close_USD.csv b/tests/test_data/shell-rdp-close_USD.csv new file mode 100644 index 00000000..1bcdcf45 --- /dev/null +++ b/tests/test_data/shell-rdp-close_USD.csv @@ -0,0 +1,4521 @@ +Date,Shell,RDP +02/01/1990,7.75,1.06 +03/01/1990,7.77,1.07 +04/01/1990,7.68,1.05 +05/01/1990,7.58,1.03 +08/01/1990,7.46,1.03 +09/01/1990,7.46,1.03 +10/01/1990,7.27,1.02 +11/01/1990,7.3,1.02 +12/01/1990,7.2,1.0 +15/01/1990,7.22,1.0 +16/01/1990,7.19,0.98 +17/01/1990,7.25,0.99 +18/01/1990,7.19,0.98 +19/01/1990,7.19,1.0 +22/01/1990,7.06,1.0 +23/01/1990,7.07,0.99 +24/01/1990,7.0,0.97 +25/01/1990,7.14,0.99 +26/01/1990,7.2,0.99 +29/01/1990,7.36,0.99 +30/01/1990,7.38,1.01 +31/01/1990,7.58,1.02 +01/02/1990,7.66,1.03 +02/02/1990,7.63,1.04 +05/02/1990,7.53,1.04 +06/02/1990,7.49,1.03 +07/02/1990,7.42,1.01 +08/02/1990,7.58,1.04 +09/02/1990,7.58,1.04 +12/02/1990,7.38,1.03 +13/02/1990,7.41,1.03 +14/02/1990,7.41,1.03 +15/02/1990,7.57,1.03 +16/02/1990,7.68, +19/02/1990,7.53,1.04 +20/02/1990,7.41,1.03 +21/02/1990,7.39,1.02 +22/02/1990,7.41,1.03 +23/02/1990,7.22,1.01 +26/02/1990,7.03,1.0 +27/02/1990,7.06, +28/02/1990,7.14,1.03 +01/03/1990,7.05,1.02 +02/03/1990,7.19,1.04 +05/03/1990,7.13,1.02 +06/03/1990,7.19,1.01 +07/03/1990,7.27,1.03 +08/03/1990,7.38,1.03 +09/03/1990,7.33,1.03 +12/03/1990,7.24,1.03 +13/03/1990,7.19,1.03 +14/03/1990,7.22,1.02 +15/03/1990,7.22,1.03 +16/03/1990,7.35,1.04 +19/03/1990,7.23,1.02 +20/03/1990,7.22,1.03 +21/03/1990,7.24,1.03 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+30/05/1990,7.33,1.04 +31/05/1990,7.35,1.04 +01/06/1990,7.35,1.04 +04/06/1990,7.36, +05/06/1990,7.3, +06/06/1990,7.16,1.02 +07/06/1990,7.11,1.02 +08/06/1990,7.11,1.02 +11/06/1990,7.13,1.01 +12/06/1990,7.19,1.02 +13/06/1990,7.22,1.03 +14/06/1990,7.19,1.03 +15/06/1990,7.17,1.02 +18/06/1990,7.09,1.02 +19/06/1990,7.22,1.01 +20/06/1990,7.3,1.02 +21/06/1990,7.24,1.02 +22/06/1990,7.22,1.01 +25/06/1990,7.28,1.01 +26/06/1990,7.3,1.01 +27/06/1990,7.24,1.01 +28/06/1990,7.09,1.01 +29/06/1990,7.19,1.0 +02/07/1990,7.16,1.0 +03/07/1990,7.09,1.0 +04/07/1990,7.14,1.0 +05/07/1990,7.03,0.99 +06/07/1990,7.08,0.99 +09/07/1990,7.02,0.99 +10/07/1990,,0.99 +11/07/1990,7.0,1.0 +12/07/1990,7.28,1.02 +13/07/1990,7.53,1.05 +16/07/1990,7.58,1.06 +17/07/1990,7.5,1.06 +18/07/1990,7.5,1.05 +19/07/1990,7.41,1.05 +20/07/1990,7.58,1.06 +23/07/1990,7.53,1.05 +24/07/1990,7.64,1.05 +25/07/1990,7.63,1.06 +26/07/1990,7.5,1.05 +27/07/1990,7.41,1.04 +30/07/1990,7.42,1.04 +31/07/1990,7.46,1.05 +01/08/1990,7.61,1.07 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a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -60,6 +60,13 @@ def test_fit(self): self.assertAlmostEqual(sc.k, 10.2728, delta=1e-4) self.assertAlmostEqual(sc.sigma, 0.0743999, delta=1e-4) + project_path = os.path.dirname(__file__) + path = project_path + '/test_data/shell-rdp-close_USD.csv' + data = pd.read_csv(path, index_col='Date').ffill() + data.index = pd.to_datetime(data.index, format="%d/%m/%Y") + sc.fit(data, delta_t=1 / 252, adf_test=False) + + def test_describe(self): sc = StochasticControlJurek() @@ -87,6 +94,12 @@ def test_optimal_weights(self): warnings.simplefilter("ignore", UserWarning) sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + with self.assertRaises(Exception): + sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=10) + + with self.assertRaises(Exception): + sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = -1) + weights = sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) weights_value = [-73.45194149467186, -66.92279595239394, -65.15408289280388, -35.43777877275913, @@ -114,6 +127,11 @@ def test_optimal_weights(self): # TODO: Add checks for other cases of gamma and utility type for 100% code coverage. # What about gamma = 0.5 and utility_type=2? + sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) + sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) + sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=1) + sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=2) + def test_stabilization_region(self): @@ -123,6 +141,12 @@ def test_stabilization_region(self): warnings.simplefilter("ignore", UserWarning) sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + with self.assertRaises(Exception): + sc.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=10) + + with self.assertRaises(Exception): + sc.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = -1) + S, min_bound, max_bound = sc.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) S_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, @@ -190,6 +214,10 @@ def test_stabilization_region(self): np.testing.assert_array_equal(min_bound, min_bound_value) np.testing.assert_array_equal(max_bound, max_bound_value) + sc.stabilization_region_calc(self.dataframe, gamma=1, utility_type=1) + sc.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + sc.stabilization_region_calc(self.dataframe, beta=0.01, gamma=2, utility_type=2) + def test_optimal_weights_fund_flows(self): From 4a6cc3d9195e69ff2aa4f2dc17aa0d6ee5c0a661 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Wed, 31 Mar 2021 21:40:08 +0530 Subject: [PATCH 072/103] Added test cases for 100% code coverage. --- .../ou_model_jurek.py | 9 +++-- .../ou_model_jurek.rst | 2 +- tests/test_ou_model_jurek.py | 36 ++++++++++++++++++- 3 files changed, 42 insertions(+), 5 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index f8160085..1841d5ad 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -411,7 +411,8 @@ def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0): A = -c_2 / c_1 + (np.sqrt(disc) / (2 * c_1)) * (1 / np.tanh(-np.sqrt(disc) * tau / 2 + np.arctanh(np.sqrt(disc) / (2 * c_2)))) - elif self.gamma > 1: + else: + # Case when self.gamma > 1. A = -c_2 / c_1 + (np.sqrt(disc) / (2 * c_1)) * np.tanh(-np.sqrt(disc) * tau / 2 + np.arctanh(2 * c_2 / np.sqrt(disc))) @@ -458,7 +459,8 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): B = (c_1 * c_5 * (c_2 * tau - 2) - (c_2 ** 2) * c_4) * tau / (2 * c_1 * (c_2 * tau - 1)) - elif self.gamma > gamma_0 + error_margin: + else: + # Case when self.gamma > gamma_0 + error_margin. B = (4 * (c_2 * c_5 - c_3 * c_4 + (c_3 * c_4 - c_2 * c_5) * np.cosh(np.sqrt(disc) * tau / 2)) + 2 * c_5 * np.sqrt(disc) * np.sinh(np.sqrt(disc) * tau / 2)) \ @@ -625,7 +627,8 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): + term_5) / denominator - elif self.gamma > 1: + else: + # Case when self.gamma > 1. # Implementation of Case IV in Appendix B.1.2. rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1. diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 4e91d7b1..4d1f962e 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -72,7 +72,7 @@ of the arbitrageur's terminal evaluation date, which affects his appetite for ri Investor Preferences ******************** -The authors considerd two alternative preferences structures for the arbitrageur in our continuous-time +The authors considered two alternative preferences structures for the arbitrageur in our continuous-time model. In the first, the authors assumed that the agent has constant relative risk aversion and maximizes the discounted utility of terminal wealth. The arbitrageur's value function at time :math:`t` - denoted by :math:`V_t` - takes the form: diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index a9f82f16..714f69bb 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -27,6 +27,7 @@ def setUpClass(cls) -> None: cls.dataframe = data[['GLD', 'GDX']] + def test_fit(self): sc = StochasticControlJurek() @@ -67,7 +68,6 @@ def test_fit(self): sc.fit(data, delta_t=1 / 252, adf_test=False) - def test_describe(self): sc = StochasticControlJurek() @@ -251,3 +251,37 @@ def test_optimal_weights_fund_flows(self): np.testing.assert_array_equal(weights, weights_value) + + def test_private_methods(self): + """ + Function tests special cases for code coverage. + """ + sc = StochasticControlJurek() + + + with warnings.catch_warnings(): + warnings.simplefilter("ignore", UserWarning) + sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + + sc.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + + t = np.arange(0, len(self.dataframe)) * (1/252) + tau = t[-1] - t + c_1 = 0.0221413 + c_2 = -20.59561 + c_3 = 9625.4458424 + disc = -844.234913 + + with warnings.catch_warnings(): + warnings.simplefilter("ignore") + sc._A_calc_1(tau, c_1, c_2, disc, 0.5) + sc._A_calc_1(tau, c_1, c_2, disc, 0.9) + sc._B_calc_1(tau, c_1, c_2, c_3, disc, 0.5) + sc._B_calc_1(tau, c_1, c_2, c_3, disc, 0.9) + + sc.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=2) + + with warnings.catch_warnings(): + warnings.simplefilter("ignore") + sc._B_calc_2(tau, c_1, c_2, c_3, disc, 0.5) + sc._B_calc_2(tau, c_1, c_2, c_3, disc, 0.9) From bffa3fe169087372fccdc54445f863d77ea7a099 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 1 Apr 2021 12:33:25 +0530 Subject: [PATCH 073/103] Removed closed form param estimation from second class and check estimations. --- .../ou_model_jurek.py | 19 ------- .../ou_model_mudchanatongsuk.py | 57 ------------------- 2 files changed, 76 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 1841d5ad..d799c0d1 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -120,8 +120,6 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = Fal params = self._estimate_params(self.spread) self.mu, self.k, self.sigma = params - #self._check_estimations() - def _estimate_params(self, spread: np.array): """ @@ -149,23 +147,6 @@ def _estimate_params(self, spread: np.array): return mu, k, sigma - # def _check_estimations(self): - # """ - # Testing against null of random walk for rate of mean reversion k. - # """ - # - # num_paths = 100000 - # - # output_params = np.zeros((num_paths, 3)) - # for i in range(num_paths): - # white_noise_process = self.sigma * np.random.randn(len(self.spread)) + self.mu - # output_params[i, :] = self._estimate_params(white_noise_process) - # - # plt.hist(output_params[:, 1], bins=20) - # plt.show() - # #TODO : This is incomplete. - - def _spread_calc(self, data: pd.DataFrame): """ This method calculates the spread on test data using the scaled weights from training data. diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 671d988e..d9fae2af 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -85,69 +85,12 @@ def fit(self, data: pd.DataFrame): self.spread = self.spread.to_numpy() # Converting from pd.Series to numpy array. self.S = self.S.to_numpy() # Converting from pd.Series to numpy array. - #self._estimate_params() params = self._estimate_params_log_likelihood() #print(f"Params from likelihood : {params[:-1]}") self.sigma, self.mu, self.k,self.theta, self.eta, self.rho = params[:-1] - # def _estimate_params(self): - # """ - # This method implements the closed form solutions for estimators of the model parameters. - # These formulas for the estimators are given in Appendix of Mudchanatongsuk (2007). - # """ - # - # N = len(self.spread) - 1 - # - # m = (self.S[N] - self.S[0]) / N - # - # S_squared = (np.power(np.diff(self.S), 2).sum() - 2 * m * (self.S[N] - self.S[0]) + N*m*m) / N - # - # - # p = (1 / (N * np.power(self.spread[:-1], 2).sum() - self.spread[:-1].sum() ** 2)) * \ - # (N * np.multiply(self.spread[1:], self.spread[:-1]).sum() - - # (self.spread[N] - self.spread[0]) * np.sum(self.spread[:-1]) - self.spread[:-1].sum() ** 2) - # # TODO : This calculation of p is incorrect. Calculation of q is correct. - # - # p = np.exp(-0.18565618 * self.delta_t) # Correct value of p calculated from likelihood params. - # print(p) - # - # q = (self.spread[N] - self.spread[0] + (1 - p) * self.spread[:-1].sum()) / N - # - # V_squared = (1 / N) * (self.spread[N] ** 2 - self.spread[0] ** 2 + (1 + p ** 2) * np.power(self.spread[:-1], 2).sum() - # - 2 * p * np.multiply(self.spread[1:], self.spread[:-1]).sum() - N * q) - # # TODO : This calculation of V_squared is incorrect. - # - # print(V_squared) - # - # self.sigma = np.sqrt(S_squared / self.delta_t) - # - # self.mu = (m / self.delta_t) + (0.5 * (self.sigma ** 2)) - # - # self.k = - np.log(p) / self.delta_t - # - # self.theta = q / (1 - p) - # - # V_squared = (0.3038416 ** 2) * (1 - p ** 2) / (2 * self.k) # Correct value of V_squared calculated from likelihood params. - # - # print(V_squared) - # - # - # C = (1/(N * np.sqrt(V_squared * S_squared))) * (np.multiply(self.spread[1:], np.diff(self.S)).sum() - # - p * np.multiply(self.spread[:-1], np.diff(self.S)).sum() - # - m * (self.spread[N] - self.spread[0]) - # - m * (1 - p) * self.spread[:-1].sum()) - # - # - # - # self.eta = np.sqrt(2 * self.k * V_squared / (1 - p ** 2)) - # - # self.rho = self.k * C * np.sqrt(V_squared * S_squared) / (self.eta * self.sigma * (1 - p)) - # - # print(f"Params from closed form : {(self.sigma, self.mu, self.k, self.theta, self.eta, self.rho)}") - - def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): """ This method calculates the final optimal portfolio weights for the calculated spread. From 486228ec225207bb782f325dc02f97e425a96328 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 1 Apr 2021 15:27:34 +0530 Subject: [PATCH 074/103] Added plotting method to Jurek Class. --- .../ou_model_jurek.py | 79 +++++++++++++++++++ .../ou_model_jurek.rst | 13 ++- .../ou_model_mudchanatongsuk.rst | 3 + tests/test_ou_model_jurek.py | 53 ++++++++++++- 4 files changed, 143 insertions(+), 5 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index d799c0d1..4d9ae806 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -15,6 +15,7 @@ import cvxpy as cp import numpy as np import pandas as pd +import matplotlib.pyplot as plt from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio @@ -667,3 +668,81 @@ def describe(self) -> pd.Series: output = pd.Series(data=data, index=index) return output + + + def plotting(self, data:pd.DataFrame, num_test_windows = 5, delta_t = 1/252, utility_type = 1,gamma = 10, beta = 0.1, r = 0.05 , f = 0.1): + """ + Method plots out of sample performance of the model on specified number of test windows. + We use a backward looking rolling window as training data and its size depends on the number of test windows chosen. + The length of training data is fixed for all test windows. + + For example, if the total data is of length 16 years, with the number of test windows set to 5, + the length of training data would be 16 - (5 + 1) = 10. (The last year is not considered for testing). + + :param data: (pd.DataFrame) Contains price series of both stocks in spread with dates as index. + :param num_test_windows: (int) Number of out of sample testing windows to plot. + :param delta_t: (float) Time difference between each index of data, calculated in years. + :param gamma: (float) coefficient of relative risk aversion. + :param f: (float) coefficient of proportionality (assumed to be positive). + :param r: (float) Rate of Returns. + :param utility_type: (int) Flag signifies type of investor preferences. + :param beta: (float) Subjective rate of time preference. (Only required for utility_type = 2). + """ + + + plt.rcParams.update({'font.size': 8}) + + data = data.ffill() + + if not np.issubdtype(data.index.dtype, np.datetime64): + raise Exception("Please make sure index of dataframe is datetime type.") + + if len(data) < (10 / delta_t): + raise Exception("Please make sure length of input data is greater than 10 years.") + + years = data.index.year.unique() + + stab_result_dataframe = pd.DataFrame(index=data.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, + columns=['Spread', 'lower bound', 'upper bound']) + optimal_result_dataframe = pd.DataFrame(index=data.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, + columns=['Weights']) + optimal_fund_flows_result_dataframe = pd.DataFrame(index=data.loc[str(years[-(num_test_windows + 1)]): + str(years[-1])].index, columns=['Weights']) + + ind = 0 + for year in np.arange(years[-(num_test_windows + 1)], years[-1], 1): + + data_train_dataframe = data.loc[str(year - (len(years) - (num_test_windows + 1))):str(year - 1)] + data_test_dataframe = data.loc[str(year)] + + self.fit(data_train_dataframe, delta_t=delta_t) + + optimal_weights = self.optimal_portfolio_weights(data_test_dataframe, gamma=gamma, + utility_type=utility_type, beta=beta, r=r) + optimal_fund_flow_weights = self.optimal_portfolio_weights_fund_flows(data_test_dataframe, gamma=gamma, + f=f, r=r) + S, min_bound, max_bound = self.stabilization_region_calc(data_test_dataframe, gamma=gamma, + utility_type=utility_type, beta=beta, r=r) + + stab_result_dataframe.iloc[ind:ind + len(S), :] = np.array([S, min_bound, max_bound]).T + optimal_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_weights]).T + optimal_fund_flows_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_fund_flow_weights]).T + ind += len(S) + + ax = stab_result_dataframe.plot(style=['c-', 'r:', 'r:'], legend=False, linewidth=1.0, figsize=(8, 4)) + ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) + ax.set_ylabel('Spread') + ax.set_title("Evolution of spread with stabilization bound") + plt.show() + + ax = optimal_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=(8, 4)) + ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) + ax.set_ylabel('Optimal Weights') + ax.set_title('Optimal allocation to the spread asset scaled by wealth') + plt.show() + + ax = optimal_fund_flows_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=(8, 4)) + ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) + ax.set_ylabel('Optimal Weights with fund flows') + ax.set_title('Optimal allocation to the spread asset with fund flows scaled by wealth') + plt.show() diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 4d1f962e..e8bb52d8 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -335,8 +335,19 @@ Implementation :figclass: align-center +Step 5: Plotting +**************** + +In this optional step, we can plot the stabilization regions and optimal portfolio weights. + +Implementation +============== + +.. automethod:: StochasticControlJurek.plotting + + Examples -####### +######## We use GLD and GDX tickers from Yahoo Finance as the dataset for this example. diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index 62b4cb19..82f93d25 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -117,6 +117,9 @@ Implementation .. automethod:: StochasticControlMudchanatongsuk.fit +.. note:: + Although the paper provides closed form solutions for parameter estimation, + this module uses log-likelihood maximization to estimate the parameters as we found the closed form solutions provided to be unstable. .. tip:: To view the estimated model parameters from training data, call the ``describe`` function. diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index 714f69bb..fcb33bb1 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -11,6 +11,7 @@ import numpy as np import pandas as pd +from unittest import mock from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek @@ -29,6 +30,9 @@ def setUpClass(cls) -> None: def test_fit(self): + """ + + """ sc = StochasticControlJurek() with warnings.catch_warnings(): @@ -69,6 +73,9 @@ def test_fit(self): def test_describe(self): + """ + + """ sc = StochasticControlJurek() with self.assertRaises(Exception): @@ -87,6 +94,9 @@ def test_describe(self): def test_optimal_weights(self): + """ + + """ sc = StochasticControlJurek() @@ -124,9 +134,6 @@ def test_optimal_weights(self): np.testing.assert_array_equal(weights, weights_value) - # TODO: Add checks for other cases of gamma and utility type for 100% code coverage. - # What about gamma = 0.5 and utility_type=2? - sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=1) @@ -134,6 +141,9 @@ def test_optimal_weights(self): def test_stabilization_region(self): + """ + + """ sc = StochasticControlJurek() @@ -214,12 +224,18 @@ def test_stabilization_region(self): np.testing.assert_array_equal(min_bound, min_bound_value) np.testing.assert_array_equal(max_bound, max_bound_value) - sc.stabilization_region_calc(self.dataframe, gamma=1, utility_type=1) + with warnings.catch_warnings(): + warnings.simplefilter("ignore", UserWarning) + sc.stabilization_region_calc(self.dataframe, gamma=1, utility_type=1) + sc.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) sc.stabilization_region_calc(self.dataframe, beta=0.01, gamma=2, utility_type=2) def test_optimal_weights_fund_flows(self): + """ + + """ sc = StochasticControlJurek() @@ -285,3 +301,32 @@ def test_private_methods(self): warnings.simplefilter("ignore") sc._B_calc_2(tau, c_1, c_2, c_3, disc, 0.5) sc._B_calc_2(tau, c_1, c_2, c_3, disc, 0.9) + + + + @mock.patch("arbitragelab.stochastic_control_approach.ou_model_jurek.plt") + def test_plotting(self, mock_plt): + """ + + """ + + sc = StochasticControlJurek() + + with self.assertRaises(Exception): + sc.plotting(self.dataframe) + + self.dataframe.index = pd.to_datetime(self.dataframe.index) + + with self.assertRaises(Exception): + sc.plotting(self.dataframe) + + project_path = os.path.dirname(__file__) + path = project_path + '/test_data/shell-rdp-close_USD.csv' + data = pd.read_csv(path, index_col='Date').ffill() + + data.index = pd.to_datetime(data.index, format="%d/%m/%Y") + + sc.plotting(data) + + # Assert plt.figure got called + assert mock_plt.show.called From ef5d00173c88a1803d1ff8bcf34cee0f74e89a90 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 1 Apr 2021 16:39:52 +0530 Subject: [PATCH 075/103] Changes to test files for 10/10 pylint. --- tests/test_ou_model_jurek.py | 123 ++++++++++++++----------- tests/test_ou_model_mudchanatongsuk.py | 54 +++++++---- 2 files changed, 103 insertions(+), 74 deletions(-) diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index fcb33bb1..66b36fe6 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -8,17 +8,25 @@ import warnings import unittest import os +from unittest import mock import numpy as np import pandas as pd -from unittest import mock from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek +# pylint: disable=protected-access class TestOUModelJurek(unittest.TestCase): + """ + Test Jurek OU model in Stochastic Control Approach module. + """ @classmethod def setUpClass(cls) -> None: + """ + Set up data and parameters. + """ + np.random.seed(0) project_path = os.path.dirname(__file__) @@ -31,13 +39,14 @@ def setUpClass(cls) -> None: def test_fit(self): """ - + Tests the fit method in the class. """ - sc = StochasticControlJurek() + + sc_jurek = StochasticControlJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) - sc.fit(self.dataframe, delta_t=1/252, adf_test=True, significance_level=0.95) + sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=True, significance_level=0.95) spread_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, 0.5440914321753456, 0.5471230270552558, 0.5566709779363245, 0.5532053519529174, @@ -59,58 +68,59 @@ def test_fit(self): 0.5039290495180081, 0.5002238140944849, 0.4947870896437365, 0.49780569727511526, 0.5020354188220554, 0.5023496206998971, 0.5054215932061087] - np.testing.assert_array_equal(sc.spread, spread_value) + np.testing.assert_array_equal(sc_jurek.spread, spread_value) - self.assertAlmostEqual(sc.mu, 0.532823, delta=1e-4) - self.assertAlmostEqual(sc.k, 10.2728, delta=1e-4) - self.assertAlmostEqual(sc.sigma, 0.0743999, delta=1e-4) + self.assertAlmostEqual(sc_jurek.mu, 0.532823, delta=1e-4) + self.assertAlmostEqual(sc_jurek.k, 10.2728, delta=1e-4) + self.assertAlmostEqual(sc_jurek.sigma, 0.0743999, delta=1e-4) project_path = os.path.dirname(__file__) path = project_path + '/test_data/shell-rdp-close_USD.csv' data = pd.read_csv(path, index_col='Date').ffill() data.index = pd.to_datetime(data.index, format="%d/%m/%Y") - sc.fit(data, delta_t=1 / 252, adf_test=False) + sc_jurek.fit(data, delta_t=1 / 252, adf_test=False) def test_describe(self): """ - + Tests the describe method in the class. """ - sc = StochasticControlJurek() + + sc_jurek = StochasticControlJurek() with self.assertRaises(Exception): - sc.describe() + sc_jurek.describe() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) - sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) index = ['Ticker of first stock', 'Ticker of second stock', 'Scaled Spread weights', 'long-term mean', 'rate of mean reversion', 'standard deviation', 'half-life'] data = ['GLD', 'GDX', [0.779, -0.221], 0.532823, 10.2728, 0.0743999, 0.067474] - pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc.describe(), check_exact=False, atol=1e-4) + pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_jurek.describe(), check_exact=False, atol=1e-4) def test_optimal_weights(self): """ - + Tests the optimal portfolio weights method in the class. """ - sc = StochasticControlJurek() + sc_jurek = StochasticControlJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) - sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) with self.assertRaises(Exception): - sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=10) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=10) with self.assertRaises(Exception): - sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = -1) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = -1) - weights = sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) weights_value = [-73.45194149467186, -66.92279595239394, -65.15408289280388, -35.43777877275913, -34.545817687919545, -42.535359317812855, -67.68919459098552, -58.56650579922123, @@ -134,32 +144,32 @@ def test_optimal_weights(self): np.testing.assert_array_equal(weights, weights_value) - sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) - sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) - sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=1) - sc.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=2) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=1) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=2) def test_stabilization_region(self): """ - + Tests the stabilization region method in the class. """ - sc = StochasticControlJurek() + sc_jurek = StochasticControlJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) - sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) with self.assertRaises(Exception): - sc.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=10) + sc_jurek.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=10) with self.assertRaises(Exception): - sc.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = -1) + sc_jurek.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = -1) - S, min_bound, max_bound = sc.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + spread, min_bound, max_bound = sc_jurek.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) - S_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, + spread_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, 0.5440914321753456, 0.5471230270552558, 0.5566709779363245, 0.5532053519529174, 0.5516073438832347, 0.5489831227316044, 0.5466971132268911, 0.5434512050224662, 0.5453702735903314, 0.5424140575831877, 0.5450224920172433, 0.5421415318431051, @@ -220,30 +230,30 @@ def test_stabilization_region(self): 0.5472310358926771, 0.5469375435302057, 0.5466166863794518] - np.testing.assert_array_equal(S, S_value) + np.testing.assert_array_equal(spread, spread_value) np.testing.assert_array_equal(min_bound, min_bound_value) np.testing.assert_array_equal(max_bound, max_bound_value) with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) - sc.stabilization_region_calc(self.dataframe, gamma=1, utility_type=1) + sc_jurek.stabilization_region_calc(self.dataframe, gamma=1, utility_type=1) - sc.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) - sc.stabilization_region_calc(self.dataframe, beta=0.01, gamma=2, utility_type=2) + sc_jurek.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + sc_jurek.stabilization_region_calc(self.dataframe, beta=0.01, gamma=2, utility_type=2) def test_optimal_weights_fund_flows(self): """ - + Tests the optimal weights with fund flows method in the class. """ - sc = StochasticControlJurek() + sc_jurek = StochasticControlJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) - sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) - weights = sc.optimal_portfolio_weights_fund_flows(self.dataframe, f=0.2, gamma = 0.5) + weights = sc_jurek.optimal_portfolio_weights_fund_flows(self.dataframe, f=0.2, gamma = 0.5) weights_value = [-61.209951245559886, -55.768996626994955, -54.29506907733657, -29.53148231063261, -28.788181406599623, -35.446132764844045, -56.407662159154604, -48.80542149935103, @@ -272,17 +282,18 @@ def test_private_methods(self): """ Function tests special cases for code coverage. """ - sc = StochasticControlJurek() + + sc_jurek = StochasticControlJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) - sc.fit(self.dataframe, delta_t=1/252, adf_test=False) + sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) - sc.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) - t = np.arange(0, len(self.dataframe)) * (1/252) - tau = t[-1] - t + time_array = np.arange(0, len(self.dataframe)) * (1/252) + tau = time_array[-1] - time_array c_1 = 0.0221413 c_2 = -20.59561 c_3 = 9625.4458424 @@ -290,35 +301,35 @@ def test_private_methods(self): with warnings.catch_warnings(): warnings.simplefilter("ignore") - sc._A_calc_1(tau, c_1, c_2, disc, 0.5) - sc._A_calc_1(tau, c_1, c_2, disc, 0.9) - sc._B_calc_1(tau, c_1, c_2, c_3, disc, 0.5) - sc._B_calc_1(tau, c_1, c_2, c_3, disc, 0.9) + sc_jurek._A_calc_1(tau, c_1, c_2, disc, 0.5) + sc_jurek._A_calc_1(tau, c_1, c_2, disc, 0.9) + sc_jurek._B_calc_1(tau, c_1, c_2, c_3, disc, 0.5) + sc_jurek._B_calc_1(tau, c_1, c_2, c_3, disc, 0.9) - sc.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=2) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=2) with warnings.catch_warnings(): warnings.simplefilter("ignore") - sc._B_calc_2(tau, c_1, c_2, c_3, disc, 0.5) - sc._B_calc_2(tau, c_1, c_2, c_3, disc, 0.9) + sc_jurek._B_calc_2(tau, c_1, c_2, c_3, disc, 0.5) + sc_jurek._B_calc_2(tau, c_1, c_2, c_3, disc, 0.9) @mock.patch("arbitragelab.stochastic_control_approach.ou_model_jurek.plt") def test_plotting(self, mock_plt): """ - + Tests the plotting method in the class. """ - sc = StochasticControlJurek() + sc_jurek = StochasticControlJurek() with self.assertRaises(Exception): - sc.plotting(self.dataframe) + sc_jurek.plotting(self.dataframe) self.dataframe.index = pd.to_datetime(self.dataframe.index) with self.assertRaises(Exception): - sc.plotting(self.dataframe) + sc_jurek.plotting(self.dataframe) project_path = os.path.dirname(__file__) path = project_path + '/test_data/shell-rdp-close_USD.csv' @@ -326,7 +337,7 @@ def test_plotting(self, mock_plt): data.index = pd.to_datetime(data.index, format="%d/%m/%Y") - sc.plotting(data) + sc_jurek.plotting(data) # Assert plt.figure got called assert mock_plt.show.called diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index 544dfce6..d4bfc963 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -15,9 +15,15 @@ class TestOUModelMudchanatongsuk(unittest.TestCase): + """ + Tests the Mudchanatongsuk OU model in the Stochastic Control Approach module. + """ @classmethod def setUpClass(cls) -> None: + """ + Setup data and params. + """ np.random.seed(0) @@ -28,13 +34,17 @@ def setUpClass(cls) -> None: cls.dataframe = data[['GLD', 'GDX']] - cls.sc = StochasticControlMudchanatongsuk() + cls.sc_mudchana = StochasticControlMudchanatongsuk() def test_fit(self): - sc = StochasticControlMudchanatongsuk() + """ + Tests the fit method in the class. + """ - sc.fit(self.dataframe) + sc_mudchana = StochasticControlMudchanatongsuk() + + sc_mudchana.fit(self.dataframe) spread_value = [2.0887923929288523, 2.1094166241052568, 2.142854916105869, 2.0874899841437258, 2.063640345328846, 2.0746168560671223, 2.1097829292924457, 2.1073878043606307, 2.1186930608205428, 2.114695107155425, @@ -52,22 +62,26 @@ def test_fit(self): 2.0383888802559467, 2.043152450272762, 2.0504190679184715, 2.034227852538867, 2.0090985697450647, 2.019908369440301, 2.009667357261374, 1.9797365648180438, 2.01008349909157, 2.0202245834522397] - np.testing.assert_array_equal(sc.spread, spread_value) - self.assertAlmostEqual(sc.sigma, 0.503695, delta=1e-4) - self.assertAlmostEqual(sc.mu, 0.114877, delta=1e-4) - self.assertAlmostEqual(sc.k, 3.99205, delta=1e-4) - self.assertAlmostEqual(sc.theta, 1.98816, delta=1e-4) - self.assertAlmostEqual(sc.eta, 0.404292, delta=1e-4) - self.assertAlmostEqual(sc.rho, 0.96202, delta=1e-4) + np.testing.assert_array_equal(sc_mudchana.spread, spread_value) + self.assertAlmostEqual(sc_mudchana.sigma, 0.503695, delta=1e-4) + self.assertAlmostEqual(sc_mudchana.mu, 0.114877, delta=1e-4) + self.assertAlmostEqual(sc_mudchana.k, 3.99205, delta=1e-4) + self.assertAlmostEqual(sc_mudchana.theta, 1.98816, delta=1e-4) + self.assertAlmostEqual(sc_mudchana.eta, 0.404292, delta=1e-4) + self.assertAlmostEqual(sc_mudchana.rho, 0.96202, delta=1e-4) def test_describe(self): - sc = StochasticControlMudchanatongsuk() + """ + Tests the describe method in the class. + """ + + sc_mudchana = StochasticControlMudchanatongsuk() with self.assertRaises(Exception): - sc.describe() + sc_mudchana.describe() - sc.fit(self.dataframe) + sc_mudchana.fit(self.dataframe) index = ['Ticker of first stock', 'Ticker of second stock', 'long-term mean of spread', 'rate of mean reversion of spread', 'standard deviation of spread', 'half-life of spread', @@ -75,18 +89,22 @@ def test_describe(self): data = ['GLD', 'GDX', 1.98816, 3.99205, 0.404292, 0.173632, 0.114877, 0.503695] - pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc.describe(), check_exact=False, atol=1e-4) + pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_mudchana.describe(), check_exact=False, atol=1e-4) def test_optimal_weights(self): - sc = StochasticControlMudchanatongsuk() + """ + Tests the optimal portfolio weights method in the class. + """ + + sc_mudchana = StochasticControlMudchanatongsuk() - sc.fit(self.dataframe) + sc_mudchana.fit(self.dataframe) with self.assertRaises(Exception): - sc.optimal_portfolio_weights(self.dataframe, gamma = 10) + sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = 10) - weights = sc.optimal_portfolio_weights(self.dataframe, gamma = -10) + weights = sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = -10) weights_value = [0.6807970425341383, 0.5788270189292528, 0.4237456386361687, 0.6450834372737371, 0.7318800196910422, 0.6725665016257416, 0.5137455982771261, 0.5117099817524071, From 9234ba74d47347c247637a8c4b6c323340a1cbe4 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 1 Apr 2021 18:03:06 +0530 Subject: [PATCH 076/103] Changes to test files. Changed tolerances and using assert_array_almost_equal. --- tests/test_ou_model_jurek.py | 12 ++++++------ tests/test_ou_model_mudchanatongsuk.py | 8 ++++---- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index 66b36fe6..9c0e22e4 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -68,7 +68,7 @@ def test_fit(self): 0.5039290495180081, 0.5002238140944849, 0.4947870896437365, 0.49780569727511526, 0.5020354188220554, 0.5023496206998971, 0.5054215932061087] - np.testing.assert_array_equal(sc_jurek.spread, spread_value) + np.testing.assert_array_almost_equal(sc_jurek.spread, spread_value, decimal=4) self.assertAlmostEqual(sc_jurek.mu, 0.532823, delta=1e-4) self.assertAlmostEqual(sc_jurek.k, 10.2728, delta=1e-4) @@ -142,7 +142,7 @@ def test_optimal_weights(self): 82.56422216475477, 96.13482957606092, 116.22091468441988, 109.1943316005652, 97.8535878146283, 100.10622031248108, 92.57663162301588] - np.testing.assert_array_equal(weights, weights_value) + np.testing.assert_array_almost_equal(weights, weights_value, decimal=4) sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) @@ -230,9 +230,9 @@ def test_stabilization_region(self): 0.5472310358926771, 0.5469375435302057, 0.5466166863794518] - np.testing.assert_array_equal(spread, spread_value) - np.testing.assert_array_equal(min_bound, min_bound_value) - np.testing.assert_array_equal(max_bound, max_bound_value) + np.testing.assert_array_almost_equal(spread, spread_value, decimal=4) + np.testing.assert_array_almost_equal(min_bound, min_bound_value, decimal=4) + np.testing.assert_array_almost_equal(max_bound, max_bound_value, decimal=4) with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) @@ -276,7 +276,7 @@ def test_optimal_weights_fund_flows(self): 81.54465651219026, 83.4218502604009, 77.14719301917991] - np.testing.assert_array_equal(weights, weights_value) + np.testing.assert_array_almost_equal(weights, weights_value, decimal=4) def test_private_methods(self): """ diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index d4bfc963..6a6627dd 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -62,10 +62,10 @@ def test_fit(self): 2.0383888802559467, 2.043152450272762, 2.0504190679184715, 2.034227852538867, 2.0090985697450647, 2.019908369440301, 2.009667357261374, 1.9797365648180438, 2.01008349909157, 2.0202245834522397] - np.testing.assert_array_equal(sc_mudchana.spread, spread_value) + np.testing.assert_array_almost_equal(sc_mudchana.spread, spread_value, decimal=4) self.assertAlmostEqual(sc_mudchana.sigma, 0.503695, delta=1e-4) self.assertAlmostEqual(sc_mudchana.mu, 0.114877, delta=1e-4) - self.assertAlmostEqual(sc_mudchana.k, 3.99205, delta=1e-4) + self.assertAlmostEqual(sc_mudchana.k, 3.99205, delta=1e-3) self.assertAlmostEqual(sc_mudchana.theta, 1.98816, delta=1e-4) self.assertAlmostEqual(sc_mudchana.eta, 0.404292, delta=1e-4) self.assertAlmostEqual(sc_mudchana.rho, 0.96202, delta=1e-4) @@ -89,7 +89,7 @@ def test_describe(self): data = ['GLD', 'GDX', 1.98816, 3.99205, 0.404292, 0.173632, 0.114877, 0.503695] - pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_mudchana.describe(), check_exact=False, atol=1e-4) + pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_mudchana.describe(), check_exact=False, rtol=1e-4) def test_optimal_weights(self): @@ -126,4 +126,4 @@ def test_optimal_weights(self): 0.3803355129092354, 0.43858981861753515, 0.4110154830924428, 0.43302883383533586, 0.4995100506045553, 0.42845097673506394, 0.40433684605306186] - np.testing.assert_array_equal(weights, weights_value) + np.testing.assert_array_almost_equal(weights, weights_value, decimal=4) From 458c3fc3339b76adb9c13b81b264a4b33a12a928 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 1 Apr 2021 18:29:10 +0530 Subject: [PATCH 077/103] Minor change to test file. --- tests/test_ou_model_mudchanatongsuk.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index 6a6627dd..126ef24e 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -89,7 +89,7 @@ def test_describe(self): data = ['GLD', 'GDX', 1.98816, 3.99205, 0.404292, 0.173632, 0.114877, 0.503695] - pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_mudchana.describe(), check_exact=False, rtol=1e-4) + pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_mudchana.describe(), check_exact=False, atol=1e-3) def test_optimal_weights(self): From 8bc38110a598d054ac444a8881ad2d9c7cc696ff Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 2 Apr 2021 13:14:31 +0530 Subject: [PATCH 078/103] Changes in both class files according to PR. --- .../stochastic_control_approach/__init__.py | 4 +- .../ou_model_jurek.py | 291 ++++++++++-------- .../ou_model_mudchanatongsuk.py | 57 ++-- .../ou_model_jurek.rst | 28 +- .../ou_model_mudchanatongsuk.rst | 12 +- tests/test_ou_model_jurek.py | 36 +-- tests/test_ou_model_mudchanatongsuk.py | 10 +- 7 files changed, 243 insertions(+), 195 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/__init__.py b/arbitragelab/stochastic_control_approach/__init__.py index 062df115..5ede59d3 100644 --- a/arbitragelab/stochastic_control_approach/__init__.py +++ b/arbitragelab/stochastic_control_approach/__init__.py @@ -2,5 +2,5 @@ This module implements Stochastic Control Approach based Statistical Arbitrage strategies. """ -from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek -from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import StochasticControlMudchanatongsuk +from arbitragelab.stochastic_control_approach.ou_model_jurek import OUModelJurek +from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import OUModelMudchanatongsuk diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 4d9ae806..46663078 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -20,7 +20,7 @@ from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio -class StochasticControlJurek: +class OUModelJurek: """ This class derives the optimal dynamic strategy for arbitrageurs with a finite horizon and non-myopic preferences facing a mean-reverting arbitrage opportunity (e.g. an equity pairs trade). @@ -35,6 +35,9 @@ class StochasticControlJurek: """ def __init__(self): + """ + Initializes the parameters of the module. + """ # Characteristics of Training Data. self.ticker_A = None # Ticker Symbol of first stock. @@ -56,48 +59,50 @@ def __init__(self): @staticmethod - def _calc_total_return_indices(data : pd.DataFrame) -> pd.DataFrame: + def _calc_total_return_indices(prices : pd.DataFrame) -> pd.DataFrame: """ This method calculates the total return indices from pricing data. This calculation follows Section IV A in Jurek (2007). - :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. + :return: (pd.DataFrame) Total return indices. """ #Calculating the daily returns. - returns_df = data.pct_change() + returns_df = prices.pct_change() returns_df = returns_df.replace([np.inf, -np.inf], np.nan).ffill().dropna() - total_return_indices = data.copy() + total_return_indices = prices.copy() total_return_indices.iloc[0, :] = 1 total_return_indices.iloc[1:, :] = pd.DataFrame.cumprod(1 + returns_df, axis=0) return total_return_indices - def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = False, significance_level: float = 0.95): + def fit(self, prices: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = False, significance_level: float = 0.95): """ This method uses inputted training data to calculate the spread and estimate the parameters of the corresponding OU process. The spread construction implementation follows Section IV A in Jurek (2007). - :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. :param delta_t: (float) Time difference between each index of data, calculated in years. :param adf_test: (bool) Flag which defines whether the adf statistic test should be conducted. :param significance_level: (float) This significance level is used in the ADF statistic test. Value can be one of the following: (0.90, 0.95, 0.99). """ - if len(data) < (10 / delta_t): - warnings.warn("Please make sure length of training data is greater than 10 years.") + if len(prices) < (10 / delta_t): + warnings.warn("Please make sure length of training data is greater than 10 years. " + "This is the time period used to fit the model in the original paper.") # Setting instance attributes. self.delta_t = delta_t - self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] + self.ticker_A, self.ticker_B = prices.columns[0], prices.columns[1] #Calculating the total return indices from pricing data. - total_return_indices = self._calc_total_return_indices(data) + total_return_indices = self._calc_total_return_indices(prices) self.time_array = np.arange(0, len(total_return_indices)) * self.delta_t # As mentioned in the paper, the vector of linear weights are calculated using co-integrating regression. @@ -116,18 +121,19 @@ def fit(self, data: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = Fal self.spread = (total_return_indices * self.scaled_spread_weights).sum(axis=1) - self.spread = self.spread.to_numpy() # TODO : This conversion seems to have changed the estimated values. Not sure why? + self.spread = self.spread.to_numpy() # This conversion seems to have changed the estimated values. params = self._estimate_params(self.spread) self.mu, self.k, self.sigma = params - def _estimate_params(self, spread: np.array): + def _estimate_params(self, spread: np.array) -> tuple: """ This method implements the closed form solutions for estimators of the model parameters. These formulas for the estimators are given in Appendix E of Jurek (2007). - :param: (np.array) Price series of the constructed spread. + :param spread: (np.array) Price series of the constructed spread. + :return: (tuple) Consists of estimated params. """ N = len(spread) @@ -148,27 +154,29 @@ def _estimate_params(self, spread: np.array): return mu, k, sigma - def _spread_calc(self, data: pd.DataFrame): + def _spread_calc(self, prices: pd.DataFrame) -> tuple: """ This method calculates the spread on test data using the scaled weights from training data. - :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. + :return: (tuple) Consists of time remaining array and spread numpy array. """ #Calculating the total return indices from pricing data. - total_return_indices = self._calc_total_return_indices(data) + total_return_indices = self._calc_total_return_indices(prices) t = np.arange(0, len(total_return_indices)) * self.delta_t tau = t[-1] - t # Stores time remaining till closure. (In years) # Calculating the spread with weights calculated from training data. S = (total_return_indices * self.scaled_spread_weights).sum(axis=1) - S = S.to_numpy() # TODO : This conversion in fit seems to have changed the estimated values. + S = S.to_numpy() return tau, S - def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, gamma: float = 1, beta: float = 0.1, r: float = 0.05): + def optimal_portfolio_weights(self, prices: pd.DataFrame, utility_type: int = 1, gamma: float = 1, + beta: float = 0.1, r: float = 0.05) -> np.array: """ Implementation of Theorem 1 and Theorem 2 in Jurek (2007). @@ -192,11 +200,12 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g of assets under management (the management fee). For utility_type = 2, C(Consumption) = beta * W. - :param data: (pd.DataFrame) Contains price series of both stocks in spread. - :param utility_type: (int) Flag signifies type of investor preferences. - :param gamma: (float) coefficient of relative risk aversion. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. + :param utility_type: (int) Flag signifies type of investor preferences. (Either 1 or 2). + :param gamma: (float) coefficient of relative risk aversion. (gamma > 0). :param beta: (float) Subjective rate of time preference. (Only required for utility_type = 2). - :param r: (float) Rate of Returns. + :param r: (float) Rate of Returns. (r > 0). + :return: (np.array) Scaled optimal portfolio weights. """ if gamma <= 0: @@ -210,7 +219,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g self.gamma = gamma self.beta = beta - tau, S = self._spread_calc(data) + tau, S = self._spread_calc(prices) W = np.ones(len(tau)) # Wealth is normalized to one. @@ -238,7 +247,7 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, utility_type: int = 1, g return N / W # We return the optimal allocation of spread asset scaled by wealth. - def optimal_portfolio_weights_fund_flows(self, data: pd.DataFrame, f: float, gamma: float = 1, r: float = 0.05): + def optimal_portfolio_weights_fund_flows(self, prices: pd.DataFrame, f: float, gamma: float = 1, r: float = 0.05) -> np.array: """ Implementation of Theorem 4 in Jurek (2007). @@ -256,26 +265,28 @@ def optimal_portfolio_weights_fund_flows(self, data: pd.DataFrame, f: float, gam f is the coefficient of proportionality for fund flows and is the drift term in the stochastic process equation for fund flows. (Refer Appendix C) - :param data: (pd.DataFrame) Contains price series of both stocks in spread. - :param gamma: (float) coefficient of relative risk aversion. - :param f: (float) coefficient of proportionality (assumed to be positive). - :param r: (float) Rate of Returns. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. + :param gamma: (float) coefficient of relative risk aversion. (gamma > 0). + :param f: (float) coefficient of proportionality (f > 0). + :param r: (float) Rate of Returns. (r > 0). + :return: (np.array) Optimal weights with fund flows. """ - N = self.optimal_portfolio_weights(data, utility_type=1, gamma=gamma, r=r) + N = self.optimal_portfolio_weights(prices, utility_type=1, gamma=gamma, r=r) return (1 / (1 + f)) * N - def stabilization_region_calc(self, data: pd.DataFrame, utility_type: int = 1, gamma: float = 1, beta: float = 0.1, r: float = 0.05): + def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamma: float = 1, beta: float = 0.1, r: float = 0.05) -> tuple: """ Implementation of Theorem 3 in Jurek (2007). - :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. :param utility_type: (int) Flag signifies type of investor preferences. :param gamma: (float) coefficient of relative risk aversion. :param beta: (float) Subjective rate of time preference. (Only required for utility_type = 2). :param r: (float) Rate of Returns. + :return: (tuple) Tuple of numpy arrays for spread, min bound and max bound. """ if gamma <= 0: @@ -289,7 +300,7 @@ def stabilization_region_calc(self, data: pd.DataFrame, utility_type: int = 1, g self.gamma = gamma self.beta = beta - tau, S = self._spread_calc(data) + tau, S = self._spread_calc(prices) if self.gamma == 1: # Calculation of A and B functions are not done in case of gamma = 1. (Refer Appendix A.1 and B.2). @@ -330,12 +341,13 @@ def stabilization_region_calc(self, data: pd.DataFrame, utility_type: int = 1, g return S, min_bound, max_bound - def _AB_calc_1(self, tau): + def _AB_calc_1(self, tau) -> tuple: """ This helper function computes the A and B functions for investors with utility_type = 1. The implementation follows Appendix A.2 in the paper. :param tau: (np.array) Array with time till completion in years. + :return: (tuple) A and B arrays. """ # Calculating value of variable c_1 in Appendix A.2.1. @@ -362,7 +374,7 @@ def _AB_calc_1(self, tau): return A, B - def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0): + def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0) -> np.array: """ This method calculates the value of function A as described in the paper for investor with utility_type = 1. The implementation follows Appendix A.2.1 in the paper. @@ -374,6 +386,7 @@ def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0): :param c_2: (float) Value of variable c_2 in Appendix A.2.1. :param disc: (float) Value of discriminant in Appendix A.2.1. :param gamma_0: (float) Value of variable gamma_0 in Appendix A.2.1. + :return: (np.array) A array. """ A = None @@ -401,7 +414,7 @@ def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0): return A - def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): + def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: """ This method calculates the value of function B as described in the paper for investor with utility_type = 1. The implementation follows Appendix A.2.2 in the paper. @@ -414,6 +427,7 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): :param c_3: (float) Value of variable c_3 in Appendix A.2.1. :param disc: (float) Value of discriminant in Appendix A.2.1. :param gamma_0: (float) Value of variable gamma_0 in Appendix A.2.1. + :return: (np.array) B array. """ # Calculating value of variable c_4 in Appendix A.2.2. @@ -451,12 +465,13 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0): return B - def _AB_calc_2(self, tau): + def _AB_calc_2(self, tau) -> tuple: """ This helper function computes the A and B functions for investors with utility_type = 2. The implementation follows Appendix B.1 in the paper. :param tau: (np.array) Array with time till completion in years. + :return: (tuple) A and B arrays. """ # Calculating value of variable c_1 in Appendix B.1.1. @@ -481,7 +496,7 @@ def _AB_calc_2(self, tau): return A, B - def _A_calc_2(self, tau, c_1, c_2, disc, gamma_0): + def _A_calc_2(self, tau, c_1, c_2, disc, gamma_0) -> np.array: """ This method calculates the value of function A as described in the paper for investor with utility_type = 2. The implementation follows Appendix B.1.1 in the paper. @@ -494,13 +509,14 @@ def _A_calc_2(self, tau, c_1, c_2, disc, gamma_0): :param c_2: (float) Value of variable c_2 in Appendix B.1.1. :param disc: (float) Value of discriminant in Appendix B.1.1. :param gamma_0: (float) Value of variable gamma_0 in Appendix B.1.1. + :return: (np.array) A array. """ # Same calculation as for general CRRA Investor. return self._A_calc_1(tau, c_1, c_2, disc, gamma_0) - def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): + def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: """ This method calculates the value of function B as described in the paper for investor with utility_type = 2. The implementation follows Appendix B.1.2 in the paper. @@ -513,6 +529,7 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): :param c_3: (float) Value of variable c_3 in Appendix B.1.1. :param disc: (float) Value of discriminant in Appendix B.1.1. :param gamma_0: (float) Value of variable gamma_0 in Appendix B.1.1. + :return: (np.array) B array. """ # Calculating value of variable c_4 in Appendix B.1.2. @@ -533,118 +550,135 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0): if 0 < self.gamma < gamma_0 - error_margin: # Implementation of Case I in Appendix B.1.2. - rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) # Repeating Phrase 1. - rep_phrase_2 = np.sqrt(c_1 * c_3) / rep_phrase_1 # Repeating Phrase 2. - rep_phrase_3 = rep_phrase_1 * tau + np.arctan(c_2 / rep_phrase_1) # Repeating Phrase 3. - - denominator = c_1 * rep_phrase_2 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. - - # The final equation for B is split into 5 terms. - - term_1 = rep_exp_1 * rep_phrase_2 * c_4 * c_5 * (c_2 - rep_phrase_1 * np.tan(rep_phrase_3)) - - term_2 = rep_exp_1 * rep_phrase_2 - 2 * rep_exp_2 * (1 / np.cos(rep_phrase_3)) - - term_3 = rep_exp_2 * (1 / np.cos(rep_phrase_3)) - rep_exp_1 * rep_phrase_2 - - term_4 = rep_exp_1 * rep_phrase_2 * rep_phrase_1 * np.tan(rep_phrase_3) - - term_5 = -term_3 - - - B = np.exp(-tau * c_2) * (term_1 - + c_1 * (c_6 * (c_2 * term_2 - + term_3 * c_5 - + term_4) - -c_3 * term_5 * c_4)) / denominator - + B = self._B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau) elif gamma_0 - error_margin <= self.gamma <= gamma_0 + error_margin: # Implementation of Case II in Appendix B.1.2. - denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 # Denominator in final equation. - - # The final equation for B is split into 4 terms. + B = self._B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau) - term_1 = rep_exp_1 * tau * c_4 * c_2 ** 3 - - term_2 = (c_4 * (rep_exp_1 * (tau * c_5 + 1) - rep_exp_2) + rep_exp_1 * tau * c_1 * c_6) * c_2 ** 2 - - term_3 = c_1 * (rep_exp_1 * tau * c_5 + 2 * (rep_exp_1 - rep_exp_2)) * c_6 * c_2 - - term_4 = (rep_exp_1 - rep_exp_2) * c_1 * c_5 * c_6 + elif gamma_0 + error_margin < self.gamma < 1: + # Implementation of Case III in Appendix B.1.2. + B = self._B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau) - B = (-term_1 + term_2 - term_3 - + term_4) / denominator + else: + # Case when self.gamma > 1. + # Implementation of Case IV in Appendix B.1.2. + B = self._B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau) - elif gamma_0 + error_margin < self.gamma < 1: - # Implementation of Case III in Appendix B.1.2. + return B - rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) # Repeated Phrase 1. - rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) # Repeated Phrase 2. - rep_phrase_3 = np.arctanh(rep_phrase_2 / c_2) - tau * rep_phrase_2 # Repeated Phrase 3. - # arccoth(x) = arctanh(1/x) - denominator = c_2 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. + @staticmethod + def _B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau): + """ + Implementation of Case IV in Appendix B.1.2. + """ - # The final equation for B is split into 5 terms. + rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1. + rep_phrase_2 = 0.5 * np.sqrt(disc) * tau - np.arctanh(2 * c_2 / np.sqrt(disc)) # Repeated Phrase 2. + denominator = 2 * c_1 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. - term_1 = rep_exp_1 * rep_phrase_1 * c_6 * c_2 ** 2 + # The final equation for B is split into 5 terms. + term_1 = 2 * rep_exp_1 * rep_phrase_1 * c_4 * c_5 * (c_2 + 0.5 * np.sqrt(disc) * np.tanh(rep_phrase_2)) + term_2 = 2 * rep_exp_1 * rep_phrase_1 - 2 * rep_exp_2 * (1 / np.cosh(rep_phrase_2)) + # sech = 1 / cosh + term_3 = rep_exp_2 * (1 / np.cosh(rep_phrase_2)) - 2 * rep_exp_1 * rep_phrase_1 + term_4 = rep_exp_1 * np.sqrt(disc) * rep_phrase_1 * np.tanh(rep_phrase_2) + term_5 = -term_3 - term_2 = rep_exp_1 * c_3 * rep_phrase_1 * c_4 + B = np.exp(-tau * c_2) * (term_1 + + c_1 * (c_6 * (c_2 * term_2 + + term_3 * c_5 + - term_4) + - c_3 * term_5 * c_4)) / denominator - term_3 = 2 * rep_exp_2 * (1 / np.sinh(rep_phrase_3)) - rep_phrase_2 * (1 / np.tanh(rep_phrase_3)) * rep_phrase_1 - # csch = 1/sinh, coth = 1/tanh + return B - term_4 = rep_exp_1 * rep_phrase_1 * c_5 - term_5 = (1 / np.sinh(rep_phrase_3)) * (c_3 * c_4 * (rep_exp_2 * rep_phrase_2 - rep_exp_1 * np.sinh(tau * rep_phrase_2) * c_5) - + rep_exp_2 * rep_phrase_2 * c_5 * c_6) - # csch = 1/sinh + @staticmethod + def _B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): + """ + Implementation of Case III in Appendix B.1.2. + """ + rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) # Repeated Phrase 1. + rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) # Repeated Phrase 2. + rep_phrase_3 = np.arctanh(rep_phrase_2 / c_2) - tau * rep_phrase_2 # Repeated Phrase 3. + # arccoth(x) = arctanh(1/x) + denominator = c_2 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. - B = np.exp(-tau * c_2) * (term_1 - (term_2 + (rep_phrase_2 * term_3 + term_4) * c_6) * c_2 - + term_5) / denominator + # The final equation for B is split into 5 terms. + term_1 = rep_exp_1 * rep_phrase_1 * c_6 * c_2 ** 2 + term_2 = rep_exp_1 * c_3 * rep_phrase_1 * c_4 + term_3 = 2 * rep_exp_2 * (1 / np.sinh(rep_phrase_3)) - rep_phrase_2 * (1 / np.tanh(rep_phrase_3)) * rep_phrase_1 + # csch = 1/sinh, coth = 1/tanh + term_4 = rep_exp_1 * rep_phrase_1 * c_5 + term_5 = (1 / np.sinh(rep_phrase_3)) * ( + c_3 * c_4 * (rep_exp_2 * rep_phrase_2 - rep_exp_1 * np.sinh(tau * rep_phrase_2) * c_5) + + rep_exp_2 * rep_phrase_2 * c_5 * c_6) + # csch = 1/sinh + B = np.exp(-tau * c_2) * (term_1 - (term_2 + (rep_phrase_2 * term_3 + term_4) * c_6) * c_2 + + term_5) / denominator - else: - # Case when self.gamma > 1. - # Implementation of Case IV in Appendix B.1.2. + return B - rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1. - rep_phrase_2 = 0.5 * np.sqrt(disc) * tau - np.arctanh(2 * c_2 / np.sqrt(disc)) # Repeated Phrase 2. - denominator = 2 * c_1 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. + @staticmethod + def _B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): + """ + Implementation of Case II in Appendix B.1.2. + """ - # The final equation for B is split into 5 terms. + denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 # Denominator in final equation. - term_1 = 2 * rep_exp_1 * rep_phrase_1 * c_4 * c_5 * (c_2 + 0.5 * np.sqrt(disc) * np.tanh(rep_phrase_2)) + # The final equation for B is split into 4 terms. + term_1 = rep_exp_1 * tau * c_4 * c_2 ** 3 + term_2 = (c_4 * (rep_exp_1 * (tau * c_5 + 1) - rep_exp_2) + rep_exp_1 * tau * c_1 * c_6) * c_2 ** 2 + term_3 = c_1 * (rep_exp_1 * tau * c_5 + 2 * (rep_exp_1 - rep_exp_2)) * c_6 * c_2 + term_4 = (rep_exp_1 - rep_exp_2) * c_1 * c_5 * c_6 - term_2 = 2 * rep_exp_1 * rep_phrase_1 - 2 * rep_exp_2 * (1 / np.cosh(rep_phrase_2)) - # sech = 1 / cosh + B = (-term_1 + term_2 - term_3 + + term_4) / denominator - term_3 = rep_exp_2 * (1 / np.cosh(rep_phrase_2)) - 2 * rep_exp_1 * rep_phrase_1 + return B - term_4 = rep_exp_1 * np.sqrt(disc) * rep_phrase_1 * np.tanh(rep_phrase_2) - term_5 = -term_3 + @staticmethod + def _B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): + """ + Implementation of Case I in Appendix B.1.2. + """ + rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) # Repeating Phrase 1. + rep_phrase_2 = np.sqrt(c_1 * c_3) / rep_phrase_1 # Repeating Phrase 2. + rep_phrase_3 = rep_phrase_1 * tau + np.arctan(c_2 / rep_phrase_1) # Repeating Phrase 3. + denominator = c_1 * rep_phrase_2 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. - B = np.exp(-tau * c_2) * (term_1 - + c_1 * ( c_6 * (c_2 * term_2 - + term_3 * c_5 - - term_4) - - c_3 * term_5 * c_4)) / denominator + # The final equation for B is split into 5 terms. + term_1 = rep_exp_1 * rep_phrase_2 * c_4 * c_5 * (c_2 - rep_phrase_1 * np.tan(rep_phrase_3)) + term_2 = rep_exp_1 * rep_phrase_2 - 2 * rep_exp_2 * (1 / np.cos(rep_phrase_3)) + term_3 = rep_exp_2 * (1 / np.cos(rep_phrase_3)) - rep_exp_1 * rep_phrase_2 + term_4 = rep_exp_1 * rep_phrase_2 * rep_phrase_1 * np.tan(rep_phrase_3) + term_5 = -term_3 + B = np.exp(-tau * c_2) * (term_1 + + c_1 * (c_6 * (c_2 * term_2 + + term_3 * c_5 + + term_4) + - c_3 * term_5 * c_4)) / denominator return B + @staticmethod def _calc_half_life(k: float) -> float: """ Function returns half life of mean reverting spread from rate of mean reversion. + :return: (float) half life. """ return np.log(2) / k # Half life of shocks. @@ -653,6 +687,7 @@ def _calc_half_life(k: float) -> float: def describe(self) -> pd.Series: """ Method returns values of instance attributes calculated from training data. + :return: (pd.Series) series describing parameter values. """ if self.sigma is None: @@ -670,7 +705,8 @@ def describe(self) -> pd.Series: return output - def plotting(self, data:pd.DataFrame, num_test_windows = 5, delta_t = 1/252, utility_type = 1,gamma = 10, beta = 0.1, r = 0.05 , f = 0.1): + def plot_results(self, prices:pd.DataFrame, num_test_windows = 5, delta_t =1 / 252, utility_type = 1, gamma = 10, + beta = 0.1, r = 0.05, f = 0.1): """ Method plots out of sample performance of the model on specified number of test windows. We use a backward looking rolling window as training data and its size depends on the number of test windows chosen. @@ -679,9 +715,9 @@ def plotting(self, data:pd.DataFrame, num_test_windows = 5, delta_t = 1/252, uti For example, if the total data is of length 16 years, with the number of test windows set to 5, the length of training data would be 16 - (5 + 1) = 10. (The last year is not considered for testing). - :param data: (pd.DataFrame) Contains price series of both stocks in spread with dates as index. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread with dates as index. :param num_test_windows: (int) Number of out of sample testing windows to plot. - :param delta_t: (float) Time difference between each index of data, calculated in years. + :param delta_t: (float) Time difference between each index of prices, calculated in years. :param gamma: (float) coefficient of relative risk aversion. :param f: (float) coefficient of proportionality (assumed to be positive). :param r: (float) Rate of Returns. @@ -692,28 +728,29 @@ def plotting(self, data:pd.DataFrame, num_test_windows = 5, delta_t = 1/252, uti plt.rcParams.update({'font.size': 8}) - data = data.ffill() + prices = prices.ffill() - if not np.issubdtype(data.index.dtype, np.datetime64): + if not np.issubdtype(prices.index.dtype, np.datetime64): raise Exception("Please make sure index of dataframe is datetime type.") - if len(data) < (10 / delta_t): - raise Exception("Please make sure length of input data is greater than 10 years.") + if len(prices) < (10 / delta_t): + raise Exception("Please make sure length of input data is greater than 10 years. " + "This is the time period used to fit the model in the paper.") - years = data.index.year.unique() + years = prices.index.year.unique() - stab_result_dataframe = pd.DataFrame(index=data.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, + stab_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, columns=['Spread', 'lower bound', 'upper bound']) - optimal_result_dataframe = pd.DataFrame(index=data.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, + optimal_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, columns=['Weights']) - optimal_fund_flows_result_dataframe = pd.DataFrame(index=data.loc[str(years[-(num_test_windows + 1)]): + optimal_fund_flows_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]): str(years[-1])].index, columns=['Weights']) ind = 0 for year in np.arange(years[-(num_test_windows + 1)], years[-1], 1): - data_train_dataframe = data.loc[str(year - (len(years) - (num_test_windows + 1))):str(year - 1)] - data_test_dataframe = data.loc[str(year)] + data_train_dataframe = prices.loc[str(year - (len(years) - (num_test_windows + 1))):str(year - 1)] + data_test_dataframe = prices.loc[str(year)] self.fit(data_train_dataframe, delta_t=delta_t) @@ -721,8 +758,8 @@ def plotting(self, data:pd.DataFrame, num_test_windows = 5, delta_t = 1/252, uti utility_type=utility_type, beta=beta, r=r) optimal_fund_flow_weights = self.optimal_portfolio_weights_fund_flows(data_test_dataframe, gamma=gamma, f=f, r=r) - S, min_bound, max_bound = self.stabilization_region_calc(data_test_dataframe, gamma=gamma, - utility_type=utility_type, beta=beta, r=r) + S, min_bound, max_bound = self.stabilization_region(data_test_dataframe, gamma=gamma, + utility_type=utility_type, beta=beta, r=r) stab_result_dataframe.iloc[ind:ind + len(S), :] = np.array([S, min_bound, max_bound]).T optimal_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_weights]).T diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index d9fae2af..a944e9da 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -17,7 +17,7 @@ import scipy.optimize as so -class StochasticControlMudchanatongsuk: +class OUModelMudchanatongsuk: """ This class implements a stochastic control approach to the problem of pairs trading. @@ -30,6 +30,9 @@ class StochasticControlMudchanatongsuk: """ def __init__(self): + """ + Initializes the parameters of the module. + """ # Characteristics of Training Data. self.ticker_A = None # Ticker Symbol of first stock. @@ -52,68 +55,69 @@ def __init__(self): @staticmethod - def _data_preprocessing(data): + def _data_preprocessing(prices) -> pd.DataFrame: """ Helper function for input data preprocessing. - :param data: (pd.DataFrame) Pricing data of both stocks in spread. + :param prices: (pd.DataFrame) Pricing data of both stocks in spread. + :return: (pd.DataFrame) processed dataframe. """ - return data.ffill() + return prices.ffill() - def fit(self, data: pd.DataFrame): + def fit(self, prices: pd.DataFrame): """ This method uses inputted training data to calculate the spread and estimate the parameters of the corresponding OU process. The spread construction implementation follows Section II A in Mudchanatongsuk (2008). - :param data: (pd.DataFrame) Contains price series of both stocks in spread. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. """ # Preprocessing - data = self._data_preprocessing(data) + prices = self._data_preprocessing(prices) # Setting instance attributes. - self.time_array = np.arange(0, len(data)) * self.delta_t - self.ticker_A, self.ticker_B = data.columns[0], data.columns[1] + self.time_array = np.arange(0, len(prices)) * self.delta_t + self.ticker_A, self.ticker_B = prices.columns[0], prices.columns[1] # Calculating the spread. - self.S = np.log(data.loc[:, self.ticker_B]) - self.spread = np.log(data.loc[:, self.ticker_A]) - self.S + self.S = np.log(prices.loc[:, self.ticker_B]) + self.spread = np.log(prices.loc[:, self.ticker_A]) - self.S self.spread = self.spread.to_numpy() # Converting from pd.Series to numpy array. self.S = self.S.to_numpy() # Converting from pd.Series to numpy array. params = self._estimate_params_log_likelihood() - #print(f"Params from likelihood : {params[:-1]}") self.sigma, self.mu, self.k,self.theta, self.eta, self.rho = params[:-1] - def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): + def optimal_portfolio_weights(self, prices: pd.DataFrame, gamma = -100) -> np.array: """ This method calculates the final optimal portfolio weights for the calculated spread. The calculation of weights follows Section III in Mudchanatongsuk (2008), specifically equation 28. - :param data: (pd.DataFrame) Contains price series of both stocks in spread. - :param gamma: (float) Parameter of utility function (gamma < 1) + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. + :param gamma: (float) Parameter of utility function (gamma < 1). + :return: (np.array) Optimal weights array. """ if gamma >= 1: raise Exception("Please make sure value of gamma is less than 1.") # Preprocessing - data = self._data_preprocessing(data) + prices = self._data_preprocessing(prices) # Setting instance attributes. self.gamma = gamma - t = np.arange(0, len(data)) * self.delta_t + t = np.arange(0, len(prices)) * self.delta_t tau = t[-1] - t # Calculating spread. - x = np.log(data.iloc[:, 0]) - np.log(data.iloc[:, 1]) + x = np.log(prices.iloc[:, 0]) - np.log(prices.iloc[:, 1]) x = x.to_numpy() # Converting from pd.Series to numpy array. # Calculating the alpha and beta functions. @@ -127,12 +131,13 @@ def optimal_portfolio_weights(self, data: pd.DataFrame, gamma = -100): return h - def _alpha_beta_calc(self, tau): + def _alpha_beta_calc(self, tau) -> tuple: """ This helper function computes the alpha and beta functions as given in equation 24 and 25 of Mudchanatongsuk (2008). :param tau: (np.array) Array with time till completion in years. + :return: (tuple) alpha and beta arrays. """ sqrt_gamma = np.sqrt(1 - self.gamma) # Repeating Calculation involving gamma. @@ -144,12 +149,13 @@ def _alpha_beta_calc(self, tau): return alpha_t, beta_t - def _alpha_calc(self, sqrt_gamma, exp_calc): + def _alpha_calc(self, sqrt_gamma, exp_calc) -> np.array: """ This helper function computes the alpha function in equation 24. :param sqrt_gamma: (float) Repeating value. :param exp_calc: (np.array) Repeating series of values. + :return: (np.array) alpha array. """ # The equation for calculation of alpha is split into two parts. @@ -160,12 +166,13 @@ def _alpha_calc(self, sqrt_gamma, exp_calc): return left_calc * (1 + right_calc) - def _beta_calc(self, sqrt_gamma, exp_calc): + def _beta_calc(self, sqrt_gamma, exp_calc) -> np.array: """ This helper function computes the beta function in equation 25. :param sqrt_gamma: (float) Repeating value. :param exp_calc: (np.array) Repeating series of values. + :return: (np.array) beta array. """ # The equation for calculation of beta is split into two parts. @@ -177,9 +184,10 @@ def _beta_calc(self, sqrt_gamma, exp_calc): return left_calc * right_calc - def _estimate_params_log_likelihood(self): + def _estimate_params_log_likelihood(self) -> tuple: """ Estimates parameters of model based on log likelihood maximization. + :return: (tuple) Consists of final estimated params. """ # Setting bounds @@ -204,12 +212,13 @@ def _estimate_params_log_likelihood(self): @staticmethod - def _compute_log_likelihood(params, *args): + def _compute_log_likelihood(params, *args) -> float: """ Helper function computes log likelihood function for a set of params. This implementation follows Appendix of Mudchanatongsuk (2008). param params: (tuple) Contains values of set params. + :return: (float) negation of log likelihood. """ # Setting given parameters @@ -252,6 +261,7 @@ def _compute_log_likelihood(params, *args): def _calc_half_life(k: float) -> float: """ Function returns half life of mean reverting spread from rate of mean reversion. + :return: (float) Half life. """ return np.log(2) / k # Half life of shocks. @@ -260,6 +270,7 @@ def _calc_half_life(k: float) -> float: def describe(self) -> pd.Series: """ Method returns values of instance attributes calculated from training data. + :return: (pd.Series) series describing parameter values. """ if self.sigma is None: diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index e8bb52d8..a5732b81 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -268,17 +268,17 @@ Implementation .. automodule:: arbitragelab.stochastic_control_approach.ou_model_jurek -.. autoclass:: StochasticControlJurek +.. autoclass:: OUModelJurek :members: __init__ -.. automethod:: StochasticControlJurek.fit +.. automethod:: OUModelJurek.fit .. tip:: To view the estimated model parameters from training data, call the ``describe`` function. - .. automethod:: StochasticControlJurek.describe + .. automethod:: OUModelJurek.describe Step 2: Getting the Optimal Portfolio Weights @@ -299,7 +299,7 @@ If we choose the investor with intermediate consumption, we also need to specify Implementation ============== -.. automethod:: StochasticControlJurek.optimal_portfolio_weights +.. automethod:: OUModelJurek.optimal_portfolio_weights Step 3: Stabilization Region **************************** @@ -309,7 +309,7 @@ In this optional step, we can calculate the boundaries of the stabilization regi Implementation ============== -.. automethod:: StochasticControlJurek.stabilization_region_calc +.. automethod:: OUModelJurek.stabilization_region .. figure:: images/stabilization_bound.png @@ -326,7 +326,7 @@ In this optional step, we calculate the optimal portfolio weights with the inclu Implementation ============== -.. automethod:: StochasticControlJurek.optimal_portfolio_weights_fund_flows +.. automethod:: OUModelJurek.optimal_portfolio_weights_fund_flows .. figure:: images/optimal_weights_fund_flows.png @@ -343,7 +343,7 @@ In this optional step, we can plot the stabilization regions and optimal portfol Implementation ============== -.. automethod:: StochasticControlJurek.plotting +.. automethod:: OUModelJurek.plot_results Examples @@ -372,9 +372,9 @@ Finally, we use the out-of-sample test data to calculate the optimal portfolio w .. code-block:: - from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek + from arbitragelab.stochastic_control_approach.ou_model_jurek import OUModelJurek - sc = StochasticControlJurek() + sc = OUModelJurek() sc.fit(data_train_dataframe) @@ -397,15 +397,15 @@ Finally, on the out-of-sample test data we calculate the stabilization region fo .. code-block:: - from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek + from arbitragelab.stochastic_control_approach.ou_model_jurek import OUModelJurek - sc = StochasticControlJurek() + sc = OUModelJurek() sc.fit(data_train_dataframe) print(sc.describe()) - S, min_bound, max_bound = sc.stabilization_region_calc(data_test_dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + S, min_bound, max_bound = sc.stabilization_region(data_test_dataframe, beta = 0.01, gamma = 0.5, utility_type=1) plt.plot(S, label='Spread') plt.plot(min_bound, color='red', linestyle='dashed') @@ -426,9 +426,9 @@ using the fitted model. .. code-block:: - from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek + from arbitragelab.stochastic_control_approach.ou_model_jurek import OUModelJurek - sc = StochasticControlJurek() + sc = OUModelJurek() sc.fit(data_train_dataframe) diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index 82f93d25..0f62e5ee 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -111,11 +111,11 @@ Implementation .. automodule:: arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk -.. autoclass:: StochasticControlMudchanatongsuk +.. autoclass:: OUModelMudchanatongsuk :members: __init__ -.. automethod:: StochasticControlMudchanatongsuk.fit +.. automethod:: OUModelMudchanatongsuk.fit .. note:: Although the paper provides closed form solutions for parameter estimation, @@ -124,7 +124,7 @@ Implementation .. tip:: To view the estimated model parameters from training data, call the ``describe`` function. - .. automethod:: StochasticControlMudchanatongsuk.describe + .. automethod:: OUModelMudchanatongsuk.describe Step 2: Getting the Optimal Portfolio Weights @@ -139,7 +139,7 @@ In this step we input the evaluation data and specify the utility function param Implementation ============== -.. automethod:: StochasticControlMudchanatongsuk.optimal_portfolio_weights +.. automethod:: OUModelMudchanatongsuk.optimal_portfolio_weights Example @@ -163,9 +163,9 @@ Finally, we use the out-of-sample test data to calculate the optimal portfolio w .. code-block:: - from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import StochasticControlMudchanatongsuk + from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import OUModelMudchanatongsuk - sc = StochasticControlMudchanatongsuk() + sc = OUModelMudchanatongsuk() sc.fit(data_train_dataframe) diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index 9c0e22e4..05763ad0 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -12,7 +12,7 @@ import numpy as np import pandas as pd -from arbitragelab.stochastic_control_approach.ou_model_jurek import StochasticControlJurek +from arbitragelab.stochastic_control_approach.ou_model_jurek import OUModelJurek # pylint: disable=protected-access @@ -42,7 +42,7 @@ def test_fit(self): Tests the fit method in the class. """ - sc_jurek = StochasticControlJurek() + sc_jurek = OUModelJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) @@ -86,7 +86,7 @@ def test_describe(self): Tests the describe method in the class. """ - sc_jurek = StochasticControlJurek() + sc_jurek = OUModelJurek() with self.assertRaises(Exception): sc_jurek.describe() @@ -108,7 +108,7 @@ def test_optimal_weights(self): Tests the optimal portfolio weights method in the class. """ - sc_jurek = StochasticControlJurek() + sc_jurek = OUModelJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) @@ -155,19 +155,19 @@ def test_stabilization_region(self): Tests the stabilization region method in the class. """ - sc_jurek = StochasticControlJurek() + sc_jurek = OUModelJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) with self.assertRaises(Exception): - sc_jurek.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=10) + sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=0.5, utility_type=10) with self.assertRaises(Exception): - sc_jurek.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = -1) + sc_jurek.stabilization_region(self.dataframe, beta = 0.01, gamma = -1) - spread, min_bound, max_bound = sc_jurek.stabilization_region_calc(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) spread_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, 0.5440914321753456, 0.5471230270552558, 0.5566709779363245, 0.5532053519529174, @@ -236,10 +236,10 @@ def test_stabilization_region(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) - sc_jurek.stabilization_region_calc(self.dataframe, gamma=1, utility_type=1) + sc_jurek.stabilization_region(self.dataframe, gamma=1, utility_type=1) - sc_jurek.stabilization_region_calc(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) - sc_jurek.stabilization_region_calc(self.dataframe, beta=0.01, gamma=2, utility_type=2) + sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=2, utility_type=2) def test_optimal_weights_fund_flows(self): @@ -247,7 +247,7 @@ def test_optimal_weights_fund_flows(self): Tests the optimal weights with fund flows method in the class. """ - sc_jurek = StochasticControlJurek() + sc_jurek = OUModelJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) @@ -283,7 +283,7 @@ def test_private_methods(self): Function tests special cases for code coverage. """ - sc_jurek = StochasticControlJurek() + sc_jurek = OUModelJurek() with warnings.catch_warnings(): @@ -318,18 +318,18 @@ def test_private_methods(self): @mock.patch("arbitragelab.stochastic_control_approach.ou_model_jurek.plt") def test_plotting(self, mock_plt): """ - Tests the plotting method in the class. + Tests the plot_results method in the class. """ - sc_jurek = StochasticControlJurek() + sc_jurek = OUModelJurek() with self.assertRaises(Exception): - sc_jurek.plotting(self.dataframe) + sc_jurek.plot_results(self.dataframe) self.dataframe.index = pd.to_datetime(self.dataframe.index) with self.assertRaises(Exception): - sc_jurek.plotting(self.dataframe) + sc_jurek.plot_results(self.dataframe) project_path = os.path.dirname(__file__) path = project_path + '/test_data/shell-rdp-close_USD.csv' @@ -337,7 +337,7 @@ def test_plotting(self, mock_plt): data.index = pd.to_datetime(data.index, format="%d/%m/%Y") - sc_jurek.plotting(data) + sc_jurek.plot_results(data) # Assert plt.figure got called assert mock_plt.show.called diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index 126ef24e..994ef803 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -11,7 +11,7 @@ import numpy as np import pandas as pd -from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import StochasticControlMudchanatongsuk +from arbitragelab.stochastic_control_approach.ou_model_mudchanatongsuk import OUModelMudchanatongsuk class TestOUModelMudchanatongsuk(unittest.TestCase): @@ -34,7 +34,7 @@ def setUpClass(cls) -> None: cls.dataframe = data[['GLD', 'GDX']] - cls.sc_mudchana = StochasticControlMudchanatongsuk() + cls.sc_mudchana = OUModelMudchanatongsuk() def test_fit(self): @@ -42,7 +42,7 @@ def test_fit(self): Tests the fit method in the class. """ - sc_mudchana = StochasticControlMudchanatongsuk() + sc_mudchana = OUModelMudchanatongsuk() sc_mudchana.fit(self.dataframe) @@ -76,7 +76,7 @@ def test_describe(self): Tests the describe method in the class. """ - sc_mudchana = StochasticControlMudchanatongsuk() + sc_mudchana = OUModelMudchanatongsuk() with self.assertRaises(Exception): sc_mudchana.describe() @@ -97,7 +97,7 @@ def test_optimal_weights(self): Tests the optimal portfolio weights method in the class. """ - sc_mudchana = StochasticControlMudchanatongsuk() + sc_mudchana = OUModelMudchanatongsuk() sc_mudchana.fit(self.dataframe) From 3a0498355ebc1ddd635e78d830945af3f5de19eb Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 2 Apr 2021 15:57:59 +0530 Subject: [PATCH 079/103] Changes to test files according to PR. --- tests/test_ou_model_jurek.py | 230 +++++++++---------------- tests/test_ou_model_mudchanatongsuk.py | 57 ++---- 2 files changed, 92 insertions(+), 195 deletions(-) diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index 05763ad0..35fb1f2e 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -30,12 +30,17 @@ def setUpClass(cls) -> None: np.random.seed(0) project_path = os.path.dirname(__file__) - cls.path = project_path + '/test_data/gld_gdx_data.csv' - data = pd.read_csv(cls.path) - data = data.set_index('Date') + path = project_path + '/test_data/gld_gdx_data.csv' + data = pd.read_csv(path) + data = data.set_index('Date') cls.dataframe = data[['GLD', 'GDX']] + path = project_path + '/test_data/shell-rdp-close_USD.csv' + data = pd.read_csv(path, index_col='Date').ffill() + data.index = pd.to_datetime(data.index, format="%d/%m/%Y") + cls.shell_rdp_data = data + def test_fit(self): """ @@ -48,37 +53,17 @@ def test_fit(self): warnings.simplefilter("ignore", UserWarning) sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=True, significance_level=0.95) - spread_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, - 0.5440914321753456, 0.5471230270552558, 0.5566709779363245, 0.5532053519529174, - 0.5516073438832347, 0.5489831227316044, 0.5466971132268911, 0.5434512050224662, - 0.5453702735903314, 0.5424140575831877, 0.5450224920172433, 0.5421415318431051, - 0.5399089411892184, 0.5417342658455901, 0.5440976512434289, 0.5467950767477552, - 0.5515669810213595, 0.5561602409477461, 0.557182448471494, 0.5561335579963324, - 0.5566339956831441, 0.5521263613656556, 0.5390771353290404, 0.5433116196626523, - 0.5423901587923536, 0.5310046126730086, 0.5299496560807411, 0.5299140307516241, - 0.5290870021197289, 0.5280183485753618, 0.5386137486358292, 0.5410873897027797, - 0.5387603530740576, 0.5352495487153268, 0.5374129802697099, 0.5448692920210395, - 0.5400420169347888, 0.5404828705175425, 0.5359861307007192, 0.5284024338590281, - 0.5358697412015444, 0.5371643904164909, 0.5331592612797672, 0.5377038488055406, - 0.5372396478215287, 0.5312962591087894, 0.5211917143212158, 0.5190644803181462, - 0.5251666364813955, 0.5239848905417022, 0.5203248327883234, 0.5243929266377997, - 0.5191150765020052, 0.5220658221349787, 0.5176793463326727, 0.516863975659782, - 0.5175054097681386, 0.5117401246636695, 0.5122159389305105, 0.5177991465134326, - 0.513038871315079, 0.5098731313766349, 0.5085175023043633, 0.5040433641772756, - 0.5039290495180081, 0.5002238140944849, 0.4947870896437365, 0.49780569727511526, - 0.5020354188220554, 0.5023496206998971, 0.5054215932061087] - - np.testing.assert_array_almost_equal(sc_jurek.spread, spread_value, decimal=4) + # Checking values for spread calc. + self.assertAlmostEqual(np.mean(sc_jurek.spread), 0.5328233514, delta=1e-7) + self.assertAlmostEqual(sc_jurek.spread[7], 0.5532053519, delta=1e-7) + self.assertAlmostEqual(sc_jurek.spread[28], 0.5423901587, delta=1e-7) + self.assertAlmostEqual(sc_jurek.spread[-1], 0.5054215932, delta=1e-7) self.assertAlmostEqual(sc_jurek.mu, 0.532823, delta=1e-4) self.assertAlmostEqual(sc_jurek.k, 10.2728, delta=1e-4) self.assertAlmostEqual(sc_jurek.sigma, 0.0743999, delta=1e-4) - project_path = os.path.dirname(__file__) - path = project_path + '/test_data/shell-rdp-close_USD.csv' - data = pd.read_csv(path, index_col='Date').ffill() - data.index = pd.to_datetime(data.index, format="%d/%m/%Y") - sc_jurek.fit(data, delta_t=1 / 252, adf_test=False) + sc_jurek.fit(self.shell_rdp_data, delta_t=1 / 252, adf_test=False) def test_describe(self): @@ -120,34 +105,41 @@ def test_optimal_weights(self): with self.assertRaises(Exception): sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = -1) + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) - weights_value = [-73.45194149467186, -66.92279595239394, -65.15408289280388, -35.43777877275913, - -34.545817687919545, -42.535359317812855, -67.68919459098552, -58.56650579922123, - -54.36327112091763, -47.45713298534966, -41.44201490315255, -32.89844175560287, - -37.96096743214949, -30.18088183878759, -37.060772390128506, -29.479402457404348, - -23.60620567684073, -28.42505229728819, -34.66288294932173, -41.78249330166799, - -54.37101206797773, -66.49171390891671, -69.2030397247047, -66.45661770001615, - -67.79578295793033, -55.93171185761935, -21.540238878824916, -32.726868430709885, - -30.316954989694864, -0.2964470572123097, 2.4712176283324236, 2.548417241307483, - 4.714693033871299, 7.519785928719447, -20.497495188429824, -27.06729132591058, - -20.947832834193054, -11.69200027231988, -17.452717588039015, -37.247605794787766, - -24.5030045585155, -25.72274610257665, -13.832747281667135, 6.28649720491654, - -13.620032093482212, -17.124887100964134, -6.494784173912921, -18.6978042520508, - -17.529819813294633, -1.6519685678067688, 25.4931602870002, 31.25446478754843, - 14.784765120158685, 17.99308095126069, 27.98439238126017, 16.914096722374268, - 31.452327361923672, 23.40469539338531, 35.68396003464806, 38.1450485471757, - 36.56085532095218, 53.20482218153802, 52.27927773305257, 36.570939606379525, - 50.92261233207725, 60.964273675008954, 65.91794540384299, 80.72165214689629, - 82.56422216475477, 96.13482957606092, 116.22091468441988, 109.1943316005652, - 97.8535878146283, 100.10622031248108, 92.57663162301588] - - np.testing.assert_array_almost_equal(weights, weights_value, decimal=4) - - sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) - sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) - sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=1) - sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=2) + self.assertAlmostEqual(np.mean(weights), -2.7252320178, delta=1e-7) + self.assertAlmostEqual(weights[7], -58.5665057992, delta=1e-7) + self.assertAlmostEqual(weights[28], -30.3169549896, delta=1e-7) + self.assertAlmostEqual(weights[-1], 92.5766316230, delta=1e-7) + + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) + + self.assertAlmostEqual(np.mean(weights), -4.8129160068, delta=1e-7) + self.assertAlmostEqual(weights[7], -42.82308043, delta=1e-7) + self.assertAlmostEqual(weights[28], -22.6539479, delta=1e-7) + self.assertAlmostEqual(weights[-1], 46.28831581, delta=1e-7) + + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) + + self.assertAlmostEqual(np.mean(weights), -2947786.5697284327, delta=1e-7) + self.assertAlmostEqual(weights[7], -9803080.87074925, delta=1e-7) + self.assertAlmostEqual(weights[28], -1762115.70956469, delta=1e-7) + self.assertAlmostEqual(weights[-1], -54007.10111104, delta=1e-7) + + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=1) + + self.assertAlmostEqual(np.mean(weights), -5.3267767287, delta=1e-7) + self.assertAlmostEqual(weights[7], -31.15603589, delta=1e-7) + self.assertAlmostEqual(weights[28], -16.4211391034, delta=1e-7) + self.assertAlmostEqual(weights[-1], 23.14415791, delta=1e-7) + + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=2) + + self.assertAlmostEqual(np.mean(weights), 28.7539986245, delta=1e-7) + self.assertAlmostEqual(weights[7], 34.13526822, delta=1e-7) + self.assertAlmostEqual(weights[28], 28.56326627, delta=1e-7) + self.assertAlmostEqual(weights[-1], 23.14415791, delta=1e-7) def test_stabilization_region(self): @@ -169,77 +161,36 @@ def test_stabilization_region(self): spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) - spread_value = [0.5588694237684244, 0.556388954154023, 0.5557158550545369, 0.5444317219668442, - 0.5440914321753456, 0.5471230270552558, 0.5566709779363245, 0.5532053519529174, - 0.5516073438832347, 0.5489831227316044, 0.5466971132268911, 0.5434512050224662, - 0.5453702735903314, 0.5424140575831877, 0.5450224920172433, 0.5421415318431051, - 0.5399089411892184, 0.5417342658455901, 0.5440976512434289, 0.5467950767477552, - 0.5515669810213595, 0.5561602409477461, 0.557182448471494, 0.5561335579963324, - 0.5566339956831441, 0.5521263613656556, 0.5390771353290404, 0.5433116196626523, - 0.5423901587923536, 0.5310046126730086, 0.5299496560807411, 0.5299140307516241, - 0.5290870021197289, 0.5280183485753618, 0.5386137486358292, 0.5410873897027797, - 0.5387603530740576, 0.5352495487153268, 0.5374129802697099, 0.5448692920210395, - 0.5400420169347888, 0.5404828705175425, 0.5359861307007192, 0.5284024338590281, - 0.5358697412015444, 0.5371643904164909, 0.5331592612797672, 0.5377038488055406, - 0.5372396478215287, 0.5312962591087894, 0.5211917143212158, 0.5190644803181462, - 0.5251666364813955, 0.5239848905417022, 0.5203248327883234, 0.5243929266377997, - 0.5191150765020052, 0.5220658221349787, 0.5176793463326727, 0.516863975659782, - 0.5175054097681386, 0.5117401246636695, 0.5122159389305105, 0.5177991465134326, - 0.513038871315079, 0.5098731313766349, 0.5085175023043633, 0.5040433641772756, - 0.5039290495180081, 0.5002238140944849, 0.4947870896437365, 0.49780569727511526, - 0.5020354188220554, 0.5023496206998971, 0.5054215932061087] - - min_bound_value = [0.5114954740261215, 0.511494304659523, 0.5114930719447892, 0.511491772862663, - 0.5114904043053522, 0.5114889630823879, 0.5114874459281928, 0.5114858495116325, - 0.5114841704478517, 0.5114824053127447, 0.5114805506604544, 0.5114786030443454, - 0.5114765590419567, 0.5114744152845064, 0.5114721684915997, 0.5114698155118698, - 0.5114673533703791, 0.5114647793237237, 0.5114620909238913, 0.5114592860920708, - 0.5114563632037615, 0.5114533211866995, 0.5114501596333154, 0.511446878929659, - 0.5114434804029621, 0.5114399664902919, 0.5114363409310583, 0.5114326089864681, - 0.5114287776894266, 0.5114248561288008, 0.5114208557724526, 0.5114167908339828, - 0.511412678688732, 0.5114085403452506, 0.5114044009791965, 0.5114002905374362, - 0.5113962444210516, 0.5113923042569426, 0.5113885187688384, 0.511384944759741, - 0.5113816482191418, 0.511378705569804, 0.511376205070451, 0.511374248392369, - 0.5113729523897055, 0.5113724510851133, 0.5113728890138528, 0.5113744592285356, - 0.5113773528151565, 0.511381797500334, 0.5113880522315185, 0.5113964110175347, - 0.5114072071883844, 0.5114208181088091, 0.5114376703799909, 0.5114582455627015, - 0.5114830864528888, 0.5115128039368494, 0.5115480844474176, 0.5115896980347043, - 0.5116385070545585, 0.5116954754648763, 0.5117616787042263, 0.5118383141092488, - 0.5119267118078763, 0.512028346006258, 0.512144846571341, 0.5122780108031038, - 0.5124298152978717, 0.5126024278381169, 0.5127982193212931, 0.5130197758849269, - 0.5132699116333537, 0.5135516827763962, 0.5138684046323441] - - max_bound_value = [0.5504663932787668, 0.5504650623703748, 0.5504636483725223, 0.5504621458535578, - 0.550460548998529, 0.5504588515790302, 0.5504570469203628, 0.5504551278657476, - 0.5504530867372842, 0.5504509152933343, 0.5504486046819679, 0.5504461453900639, - 0.5504435271876233, 0.5504407390667989, 0.5504377691750882, 0.5504346047420877, - 0.5504312319991208, 0.5504276360910032, 0.5504238009790952, 0.5504197093347314, - 0.5504153424219909, 0.5504106799686727, 0.5504057000242086, 0.5504003788031157, - 0.5503946905124223, 0.5503886071613505, 0.5503820983513332, 0.550375131044248, - 0.5503676693065147, 0.5503596740264586, 0.5503511026020539, 0.5503419085958711, - 0.5503320413537078, 0.5503214455830255, 0.5503100608869134, 0.550297821248873, - 0.5502846544632468, 0.5502704815056058, 0.5502552158368782, 0.5502387626344095, - 0.5502210179425316, 0.5502018677345667, 0.5501811868775095, 0.5501588379899172, - 0.5501346701828164, 0.5501085176726986, 0.550080198254951, 0.5500495116253599, - 0.5500162375366732, 0.5499801337766138, 0.5499409339532445, 0.5498983539501722, - 0.5498520537857988, 0.5498016879649662, 0.5497468668698894, 0.5496871622327966, - 0.5496221034636182, 0.5495511736884243, 0.5494738054880556, 0.5493893763277539, - 0.5492972036697708, 0.5491965397614428, 0.5490865660904667, 0.5489663874959719, - 0.5488350259169966, 0.5486914137468271, 0.5485343867390974, 0.5483626763748868, - 0.5481749015425326, 0.5479695592938455, 0.5477450143079432, 0.547499486496596, - 0.5472310358926771, 0.5469375435302057, 0.5466166863794518] - - - np.testing.assert_array_almost_equal(spread, spread_value, decimal=4) - np.testing.assert_array_almost_equal(min_bound, min_bound_value, decimal=4) - np.testing.assert_array_almost_equal(max_bound, max_bound_value, decimal=4) + self.assertAlmostEqual(np.mean(spread), 0.5328233514, delta=1e-7) + self.assertAlmostEqual(np.mean(min_bound), 0.511643929, delta=1e-7) + self.assertAlmostEqual(np.mean(max_bound), 0.549827869, delta=1e-7) + + self.assertAlmostEqual(np.min(spread), 0.494787089, delta=1e-7) + self.assertAlmostEqual(np.min(min_bound), 0.511372451, delta=1e-7) + self.assertAlmostEqual(np.min(max_bound), 0.546616686, delta=1e-7) + + self.assertAlmostEqual(np.max(spread), 0.558869423, delta=1e-7) + self.assertAlmostEqual(np.max(min_bound), 0.513868404, delta=1e-7) + self.assertAlmostEqual(np.max(max_bound), 0.550466393, delta=1e-7) with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) sc_jurek.stabilization_region(self.dataframe, gamma=1, utility_type=1) - sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) - sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=2, utility_type=2) + + spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=2, utility_type=2) + + self.assertAlmostEqual(np.mean(spread), 0.5328233514, delta=1e-7) + self.assertAlmostEqual(np.mean(min_bound), 0.5276749084, delta=1e-7) + self.assertAlmostEqual(np.mean(max_bound), 0.5850429718, delta=1e-7) + + self.assertAlmostEqual(np.min(spread), 0.494787089, delta=1e-7) + self.assertAlmostEqual(np.min(min_bound), 0.4974942641, delta=1e-7) + self.assertAlmostEqual(np.min(max_bound), 0.5625208403, delta=1e-7) + + self.assertAlmostEqual(np.max(spread), 0.558869423, delta=1e-7) + self.assertAlmostEqual(np.max(min_bound), 0.5556367547, delta=1e-7) + self.assertAlmostEqual(np.max(max_bound), 0.6107958587, delta=1e-7) def test_optimal_weights_fund_flows(self): @@ -255,28 +206,11 @@ def test_optimal_weights_fund_flows(self): weights = sc_jurek.optimal_portfolio_weights_fund_flows(self.dataframe, f=0.2, gamma = 0.5) - weights_value = [-61.209951245559886, -55.768996626994955, -54.29506907733657, -29.53148231063261, - -28.788181406599623, -35.446132764844045, -56.407662159154604, -48.80542149935103, - -45.30272593409803, -39.54761082112472, -34.53501241929379, -27.41536812966906, - -31.63413952679124, -25.15073486565633, -30.883976991773757, -24.566168714503625, - -19.671838064033942, -23.68754358107349, -28.88573579110144, -34.81874441805666, - -45.30917672331478, -55.40976159076393, -57.66919977058725, -55.38051475001346, - -56.49648579827527, -46.60975988134946, -17.950199065687432, -27.272390358924905, - -25.264129158079054, -0.2470392143435914, 2.059348023610353, 2.1236810344229027, - 3.928910861559416, 6.266488273932873, -17.081245990358187, -22.556076104925484, - -17.456527361827547, -9.743333560266567, -14.543931323365847, -31.039671495656474, - -20.419170465429584, -21.43562175214721, -11.52728940138928, 5.238747670763784, - -11.350026744568511, -14.270739250803446, -5.412320144927434, -15.581503543375668, - -14.608183177745529, -1.3766404731723074, 21.244300239166837, 26.045387322957026, - 12.320637600132239, 14.994234126050577, 23.320326984383478, 14.095080601978557, - 26.21027280160306, 19.503912827821093, 29.736633362206717, 31.787540455979748, - 30.467379434126816, 44.33735181794835, 43.56606477754381, 30.475783005316273, - 42.435510276731044, 50.803561395840795, 54.93162116986916, 67.2680434557469, - 68.80351847062897, 80.11235798005077, 96.85076223701657, 90.99527633380434, - 81.54465651219026, 83.4218502604009, 77.14719301917991] - - - np.testing.assert_array_almost_equal(weights, weights_value, decimal=4) + self.assertAlmostEqual(np.mean(weights), -2.2710266815, delta=1e-7) + self.assertAlmostEqual(weights[7], -48.8054214993, delta=1e-7) + self.assertAlmostEqual(weights[28], -25.2641291580, delta=1e-7) + self.assertAlmostEqual(weights[-1], 77.1471930191, delta=1e-7) + def test_private_methods(self): """ @@ -285,7 +219,6 @@ def test_private_methods(self): sc_jurek = OUModelJurek() - with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) @@ -314,7 +247,6 @@ def test_private_methods(self): sc_jurek._B_calc_2(tau, c_1, c_2, c_3, disc, 0.9) - @mock.patch("arbitragelab.stochastic_control_approach.ou_model_jurek.plt") def test_plotting(self, mock_plt): """ @@ -331,13 +263,7 @@ def test_plotting(self, mock_plt): with self.assertRaises(Exception): sc_jurek.plot_results(self.dataframe) - project_path = os.path.dirname(__file__) - path = project_path + '/test_data/shell-rdp-close_USD.csv' - data = pd.read_csv(path, index_col='Date').ffill() - - data.index = pd.to_datetime(data.index, format="%d/%m/%Y") - - sc_jurek.plot_results(data) + sc_jurek.plot_results(self.shell_rdp_data) # Assert plt.figure got called assert mock_plt.show.called diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index 994ef803..b27b58df 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -28,14 +28,12 @@ def setUpClass(cls) -> None: np.random.seed(0) project_path = os.path.dirname(__file__) - cls.path = project_path + '/test_data/gld_gdx_data.csv' - data = pd.read_csv(cls.path) - data = data.set_index('Date') + path = project_path + '/test_data/gld_gdx_data.csv' + data = pd.read_csv(path) + data = data.set_index('Date') cls.dataframe = data[['GLD', 'GDX']] - cls.sc_mudchana = OUModelMudchanatongsuk() - def test_fit(self): """ @@ -46,23 +44,13 @@ def test_fit(self): sc_mudchana.fit(self.dataframe) - spread_value = [2.0887923929288523, 2.1094166241052568, 2.142854916105869, 2.0874899841437258, 2.063640345328846, - 2.0746168560671223, 2.1097829292924457, 2.1073878043606307, 2.1186930608205428, 2.114695107155425, - 2.103095768137663, 2.1215705039862782, 2.124685352890708, 2.1157789172191848, 2.1269984320130346, - 2.120925503747776, 2.0763581413867684, 2.0595664254555057, 2.0523098321895366, 2.0797748079356957, - 2.1197252327440586, 2.131219793094243, 2.082081096325099, 2.0929293564196105, 2.1285514677643356, - 2.117750899307466, 2.0830138676604886, 2.106107155811972, 2.0496029865939436, 2.0050226960285182, - 1.9786263643353657, 1.9816431811190234, 1.9894204445041153, 1.9514558194020695, 1.9853812497671273, - 1.9846230785716679, 1.939022254160427, 1.9350347152497411, 1.9579985647080247, 1.996822168058443, - 1.963797288878891, 1.9847212944236645, 1.9674718306977712, 1.941258381912097, 1.971988526032174, - 1.9723574683305594, 1.973661841888858, 2.013718843187712, 2.0205219195979014, 2.0100021771087766, - 2.0004053530573787, 2.012571119972438, 2.0470873187820344, 2.0774352146534167, 2.053195021245263, - 2.0774606535295734, 2.06082098723021, 2.0742880142111084, 2.060417339214223, 2.0530928294396382, - 2.0890217923893957, 2.059036586082702, 2.035044438470959, 2.072153226841589, 2.069307015169184, - 2.0383888802559467, 2.043152450272762, 2.0504190679184715, 2.034227852538867, 2.0090985697450647, - 2.019908369440301, 2.009667357261374, 1.9797365648180438, 2.01008349909157, 2.0202245834522397] - - np.testing.assert_array_almost_equal(sc_mudchana.spread, spread_value, decimal=4) + # Checking values for spread calc. + self.assertAlmostEqual(np.mean(sc_mudchana.spread), 2.0465361303, delta=1e-7) + # TODO : Why is the mean value of spread not equal to the estimated theta param below? + self.assertAlmostEqual(sc_mudchana.spread[7], 2.1073878043, delta=1e-7) + self.assertAlmostEqual(sc_mudchana.spread[28], 2.0496029865, delta=1e-7) + self.assertAlmostEqual(sc_mudchana.spread[-1], 2.0202245834, delta=1e-7) + self.assertAlmostEqual(sc_mudchana.sigma, 0.503695, delta=1e-4) self.assertAlmostEqual(sc_mudchana.mu, 0.114877, delta=1e-4) self.assertAlmostEqual(sc_mudchana.k, 3.99205, delta=1e-3) @@ -106,24 +94,7 @@ def test_optimal_weights(self): weights = sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = -10) - weights_value = [0.6807970425341383, 0.5788270189292528, 0.4237456386361687, 0.6450834372737371, - 0.7318800196910422, 0.6725665016257416, 0.5137455982771261, 0.5117099817524071, - 0.4536787173239446, 0.4587916338411348, 0.4947409799799004, 0.40935585749175935, - 0.38656582779882165, 0.4119577215551326, 0.3576746243419241, 0.37205756995215905, - 0.5364494177553357, 0.5912391763672612, 0.6087201255096889, 0.4933662450056616, - 0.3322708500364613, 0.2807566340156271, 0.45706866084645936, 0.40803843763022246, - 0.2683653938434968, 0.3009241934120373, 0.4202148927130246, 0.32903803274992643, - 0.5246204647066117, 0.6749545941905897, 0.7588892323365495, 0.7385587466201069, - 0.7020478426104525, 0.8238791404743722, 0.6979215228988004, 0.6917047438277323, - 0.8365209290118862, 0.8401240368143309, 0.754516641656195, 0.6183636050618108, - 0.7182449688122026, 0.6425285645177642, 0.6901494231876113, 0.7653424279618145, - 0.6605525316290899, 0.652089070778512, 0.6409423355789974, 0.5118482097864904, - 0.4857268994701272, 0.5119999415779317, 0.5350930783653811, 0.49397895578467543, - 0.3888903487219631, 0.29800762140526377, 0.3642822152122685, 0.29285532211506354, - 0.33686879455357427, 0.2971957603672995, 0.3329060663478341, 0.35032173033381425, - 0.2523906371601354, 0.3301480022615564, 0.390645486517426, 0.29293440407814975, - 0.29903173795128984, 0.3754395278348421, 0.36179056247411795, 0.34247802333072985, - 0.3803355129092354, 0.43858981861753515, 0.4110154830924428, 0.43302883383533586, - 0.4995100506045553, 0.42845097673506394, 0.40433684605306186] - - np.testing.assert_array_almost_equal(weights, weights_value, decimal=4) + self.assertAlmostEqual(np.mean(weights), 0.4986890920, delta=1e-7) + self.assertAlmostEqual(weights[7], 0.5117099817, delta=1e-7) + self.assertAlmostEqual(weights[28], 0.5246204647, delta=1e-7) + self.assertAlmostEqual(weights[-1], 0.4043368460, delta=1e-7) From edfdb3123815e9f8b77fa5a5205d477f85d664b0 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Fri, 2 Apr 2021 22:35:42 +0530 Subject: [PATCH 080/103] Changes to docs according to PR. --- .../images/jurek_describe.png | Bin 0 -> 27605 bytes .../images/mudchana_describe.png | Bin 0 -> 34408 bytes .../introduction.rst | 44 +++++++++++-- .../ou_model_jurek.rst | 58 ++++++++++++++---- .../ou_model_mudchanatongsuk.rst | 13 ++++ tests/test_ou_model_mudchanatongsuk.py | 2 +- 6 files changed, 98 insertions(+), 19 deletions(-) create mode 100644 docs/source/stochastic_control_approach/images/jurek_describe.png create mode 100644 docs/source/stochastic_control_approach/images/mudchana_describe.png diff --git a/docs/source/stochastic_control_approach/images/jurek_describe.png b/docs/source/stochastic_control_approach/images/jurek_describe.png new file mode 100644 index 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b/docs/source/stochastic_control_approach/introduction.rst index 0f0eeea5..946aaf0f 100644 --- a/docs/source/stochastic_control_approach/introduction.rst +++ b/docs/source/stochastic_control_approach/introduction.rst @@ -1,9 +1,43 @@ .. _stochastic_control_approach_strategies-introduction: -============ -Introduction -============ +.. note:: + The following documentation appears in Section 5 of the following work: -Stochastic Control Approach Strategies -###################################### + `Krauss (2015), Statistical arbitrage pairs trading strategies:Review and outlook `__ + +====================================================== +Introduction to Stochastic Control Approach Strategies +====================================================== + +Modeling asset pricing dynamics with the Ornstein-Uhlenbeck process +################################################################### + +OU Model Jurek +************** + +`Jurek and Yang (2007) `__ provide the paper with the +highest impact in this domain. In their setup, they allow non-myopic arbitrageurs to allocate their capital +to a mean-reverting spread or to a risk free asset. The former evolves according to an Ornstein-Uhlenbeck process +and the latter is compounded continuously with the riskfree rate. Two scenarios for investor preferences are considered +over a finite time horizon: constant relative risk aversion and the recursive Epstein-Zinutility function. +Utilizing the asset price dynamics, Jurek and Yang develop the budget constraints +and the wealth dynamics of the arbitrageurs’ assets. + + +Applying stochastic control theory, the authors are able to derive the Hamilton-Jacobi-Bellmann (HJB) equation and +subsequently find closed-form solutions for the value and policy functions for both scenarios. Jurek and Yang provide +the most comprehensive discussion of the stochastic control approach applied to an Ornstein-Uhlenbeck framework. + +OU Model Mudchanatongsuk +************************ + +`Mudchanatongsuk et al.(2008) `__ also solves +the stochastic control problem for pairs trading under power utility for terminal wealth. +Their ansatz mostly differs in the assumed asset pricing dynamics, but the spread also relies on an OU-process. + + +References +########## + +* `Krauss, Christopher (2015) : Statistical arbitrage pairs trading strategies:Review and outlook, IWQW Discussion Papers, No. 09/2015, `__ diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index a5732b81..3254608f 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -37,6 +37,14 @@ partial equilibrium. Modelling ######### +.. note:: + In this module and the corresponding paper, + + :math:`\kappa` denotes the rate of mean reversion of the spread, + :math:`\mu` denotes the long run mean and, + :math:`\sigma` denotes the standard deviation of the spread. + + To capture the presence of horizon and divergence risk, the authors model the dynamics of the mispricing using a mean-reverting stochastic process. Under this process, although the mispricing is guaranteed to be eliminated at some future date, the timing of convergence, as well as the maximum magnitude @@ -99,6 +107,11 @@ where :math:`f\left(C_{s}, J_{s}\right)` is the normalized aggregator for the co Here the authors considered the special case of a unit elasticity of intertemporal substitution (:math:`\psi = 1`). + +Here :math:`C_t` denotes the instantaneous consumption (e.g. cash flow). :math:`\beta` is the rate of time preference, and +:math:`\gamma` is the coefficient of relative risk aversion. + + .. note:: In this paper, the choice of preference structures is driven by economic intuition regarding the incentives @@ -151,7 +164,8 @@ The evolution of wealth which determines the budget constraints is written as, d W_{t}=N_{t} d S_{t}+M_{t} d B_{t}-C_{t} 1\left[C_{t}>0\right] d t -where :math:`N_t` denotes the number of units of spread and :math:`M_t` denotes the number of riskless assets. +where :math:`N_t` denotes the number of units of spread, :math:`M_t` denotes the number of riskless assets and, +:math:`1[C_{t}>0]` is an indicator variable for whether intermediate consumption is taking place. For the terminal wealth problem, the optimal portfolio allocation is given by: @@ -216,7 +230,7 @@ Paradoxically, clients are most likely to withdraw funds after performance has b (i.e. spreads have been widening) and investment opportunities are the best. In the presence of fund flows the evolution of wealth under management will depend not only -on performance, denoted by :math:`\Pi_t`, but also on fund flows, :math:`F_t`.Consequently: +on performance, denoted by :math:`\Pi_t`, but also on fund flows, :math:`F_t`. Consequently: .. math:: @@ -249,8 +263,10 @@ this flow to commensurately decrease the amount of risk taken on by the underlyi How to use this submodule ######################### -This submodule contains two public methods. One for estimating the parameters of the model using training data, -and the second method is for calculating the final optimal portfolio weights using evaluation data. +This submodule contains five public methods, of which two methods are necessary to calculate the optimal weights. +The first method is for estimating the parameters of the model +using training data, and the second method is for calculating the final optimal portfolio weights using evaluation data. + Step 1: Model fitting ********************* @@ -280,6 +296,11 @@ Implementation .. automethod:: OUModelJurek.describe + .. figure:: images/jurek_describe.png + :scale: 100 % + :align: center + :figclass: align-center + Step 2: Getting the Optimal Portfolio Weights ********************************************* @@ -291,9 +312,14 @@ If we choose the investor with intermediate consumption, we also need to specify .. figure:: images/optimal_weights.png - :scale: 100 % - :align: center - :figclass: align-center + :scale: 100 % + :align: center + :figclass: align-center + + An example showcasing the optimal allocation to the spread asset (in cyan) scaled by wealth, :math:`N_t/W_t`. + In the out-of-sample trading simulation the agent uses a fixed length backward-looking window + to estimate the parameters of the model, and uses those estimates to trade in the test window. + For the plots in this doc, five test windows are shown. Implementation @@ -313,9 +339,12 @@ Implementation .. figure:: images/stabilization_bound.png - :scale: 100 % - :align: center - :figclass: align-center + :scale: 100 % + :align: center + :figclass: align-center + + An example showcasing the evolution of the Royal Dutch - Shell spread asset (in cyan), :math:`S_t`, + within each trading period, and the corresponding stabilization bound (in red). Step 4: Optimal Portfolio Weights with Fund Flows @@ -330,9 +359,12 @@ Implementation .. figure:: images/optimal_weights_fund_flows.png - :scale: 100 % - :align: center - :figclass: align-center + :scale: 100 % + :align: center + :figclass: align-center + + An example showcasing the optimal allocation to the spread asset (in cyan) scaled by wealth, :math:`N_t/W_t`, + for the case with fund flows. Step 5: Plotting diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index 0f62e5ee..8b4aad64 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -26,6 +26,14 @@ is obtained in closed form via the corresponding Hamilton-Jacobi-Bellman equatio Modelling ######### +.. note:: + In this module and the corresponding paper, + + :math:`k` denotes the rate of mean reversion of the spread, + :math:`\theta` denotes the long run mean and, + :math:`\eta` denotes the standard deviation of the spread. + + Let :math:`A(t)` and :math:`B(t)` denote respectively the prices of the pair of stocks :math:`A` and :math:`B` at time :math:`t`. The authors assume that stock :math:`B` follows a geometric Brownian motion, @@ -126,6 +134,11 @@ Implementation .. automethod:: OUModelMudchanatongsuk.describe + .. figure:: images/mudchana_describe.png + :scale: 100 % + :align: center + :figclass: align-center + Step 2: Getting the Optimal Portfolio Weights ********************************************* diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index b27b58df..5ac6f518 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -94,7 +94,7 @@ def test_optimal_weights(self): weights = sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = -10) - self.assertAlmostEqual(np.mean(weights), 0.4986890920, delta=1e-7) + self.assertAlmostEqual(np.mean(weights), 0.4986890920, delta=1e-5) self.assertAlmostEqual(weights[7], 0.5117099817, delta=1e-7) self.assertAlmostEqual(weights[28], 0.5246204647, delta=1e-7) self.assertAlmostEqual(weights[-1], 0.4043368460, delta=1e-7) From e88b504416ed7f51f13a6a85dbd72efa441f89ae Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 5 Apr 2021 12:54:10 +0530 Subject: [PATCH 081/103] Minor changes to delta in test cases for CircleCI. --- tests/test_ou_model_mudchanatongsuk.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index 5ac6f518..d05ac996 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -95,6 +95,6 @@ def test_optimal_weights(self): weights = sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = -10) self.assertAlmostEqual(np.mean(weights), 0.4986890920, delta=1e-5) - self.assertAlmostEqual(weights[7], 0.5117099817, delta=1e-7) - self.assertAlmostEqual(weights[28], 0.5246204647, delta=1e-7) - self.assertAlmostEqual(weights[-1], 0.4043368460, delta=1e-7) + self.assertAlmostEqual(weights[7], 0.5117099817, delta=1e-4) + self.assertAlmostEqual(weights[28], 0.5246204647, delta=1e-4) + self.assertAlmostEqual(weights[-1], 0.4043368460, delta=1e-4) From 6430a4423c396954d13d3e528593eee54e4890c8 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 5 Apr 2021 15:51:31 +0530 Subject: [PATCH 082/103] Added inline comments,docstrings and new exceptions. --- .../ou_model_jurek.py | 108 ++++++++++++++++-- .../ou_model_mudchanatongsuk.py | 16 ++- tests/test_ou_model_jurek.py | 68 ++++++++--- tests/test_ou_model_mudchanatongsuk.py | 15 ++- 4 files changed, 183 insertions(+), 24 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 46663078..98ff5b09 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -119,6 +119,7 @@ def fit(self, prices: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = F # Scaling the weights such that they sum to 1. self.scaled_spread_weights = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() + # Calculating the final spread value from the scaled weights. self.spread = (total_return_indices * self.scaled_spread_weights).sum(axis=1) self.spread = self.spread.to_numpy() # This conversion seems to have changed the estimated values. @@ -145,6 +146,7 @@ def _estimate_params(self, spread: np.array) -> tuple: k = (-1 / self.delta_t) * np.log(np.multiply(spread[1:] - mu, spread[:-1] - mu).sum() / np.power(spread[1:] - mu, 2).sum()) + # Part of sigma estimation formula. sigma_calc_sum = np.power((spread[1:] - mu - np.exp(-k * self.delta_t) * (spread[:-1] - mu)) / np.exp(-k * self.delta_t), 2).sum() @@ -208,6 +210,9 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, utility_type: int = 1, :return: (np.array) Scaled optimal portfolio weights. """ + if self.sigma is None: + raise Exception("Please run the fit method before calling this method.") + if gamma <= 0: raise Exception("The value of gamma should be positive.") @@ -236,6 +241,7 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, utility_type: int = 1, A = None B = None + # A and B functions are used in the final weights calculation. if utility_type == 1: A, B = self._AB_calc_1(tau) @@ -272,6 +278,7 @@ def optimal_portfolio_weights_fund_flows(self, prices: pd.DataFrame, f: float, g :return: (np.array) Optimal weights with fund flows. """ + # Calculating the scaled optimal portfolio weights. N = self.optimal_portfolio_weights(prices, utility_type=1, gamma=gamma, r=r) return (1 / (1 + f)) * N @@ -289,6 +296,9 @@ def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamm :return: (tuple) Tuple of numpy arrays for spread, min bound and max bound. """ + if self.sigma is None: + raise Exception("Please run the fit method before calling this method.") + if gamma <= 0: raise Exception("The value of gamma should be positive.") @@ -300,6 +310,7 @@ def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamm self.gamma = gamma self.beta = beta + # Calculating the time left array and the spread. tau, S = self._spread_calc(prices) if self.gamma == 1: @@ -310,6 +321,7 @@ def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamm A = None B = None + # A and B functions are used in the final weights calculation. if utility_type == 1: A, B = self._AB_calc_1(tau) @@ -320,20 +332,26 @@ def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamm phi = (2 * A / self.gamma) - ((self.k + self.r) / (self.gamma * self.sigma ** 2)) # Note : phi < 0. + # term_1 and term_2 calculations are part of the constraint equation calculation below. term_1 = (self.k * self.mu + (self.sigma ** 2) * B) / (self.gamma * self.sigma ** 2) term_2 = np.sqrt(-phi) + # Initializing the upper bound and lower bound arrays. max_bound = np.zeros(len(tau)) min_bound = np.zeros(len(tau)) + # Iterating over each time step in the array. for ind in range(len(tau)): - s = cp.Variable() + s = cp.Variable() # Setting an optimization variable for spread. + # Defining the constraint equation involving spread. constraint = [cp.abs(phi[ind] * s + term_1[ind]) <= term_2[ind] - 1e-6] + # Solving the maximization problem to calculate the upper bound. prob_max = cp.Problem(cp.Maximize(s), constraint) prob_max.solve() max_bound[ind] = prob_max.value + # Solving the minimization problem to calculate the lower bound. prob_min = cp.Problem(cp.Minimize(s), constraint) prob_min.solve() min_bound[ind] = prob_min.value @@ -574,7 +592,19 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: @staticmethod def _B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau): """ - Implementation of Case IV in Appendix B.1.2. + Method calculates value of function B according to Case IV in Appendix B.1.2. + + :param c_1: (float) Value of variable c_1 in Appendix B.1.1. + :param c_2: (float) Value of variable c_2 in Appendix B.1.1. + :param c_3: (float) Value of variable c_3 in Appendix B.1.1. + :param c_4: (float) Value of variable c_4 in Appendix B.1.2. + :param c_5: (float) Value of variable c_5 in Appendix B.1.2. + :param c_6: (float) Value of variable c_6 in Appendix B.1.2. + :param disc: (float) Value of discriminant in Appendix B.1.1. + :param rep_exp_1: (np.array) Repeating Exponential Form with variable c_2. + :param rep_exp_2: (np.array) Repeating Exponential Form with variable c_5. + :param tau: (np.array) Array with time till completion in years. + :return: (np.array) Final value of B. """ rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1. @@ -583,12 +613,17 @@ def _B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau): # The final equation for B is split into 5 terms. term_1 = 2 * rep_exp_1 * rep_phrase_1 * c_4 * c_5 * (c_2 + 0.5 * np.sqrt(disc) * np.tanh(rep_phrase_2)) + term_2 = 2 * rep_exp_1 * rep_phrase_1 - 2 * rep_exp_2 * (1 / np.cosh(rep_phrase_2)) # sech = 1 / cosh + term_3 = rep_exp_2 * (1 / np.cosh(rep_phrase_2)) - 2 * rep_exp_1 * rep_phrase_1 + term_4 = rep_exp_1 * np.sqrt(disc) * rep_phrase_1 * np.tanh(rep_phrase_2) + term_5 = -term_3 + # Calculating the final value of function B. B = np.exp(-tau * c_2) * (term_1 + c_1 * (c_6 * (c_2 * term_2 + term_3 * c_5 @@ -601,7 +636,18 @@ def _B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau): @staticmethod def _B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): """ - Implementation of Case III in Appendix B.1.2. + Method calculates value of function B according to Case III in Appendix B.1.2. + + :param c_1: (float) Value of variable c_1 in Appendix B.1.1. + :param c_2: (float) Value of variable c_2 in Appendix B.1.1. + :param c_3: (float) Value of variable c_3 in Appendix B.1.1. + :param c_4: (float) Value of variable c_4 in Appendix B.1.2. + :param c_5: (float) Value of variable c_5 in Appendix B.1.2. + :param c_6: (float) Value of variable c_6 in Appendix B.1.2. + :param rep_exp_1: (np.array) Repeating Exponential Form with variable c_2. + :param rep_exp_2: (np.array) Repeating Exponential Form with variable c_5. + :param tau: (np.array) Array with time till completion in years. + :return: (np.array) Final value of B. """ rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) # Repeated Phrase 1. @@ -612,15 +658,20 @@ def _B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): # The final equation for B is split into 5 terms. term_1 = rep_exp_1 * rep_phrase_1 * c_6 * c_2 ** 2 + term_2 = rep_exp_1 * c_3 * rep_phrase_1 * c_4 + term_3 = 2 * rep_exp_2 * (1 / np.sinh(rep_phrase_3)) - rep_phrase_2 * (1 / np.tanh(rep_phrase_3)) * rep_phrase_1 # csch = 1/sinh, coth = 1/tanh + term_4 = rep_exp_1 * rep_phrase_1 * c_5 + term_5 = (1 / np.sinh(rep_phrase_3)) * ( c_3 * c_4 * (rep_exp_2 * rep_phrase_2 - rep_exp_1 * np.sinh(tau * rep_phrase_2) * c_5) + rep_exp_2 * rep_phrase_2 * c_5 * c_6) # csch = 1/sinh + # Calculating the final value of function B. B = np.exp(-tau * c_2) * (term_1 - (term_2 + (rep_phrase_2 * term_3 + term_4) * c_6) * c_2 + term_5) / denominator @@ -630,17 +681,31 @@ def _B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): @staticmethod def _B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): """ - Implementation of Case II in Appendix B.1.2. + Method calculates value of function B according to Case II in Appendix B.1.2. + + :param c_1: (float) Value of variable c_1 in Appendix B.1.1. + :param c_2: (float) Value of variable c_2 in Appendix B.1.1. + :param c_4: (float) Value of variable c_4 in Appendix B.1.2. + :param c_5: (float) Value of variable c_5 in Appendix B.1.2. + :param c_6: (float) Value of variable c_6 in Appendix B.1.2. + :param rep_exp_1: (np.array) Repeating Exponential Form with variable c_2. + :param rep_exp_2: (np.array) Repeating Exponential Form with variable c_5. + :param tau: (np.array) Array with time till completion in years. + :return: (np.array) Final value of B. """ denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 # Denominator in final equation. # The final equation for B is split into 4 terms. term_1 = rep_exp_1 * tau * c_4 * c_2 ** 3 + term_2 = (c_4 * (rep_exp_1 * (tau * c_5 + 1) - rep_exp_2) + rep_exp_1 * tau * c_1 * c_6) * c_2 ** 2 + term_3 = c_1 * (rep_exp_1 * tau * c_5 + 2 * (rep_exp_1 - rep_exp_2)) * c_6 * c_2 + term_4 = (rep_exp_1 - rep_exp_2) * c_1 * c_5 * c_6 + # Calculating the final value of function B. B = (-term_1 + term_2 - term_3 + term_4) / denominator @@ -650,7 +715,18 @@ def _B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): @staticmethod def _B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): """ - Implementation of Case I in Appendix B.1.2. + Method calculates value of function B according to Case I in Appendix B.1.2. + + :param c_1: (float) Value of variable c_1 in Appendix B.1.1. + :param c_2: (float) Value of variable c_2 in Appendix B.1.1. + :param c_3: (float) Value of variable c_3 in Appendix B.1.1. + :param c_4: (float) Value of variable c_4 in Appendix B.1.2. + :param c_5: (float) Value of variable c_5 in Appendix B.1.2. + :param c_6: (float) Value of variable c_6 in Appendix B.1.2. + :param rep_exp_1: (np.array) Repeating Exponential Form with variable c_2. + :param rep_exp_2: (np.array) Repeating Exponential Form with variable c_5. + :param tau: (np.array) Array with time till completion in years. + :return: (np.array) Final value of B. """ rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) # Repeating Phrase 1. @@ -660,11 +736,16 @@ def _B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): # The final equation for B is split into 5 terms. term_1 = rep_exp_1 * rep_phrase_2 * c_4 * c_5 * (c_2 - rep_phrase_1 * np.tan(rep_phrase_3)) + term_2 = rep_exp_1 * rep_phrase_2 - 2 * rep_exp_2 * (1 / np.cos(rep_phrase_3)) + term_3 = rep_exp_2 * (1 / np.cos(rep_phrase_3)) - rep_exp_1 * rep_phrase_2 + term_4 = rep_exp_1 * rep_phrase_2 * rep_phrase_1 * np.tan(rep_phrase_3) + term_5 = -term_3 + # Calculating the final value of function B. B = np.exp(-tau * c_2) * (term_1 + c_1 * (c_6 * (c_2 * term_2 + term_3 * c_5 @@ -693,13 +774,15 @@ def describe(self) -> pd.Series: if self.sigma is None: raise Exception("Please run the fit method before calling describe.") + # List defines the indexes of the final pandas object. index = ['Ticker of first stock', 'Ticker of second stock', 'Scaled Spread weights', 'long-term mean', 'rate of mean reversion', 'standard deviation', 'half-life'] + # List defines the values of the final pandas object. data = [self.ticker_A, self.ticker_B, np.round(self.scaled_spread_weights.values, 3), self.mu, self.k, self.sigma, self._calc_half_life(self.k)] - # Combine data and indexes into the pandas Series + # Combine data and indexes into the pandas Series. output = pd.Series(data=data, index=index) return output @@ -725,9 +808,10 @@ def plot_results(self, prices:pd.DataFrame, num_test_windows = 5, delta_t =1 / 2 :param beta: (float) Subjective rate of time preference. (Only required for utility_type = 2). """ - + # Setting font size of plots. plt.rcParams.update({'font.size': 8}) + # Price series preprocessing. prices = prices.ffill() if not np.issubdtype(prices.index.dtype, np.datetime64): @@ -737,18 +821,24 @@ def plot_results(self, prices:pd.DataFrame, num_test_windows = 5, delta_t =1 / 2 raise Exception("Please make sure length of input data is greater than 10 years. " "This is the time period used to fit the model in the paper.") + # Getting the list of years in input data. years = prices.index.year.unique() + # Initializing a dataframe which stores stabilization region results. stab_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, columns=['Spread', 'lower bound', 'upper bound']) + # Initializing a dataframe which stores optimal weights. optimal_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, columns=['Weights']) + # Initializing a dataframe which stores optimal weights in the case with fund flows. optimal_fund_flows_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]): str(years[-1])].index, columns=['Weights']) ind = 0 + # Iterating over the test windows. for year in np.arange(years[-(num_test_windows + 1)], years[-1], 1): + # Setting the train and test data. data_train_dataframe = prices.loc[str(year - (len(years) - (num_test_windows + 1))):str(year - 1)] data_test_dataframe = prices.loc[str(year)] @@ -761,23 +851,27 @@ def plot_results(self, prices:pd.DataFrame, num_test_windows = 5, delta_t =1 / 2 S, min_bound, max_bound = self.stabilization_region(data_test_dataframe, gamma=gamma, utility_type=utility_type, beta=beta, r=r) + # Adding the final results to their corresponding dataframes for each test window. stab_result_dataframe.iloc[ind:ind + len(S), :] = np.array([S, min_bound, max_bound]).T optimal_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_weights]).T optimal_fund_flows_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_fund_flow_weights]).T ind += len(S) + # Plotting the stabilization bound plot. ax = stab_result_dataframe.plot(style=['c-', 'r:', 'r:'], legend=False, linewidth=1.0, figsize=(8, 4)) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Spread') ax.set_title("Evolution of spread with stabilization bound") plt.show() + # Plotting the optimal weights allocation plot. ax = optimal_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=(8, 4)) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Optimal Weights') ax.set_title('Optimal allocation to the spread asset scaled by wealth') plt.show() + # Plotting the optimal weights allocation plot in the case with fund flows. ax = optimal_fund_flows_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=(8, 4)) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Optimal Weights with fund flows') diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index a944e9da..3aca169c 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -105,6 +105,9 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, gamma = -100) -> np.ar :return: (np.array) Optimal weights array. """ + if self.sigma is None: + raise Exception("Please run the fit method before calling this method.") + if gamma >= 1: raise Exception("Please make sure value of gamma is less than 1.") @@ -143,7 +146,9 @@ def _alpha_beta_calc(self, tau) -> tuple: sqrt_gamma = np.sqrt(1 - self.gamma) # Repeating Calculation involving gamma. exp_calc = np.exp(2 * self.k * tau / sqrt_gamma) # Repeating Calculation involving gamma and tau series. + # Calculating the alpha function output. alpha_t = self._alpha_calc(sqrt_gamma, exp_calc) + # Calculating the beta function output. beta_t = self._beta_calc(sqrt_gamma, exp_calc) return alpha_t, beta_t @@ -194,11 +199,13 @@ def _estimate_params_log_likelihood(self) -> tuple: # sigma, mu, k, theta, eta, rho bounds = ((1e-5, None), (None, None), (1e-5, None), (None, None), (1e-5, None), (-1 + 1e-5, 1 - 1e-5)) + # Setting initial value of theta to the mean of the spread. theta_init = np.mean(self.spread) # Initial guesses for sigma, mu, k, theta, eta, rho initial_guess = np.array((1, 0, 1, theta_init, 1, 0.5)) + # Using scipy minimize to calculate the max log likelihood. result = so.minimize(self._compute_log_likelihood, initial_guess, args=(self.spread, self.S, self.delta_t), bounds=bounds, options={'maxiter': 100000}) @@ -225,8 +232,10 @@ def _compute_log_likelihood(params, *args) -> float: sigma, mu, k ,theta, eta, rho = params X,S, dt = args + # Setting y as given in Appendix. y = np.array([X, S]) + # Calculating matrix as given in equation (41) in the paper. matrix = np.zeros((2,2)) matrix[0, 0] = (eta ** 2) * (1 - np.exp(-2 * k * dt)) / (2 * k) matrix[0, 1] = rho * eta * sigma * (1 - np.exp(k * dt)) / k @@ -237,12 +246,14 @@ def _compute_log_likelihood(params, *args) -> float: S = S[:-1] y = y[:, 1:] + # Calculation follows equation (40) in the paper. E_y = np.zeros((2, len(X))) E_y[0, :] = X * np.exp(-k * dt) + theta * (1 - np.exp(-k * dt)) E_y[1, :] = S + (mu - 0.5 * sigma ** 2) * dt vec = y - E_y + # Calculating the joint density function given in equation (39) in the paper. with np.errstate(all='raise'): # This was done due to np.nan's outputted in final result of scipy minimize. try: f_y_denm = (2 * math.pi * np.sqrt(np.linalg.det(matrix))) @@ -251,9 +262,10 @@ def _compute_log_likelihood(params, *args) -> float: except FloatingPointError: return 0 - + # Calculating the final log likelihood given in equation (38) in the paper. log_likelihood = np.log(f_y).sum() + # Returning the negation as we are using scipy minimize. return -log_likelihood @@ -276,10 +288,12 @@ def describe(self) -> pd.Series: if self.sigma is None: raise Exception("Please run the fit method before calling describe.") + # List defines the indexes of the final pandas object. index = ['Ticker of first stock', 'Ticker of second stock', 'long-term mean of spread', 'rate of mean reversion of spread', 'standard deviation of spread', 'half-life of spread', 'Drift of stock B', 'standard deviation of stock B'] + # List defines the values of the final pandas object. data = [self.ticker_A, self.ticker_B, self.theta, self.k, self.eta, self._calc_half_life(self.k), self.mu, self.sigma] diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index 35fb1f2e..0ada39cd 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -31,11 +31,13 @@ def setUpClass(cls) -> None: project_path = os.path.dirname(__file__) + # Setting up the first dataset. path = project_path + '/test_data/gld_gdx_data.csv' data = pd.read_csv(path) data = data.set_index('Date') cls.dataframe = data[['GLD', 'GDX']] + # Setting up the second dataset. path = project_path + '/test_data/shell-rdp-close_USD.csv' data = pd.read_csv(path, index_col='Date').ffill() data.index = pd.to_datetime(data.index, format="%d/%m/%Y") @@ -47,22 +49,26 @@ def test_fit(self): Tests the fit method in the class. """ + # Creating an object of the class. sc_jurek = OUModelJurek() + # Testing for the adf test statistic warning. with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=True, significance_level=0.95) - # Checking values for spread calc. + # Checking parameter values for spread calculation. self.assertAlmostEqual(np.mean(sc_jurek.spread), 0.5328233514, delta=1e-7) self.assertAlmostEqual(sc_jurek.spread[7], 0.5532053519, delta=1e-7) self.assertAlmostEqual(sc_jurek.spread[28], 0.5423901587, delta=1e-7) self.assertAlmostEqual(sc_jurek.spread[-1], 0.5054215932, delta=1e-7) + # Checking other parameter values. self.assertAlmostEqual(sc_jurek.mu, 0.532823, delta=1e-4) self.assertAlmostEqual(sc_jurek.k, 10.2728, delta=1e-4) self.assertAlmostEqual(sc_jurek.sigma, 0.0743999, delta=1e-4) + # Testing for the adf_test=False flag. sc_jurek.fit(self.shell_rdp_data, delta_t=1 / 252, adf_test=False) @@ -71,8 +77,10 @@ def test_describe(self): Tests the describe method in the class. """ + # Creating an object of the class. sc_jurek = OUModelJurek() + # Testing for the run fit before this method exception. with self.assertRaises(Exception): sc_jurek.describe() @@ -85,6 +93,7 @@ def test_describe(self): data = ['GLD', 'GDX', [0.779, -0.221], 0.532823, 10.2728, 0.0743999, 0.067474] + # Testing the output of describe method. pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_jurek.describe(), check_exact=False, atol=1e-4) @@ -93,49 +102,56 @@ def test_optimal_weights(self): Tests the optimal portfolio weights method in the class. """ + # Creating an object of the class. sc_jurek = OUModelJurek() + # Testing for the run fit before this method exception. + with self.assertRaises(Exception): + sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) + # Testing for the invalid utility_type exception. with self.assertRaises(Exception): sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=10) + # Testing for the invalid gamma exception. with self.assertRaises(Exception): sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = -1) weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) - + # Checking the values of weights for gamma = 0.5 and utility_type=1. self.assertAlmostEqual(np.mean(weights), -2.7252320178, delta=1e-7) self.assertAlmostEqual(weights[7], -58.5665057992, delta=1e-7) self.assertAlmostEqual(weights[28], -30.3169549896, delta=1e-7) self.assertAlmostEqual(weights[-1], 92.5766316230, delta=1e-7) weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) - + # Checking the values of weights for gamma = 1 and utility_type=1. self.assertAlmostEqual(np.mean(weights), -4.8129160068, delta=1e-7) self.assertAlmostEqual(weights[7], -42.82308043, delta=1e-7) self.assertAlmostEqual(weights[28], -22.6539479, delta=1e-7) self.assertAlmostEqual(weights[-1], 46.28831581, delta=1e-7) weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) - + # Checking the values of weights for gamma = 0.5 and utility_type=2. self.assertAlmostEqual(np.mean(weights), -2947786.5697284327, delta=1e-7) self.assertAlmostEqual(weights[7], -9803080.87074925, delta=1e-7) self.assertAlmostEqual(weights[28], -1762115.70956469, delta=1e-7) self.assertAlmostEqual(weights[-1], -54007.10111104, delta=1e-7) weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=1) - + # Checking the values of weights for gamma = 2 and utility_type=1. self.assertAlmostEqual(np.mean(weights), -5.3267767287, delta=1e-7) self.assertAlmostEqual(weights[7], -31.15603589, delta=1e-7) self.assertAlmostEqual(weights[28], -16.4211391034, delta=1e-7) self.assertAlmostEqual(weights[-1], 23.14415791, delta=1e-7) weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=2) - + # Checking the values of weights for gamma = 2 and utility_type=2. self.assertAlmostEqual(np.mean(weights), 28.7539986245, delta=1e-7) self.assertAlmostEqual(weights[7], 34.13526822, delta=1e-7) self.assertAlmostEqual(weights[28], 28.56326627, delta=1e-7) @@ -147,47 +163,60 @@ def test_stabilization_region(self): Tests the stabilization region method in the class. """ + # Creating an object of the class. sc_jurek = OUModelJurek() + # Testing for the run fit before this method exception. + with self.assertRaises(Exception): + sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) + # Testing for the invalid utility_type exception. with self.assertRaises(Exception): sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=0.5, utility_type=10) + # Testing for the invalid gamma exception. with self.assertRaises(Exception): sc_jurek.stabilization_region(self.dataframe, beta = 0.01, gamma = -1) - spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + # Testing for gamma = 1 warning. + with warnings.catch_warnings(): + warnings.simplefilter("ignore", UserWarning) + sc_jurek.stabilization_region(self.dataframe, gamma=1, utility_type=1) + + spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + # Checking the mean value of spread, min_bound and max_bound. self.assertAlmostEqual(np.mean(spread), 0.5328233514, delta=1e-7) self.assertAlmostEqual(np.mean(min_bound), 0.511643929, delta=1e-7) self.assertAlmostEqual(np.mean(max_bound), 0.549827869, delta=1e-7) + # Checking the min value of spread, min_bound and max_bound. self.assertAlmostEqual(np.min(spread), 0.494787089, delta=1e-7) self.assertAlmostEqual(np.min(min_bound), 0.511372451, delta=1e-7) self.assertAlmostEqual(np.min(max_bound), 0.546616686, delta=1e-7) + # Checking the max value of spread, min_bound and max_bound. self.assertAlmostEqual(np.max(spread), 0.558869423, delta=1e-7) self.assertAlmostEqual(np.max(min_bound), 0.513868404, delta=1e-7) self.assertAlmostEqual(np.max(max_bound), 0.550466393, delta=1e-7) - with warnings.catch_warnings(): - warnings.simplefilter("ignore", UserWarning) - sc_jurek.stabilization_region(self.dataframe, gamma=1, utility_type=1) - spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=2, utility_type=2) - + # Checking the mean value of spread, min_bound and max_bound. self.assertAlmostEqual(np.mean(spread), 0.5328233514, delta=1e-7) self.assertAlmostEqual(np.mean(min_bound), 0.5276749084, delta=1e-7) self.assertAlmostEqual(np.mean(max_bound), 0.5850429718, delta=1e-7) + # Checking the min value of spread, min_bound and max_bound. self.assertAlmostEqual(np.min(spread), 0.494787089, delta=1e-7) self.assertAlmostEqual(np.min(min_bound), 0.4974942641, delta=1e-7) self.assertAlmostEqual(np.min(max_bound), 0.5625208403, delta=1e-7) + # Checking the max value of spread, min_bound and max_bound. self.assertAlmostEqual(np.max(spread), 0.558869423, delta=1e-7) self.assertAlmostEqual(np.max(min_bound), 0.5556367547, delta=1e-7) self.assertAlmostEqual(np.max(max_bound), 0.6107958587, delta=1e-7) @@ -198,6 +227,7 @@ def test_optimal_weights_fund_flows(self): Tests the optimal weights with fund flows method in the class. """ + # Creating an object of the class. sc_jurek = OUModelJurek() with warnings.catch_warnings(): @@ -217,14 +247,14 @@ def test_private_methods(self): Function tests special cases for code coverage. """ + # Creating an object of the class. sc_jurek = OUModelJurek() with warnings.catch_warnings(): warnings.simplefilter("ignore", UserWarning) sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) - sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) - + # Representative values of parameters. time_array = np.arange(0, len(self.dataframe)) * (1/252) tau = time_array[-1] - time_array c_1 = 0.0221413 @@ -232,6 +262,10 @@ def test_private_methods(self): c_3 = 9625.4458424 disc = -844.234913 + # For utility_type=1. + sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + + # Running below cases with gamma values for code coverage. with warnings.catch_warnings(): warnings.simplefilter("ignore") sc_jurek._A_calc_1(tau, c_1, c_2, disc, 0.5) @@ -239,8 +273,10 @@ def test_private_methods(self): sc_jurek._B_calc_1(tau, c_1, c_2, c_3, disc, 0.5) sc_jurek._B_calc_1(tau, c_1, c_2, c_3, disc, 0.9) + # For utility_type = 2. sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=2) + # Running below cases with gamma values for code coverage. with warnings.catch_warnings(): warnings.simplefilter("ignore") sc_jurek._B_calc_2(tau, c_1, c_2, c_3, disc, 0.5) @@ -253,16 +289,20 @@ def test_plotting(self, mock_plt): Tests the plot_results method in the class. """ + # Creating an object of the class. sc_jurek = OUModelJurek() + # Tests not datetime index exception. with self.assertRaises(Exception): sc_jurek.plot_results(self.dataframe) self.dataframe.index = pd.to_datetime(self.dataframe.index) + # Tests length of dataframe exception. with self.assertRaises(Exception): sc_jurek.plot_results(self.dataframe) + # Using a different dataset with atleast 10 years of data. sc_jurek.plot_results(self.shell_rdp_data) # Assert plt.figure got called diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index d05ac996..7b804d31 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -40,17 +40,19 @@ def test_fit(self): Tests the fit method in the class. """ + # Creating an object of the class. sc_mudchana = OUModelMudchanatongsuk() sc_mudchana.fit(self.dataframe) - # Checking values for spread calc. + # Checking parameter values for spread calculation. self.assertAlmostEqual(np.mean(sc_mudchana.spread), 2.0465361303, delta=1e-7) # TODO : Why is the mean value of spread not equal to the estimated theta param below? self.assertAlmostEqual(sc_mudchana.spread[7], 2.1073878043, delta=1e-7) self.assertAlmostEqual(sc_mudchana.spread[28], 2.0496029865, delta=1e-7) self.assertAlmostEqual(sc_mudchana.spread[-1], 2.0202245834, delta=1e-7) + # Checking other parameter values. self.assertAlmostEqual(sc_mudchana.sigma, 0.503695, delta=1e-4) self.assertAlmostEqual(sc_mudchana.mu, 0.114877, delta=1e-4) self.assertAlmostEqual(sc_mudchana.k, 3.99205, delta=1e-3) @@ -64,8 +66,10 @@ def test_describe(self): Tests the describe method in the class. """ + # Creating an object of the class. sc_mudchana = OUModelMudchanatongsuk() + # Testing for the run fit before this method exception. with self.assertRaises(Exception): sc_mudchana.describe() @@ -77,6 +81,7 @@ def test_describe(self): data = ['GLD', 'GDX', 1.98816, 3.99205, 0.404292, 0.173632, 0.114877, 0.503695] + # Testing the output of describe method. pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_mudchana.describe(), check_exact=False, atol=1e-3) @@ -85,15 +90,21 @@ def test_optimal_weights(self): Tests the optimal portfolio weights method in the class. """ + # Creating an object of the class. sc_mudchana = OUModelMudchanatongsuk() + # Testing for the run fit before this method exception. + with self.assertRaises(Exception): + sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = -10) + sc_mudchana.fit(self.dataframe) + # Testing for invalid value of gamma exception. with self.assertRaises(Exception): sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = 10) weights = sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = -10) - + # Checking the values of weights. self.assertAlmostEqual(np.mean(weights), 0.4986890920, delta=1e-5) self.assertAlmostEqual(weights[7], 0.5117099817, delta=1e-4) self.assertAlmostEqual(weights[28], 0.5246204647, delta=1e-4) From d79136370f72182bc437180735f3ad5df4a6552e Mon Sep 17 00:00:00 2001 From: hansenpei Date: Mon, 5 Apr 2021 13:41:48 -0400 Subject: [PATCH 083/103] Added Alternative C-vine Structure Added the alternative method for C-vine candidates in contrast to the original literature. Also fixed typos in docs. --- .../copula_approach/vinecop_generate.py | 50 +++++++++++++++++-- .../copula_approach/vine_copula_intro.rst | 2 +- tests/test_vinecop_generate.py | 42 ++++++++++++++++ 3 files changed, 89 insertions(+), 5 deletions(-) diff --git a/arbitragelab/copula_approach/vinecop_generate.py b/arbitragelab/copula_approach/vinecop_generate.py index d074d13f..cf75828a 100644 --- a/arbitragelab/copula_approach/vinecop_generate.py +++ b/arbitragelab/copula_approach/vinecop_generate.py @@ -49,14 +49,21 @@ def __init__(self, cvine_cop: pv.Vinecop = None): # The pv.Vinecop being wrapped self.cvine_cop = cvine_cop - def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = True): + def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = True, alt_cvine_structure=False): """ Auto fit data to the C-vine copula by selecting the center stock. The method will loop through all possible C-vine structures and choose the best fit by AIC. The targeted stock will never show up in the center of the tree, thus some C-vine structures need not be included. This - method is relatively slow, and the complexity is O(n!) with n being the number of stocks. Hence please keep - n <= 7. + method is relatively slow, and the complexity is O(n!) with n being the number of stocks and there is no way + to work around this. Hence please keep n <= 7. + + The original method suggested in [Stubinger et al. 2016] says the target stock should not be at the center of + each level of the C-vine tree, due to the way conditional probabilities are calculated. However the C-vine + structure effectively orders the variables by their importance of dependency, the target stock makes sense to + be the most important node. I.e, for the C-vine structure (4, 2, 1, 3), variable 3 should be the target stock, + in contrast to variable 4 as suggested in [Stubinger et al. 2016]. Therefore we provide both options by toggling + the alt_cvine_structure variable. The original pv.Vinecop will be returned just in case there is some usage not covered by this class. @@ -64,6 +71,8 @@ def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = :param pv_target_idx: (int) Optional. The stock to be targeted for trading. This is indexed from 1, hence 1 corresponds to the 0th column data in the data frame. Defaults to 1. :param if_renew: (bool) Optional. Whether to update the class attribute cvine_cop. Defaults to True. + :param alt_cvine_structure: (bool) Optional. Whether to use the alternative method to generate possible C-vines. + Defaults to False. :return: (pv.Vinecop) The fitted pv.Vinecop object. """ @@ -71,7 +80,10 @@ def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = data_np = data.to_numpy() # pyvinecopulib uses numpy arrays for fitting. data_dim = len(data.columns) # Number of stocks. # List of all possible C-vine structures, a list of tuples. - possible_cvine_structures = self._get_possible_cvine_structs(data_dim, pv_target_idx) + if alt_cvine_structure: # Alternative method to generate C-vine structures. + possible_cvine_structures = self._get_possible_cvine_structs_alt(data_dim, pv_target_idx) + else: # The original method to generate C-vine structures. + possible_cvine_structures = self._get_possible_cvine_structs(data_dim, pv_target_idx) # Fit among all possible structures. controls = pv.FitControlsVinecop(family_set=self._bicop_family) # Bivar copula constituents for the C-vine. @@ -96,6 +108,36 @@ def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = return fitted_cvine_cop + @staticmethod + def _get_possible_cvine_structs_alt(data_dim: int, pv_target_idx: int) -> List[tuple]: + """ + Get all possible C-vine structures specified by the dimension and the targeted node, alternative method. + + A C-vine copula is uniquely determined by an ordered tuple, listing the center of each tree at every level + read backwards. For example, for a 4-dim C-vine characterized by (4, 2, 1, 3), node 3 is the center for the + 0th tree, node 1 is the center for the 1st tree and so on. Because the C-vine effectively orders the variables + by their importance of dependency, the target stock makes sense to be the most important node. I.e, for the + C-vine structure (4, 2, 1, 3), variable 3 should be the target stock, in contrast to variable 4 as suggested + in [Stubinger et al. 2016]. + + :param data_dim: (int) The number of stocks. + :param pv_target_idx: (int). The stock to be targeted for trading. This is indexed from 1, hence 1 corresponds + to the 0th column data in a pandas data frame. + :return: (List[tuple]) The list of all possible C-vine structures stored as tuples. + """ + + # Initiating + all_items = list(range(1, data_dim + 1)) # All the nodes, indexed from 1 + all_structures = permutations(all_items) # All the possible structures, as permutations of the nodes + + # Loop through all the structures + valid_structures = [] + for structure in all_structures: + if structure[-1] == pv_target_idx: # Only keep the ones where the targeted index is the last element + valid_structures.append(structure) + + return valid_structures + @staticmethod def _get_possible_cvine_structs(data_dim: int, pv_target_idx: int) -> List[tuple]: """ diff --git a/docs/source/copula_approach/vine_copula_intro.rst b/docs/source/copula_approach/vine_copula_intro.rst index 58c48c6e..cc20768b 100644 --- a/docs/source/copula_approach/vine_copula_intro.rst +++ b/docs/source/copula_approach/vine_copula_intro.rst @@ -28,7 +28,7 @@ In reality, when there are only 2 dimensions, under most cases you can still mod with the existing bivariate copulas. However when it goes to higher dimensions, the copula model becomes quite rigid and loses a lot of details in the model. -Therefore, vine copula is invented exactly to address this high dimensional probablistic modeling problem. Instead of using an +Therefore, vine copula is invented exactly to address this high dimensional probabilistic modeling problem. Instead of using an N-dimensional copula directly, it decomposes the probability density into conditional probabilities, and further decomposes conditional probabilities into bivariate copulas. To sum up, **the idea is that we decompose the high dimensional pdf into bivariate copulas and marginal densities**. diff --git a/tests/test_vinecop_generate.py b/tests/test_vinecop_generate.py index 83f93be8..54a6a678 100644 --- a/tests/test_vinecop_generate.py +++ b/tests/test_vinecop_generate.py @@ -101,6 +101,27 @@ def test_get_possible_cvine_structs(self) -> None: structures_3_set = set(structures_3) self.assertEqual(structures_3_set, expected_structures_3) + def test_get_possible_cvine_structs_alt(self) -> None: + """ + Test CVineCop._get_possible_cvine_structs_alt. + """ + + cvinecop = vg.CVineCop() + structures_5 = cvinecop._get_possible_cvine_structs_alt(data_dim=5, pv_target_idx=2) + self.assertTrue(isinstance(structures_5, list)) + expected_structures_5 = {(1, 3, 4, 5, 2), (1, 3, 5, 4, 2), (1, 4, 3, 5, 2), (1, 4, 5, 3, 2), (1, 5, 3, 4, 2), + (1, 5, 4, 3, 2), (3, 1, 4, 5, 2), (3, 1, 5, 4, 2), (3, 4, 1, 5, 2), (3, 4, 5, 1, 2), + (3, 5, 1, 4, 2), (3, 5, 4, 1, 2), (4, 1, 3, 5, 2), (4, 1, 5, 3, 2), (4, 3, 1, 5, 2), + (4, 3, 5, 1, 2), (4, 5, 1, 3, 2), (4, 5, 3, 1, 2), (5, 1, 3, 4, 2), (5, 1, 4, 3, 2), + (5, 3, 1, 4, 2), (5, 3, 4, 1, 2), (5, 4, 1, 3, 2), (5, 4, 3, 1, 2)} + structures_5_set = set(structures_5) + self.assertEqual(structures_5_set, expected_structures_5) + + structures_3 = cvinecop._get_possible_cvine_structs_alt(data_dim=3, pv_target_idx=1) + expected_structures_3 = {(2, 3, 1), (3, 2, 1)} + structures_3_set = set(structures_3) + self.assertEqual(structures_3_set, expected_structures_3) + def test_get_condi_probs_priv(self) -> None: """ Test the _get_condi_probs function from CVineCop. @@ -261,6 +282,27 @@ def test_fit_auto(self) -> None: expected_aic_2 = -382.98496652926514 self.assertAlmostEqual(aic_2, expected_aic_2, places=3) + def test_fit_auto_alt(self) -> None: + """ + Test the fit_auto function in CVinecop class using the alternative method. + """ + + cvinecop = vg.CVineCop() + + # 1. With renewal + cvinecop.fit_auto(data=self.quantiles_data_train, pv_target_idx=1, if_renew=True, alt_cvine_structure=True) + # Check its aic value on the training data + aic_1 = cvinecop.aic(u=self.quantiles_data_train, num_threads=1) + expected_aic_1 = -379.8244061045313 + self.assertAlmostEqual(aic_1, expected_aic_1, places=3) + + # 2. Without renewal, fit the cvine copula using the test set. + cvinecop.fit_auto(data=self.quantiles_data_test, pv_target_idx=1, if_renew=False) + # Check its aic value on the training data. Should still get the same result. + aic_2 = cvinecop.aic(u=self.quantiles_data_train, num_threads=1) + expected_aic_2 = -379.8244061045313 + self.assertAlmostEqual(aic_2, expected_aic_2, places=3) + def test_strat_init(self) -> None: """ Test the __init__ function from CVineCopStrat. From e8e7ff356f44c8bedd9f933db9f584ecd9c89689 Mon Sep 17 00:00:00 2001 From: hansenpei Date: Mon, 5 Apr 2021 21:54:58 -0400 Subject: [PATCH 084/103] Minor update and typo fix on docs Minor update and typo fix on docs --- .../source/copula_approach/cvine_copula_strategy.rst | 6 ++++-- docs/source/copula_approach/vine_copula_intro.rst | 12 ++++++------ 2 files changed, 10 insertions(+), 8 deletions(-) diff --git a/docs/source/copula_approach/cvine_copula_strategy.rst b/docs/source/copula_approach/cvine_copula_strategy.rst index 44591181..ad578808 100644 --- a/docs/source/copula_approach/cvine_copula_strategy.rst +++ b/docs/source/copula_approach/cvine_copula_strategy.rst @@ -125,11 +125,13 @@ Therefore, to make stock 1 never at the center (except at the tree root), it is Moreover, I think if we treat stock 1 as the key stock, it should be **at the center of every level of the tree**, because it makes intuitive sense to model all other stocks' and their bivariate copula densities relation given the stock 1's information. Stock 1 is the object of interest, and therefore should be the governing quantity here. + C-vine structure intrinsically orders the marginal variables by their importance of interdependencies from its ordered tuple representation, + and the target stock should be the most important (therefore at the end of the tuple). + It is strange to argue that the least important stock in terms of interdependencies should become the target stock. I.e., 1 should be put at the end of the tuple, not at the beginning, and there are still 6 many possible structures for 4 stocks. - Currently we provide only the implementation in [Stübinger et al. 2018]. In the future we will provide the alternative method - that puts the target stock at the center. + Currently we provide the implementation in [Stübinger et al. 2018] and the alternative method that puts the target stock at the center. After chosen the 6 possible vine structures, we then fit everyone of them and calculate the associated AIC value. We choose the final C-vine structure among candidates with the lowest AIC value. diff --git a/docs/source/copula_approach/vine_copula_intro.rst b/docs/source/copula_approach/vine_copula_intro.rst index cc20768b..d783be03 100644 --- a/docs/source/copula_approach/vine_copula_intro.rst +++ b/docs/source/copula_approach/vine_copula_intro.rst @@ -159,7 +159,7 @@ Formal Definitions Vine Copula Types ***************** Every vine copula has a Regular Vine structure (R-vine). And there are 2 specific subgenres of R-vine called -Cannonical Vine and Drawable Vine. Those structure hold true for every layer of the tree. +Canonical Vine and Drawable Vine. Those structure hold true for every layer of the tree. They can be visualized as follows: .. figure:: images/Rvine_Cvine_Dvine.png @@ -177,7 +177,7 @@ For an R-vine, for each level of the tree, it needs to satisfy the following con layer 1, node 1 and node 3 makes a (1,3) node in layer 2. For a C-vine, it must be an R-vine at first, but for every layer of the tree there is a center component. This structure -makes it possible to represend the C-vine structure using an ordered tuple: reading backwards, each number represents +makes it possible to represent the C-vine structure using an ordered tuple: reading backwards, each number represents the centered component at each level of the tree. For a D-vine, each tree is a *path*: there is one road that goes through all the nodes. @@ -311,7 +311,7 @@ integration from the probability density. Cumulative Density ****************** -When dealing with "traditional" copula models, this is from the definition, and is thus ususally the easiest one to be computed. +When dealing with "traditional" copula models, this is from the definition, and is thus usually the easiest one to be computed. In vine copula models this is the hardest one in contrast, because vine copula starts from probability densities, not from cumulative densities. Hence this quantity needs to be numerically integrated across the hypercube :math:`[0, 1]^4`. Often people use Monte-Carlo integration for this computation. This quantity is not used as often in trading applications. @@ -321,14 +321,14 @@ Sample and Fitting Those are very interesting topics but are beyond our scope here. Interested readers can refer to [Dißmann et al. 2012] for more details. This is an active research field and involves a lot of heavy lifting. Luckily, a lot of great algorithms are already nicely -blackboxed, handled automatically by softwares. Specifically, sample generation is a pretty much solved problem, whereas determine -the best R-vine structure given data and determing all copula types and parameters are still discussed, but some algorithms are available. +blackboxed, handled automatically by software. Specifically, sample generation is a pretty much solved problem, whereas determine +the best R-vine structure given data and determine all copula types and parameters are still under discussion, but some algorithms are available. Thus, sampling is very fast, and fitting can be slow. .. Note:: 1. When working with copula models, whether it is a "traditional" copula model or vine copula, we always fit the - pseudo-observations, i.e., quanties data, instead of the real data. + pseudo-observations, i.e., quantiles data, instead of the real data. 2. For fitting a vine copula, we need to determine the best tree structure that reflects the data, along with specifying the type of bivariate copulas and their parameters. The amount of calculation is huge. From 6435d0be475b62aa7b85cf2cf572e669796dc0e0 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Tue, 6 Apr 2021 15:45:01 +0530 Subject: [PATCH 085/103] Removing TODO in unittest file. --- tests/test_ou_model_mudchanatongsuk.py | 1 - 1 file changed, 1 deletion(-) diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index 7b804d31..46c3ad32 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -47,7 +47,6 @@ def test_fit(self): # Checking parameter values for spread calculation. self.assertAlmostEqual(np.mean(sc_mudchana.spread), 2.0465361303, delta=1e-7) - # TODO : Why is the mean value of spread not equal to the estimated theta param below? self.assertAlmostEqual(sc_mudchana.spread[7], 2.1073878043, delta=1e-7) self.assertAlmostEqual(sc_mudchana.spread[28], 2.0496029865, delta=1e-7) self.assertAlmostEqual(sc_mudchana.spread[-1], 2.0202245834, delta=1e-7) From 04e930a3d8ae7debb47af422603d8751b58f5399 Mon Sep 17 00:00:00 2001 From: hansenpei Date: Tue, 6 Apr 2021 12:15:21 -0400 Subject: [PATCH 086/103] Typo fix in vine cop doc Typo fix in vine cop doc --- docs/source/copula_approach/vine_copula_intro.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/source/copula_approach/vine_copula_intro.rst b/docs/source/copula_approach/vine_copula_intro.rst index d783be03..d51c89c3 100644 --- a/docs/source/copula_approach/vine_copula_intro.rst +++ b/docs/source/copula_approach/vine_copula_intro.rst @@ -18,7 +18,7 @@ directly look at how they are "related". Indeed, traders and analysts have been using copula to exploit statistical arbitrage under the pairs trading framework for some time, and we have implemented some of the most popular methods in :code:`ArbitrageLab`. However, it is natural to expand beyond dealing with just a pair of stocks: There already exist a great amount of competing -stat arb methods alongside with copula, thinning the potential alpha. It is also intuitive for human to think about relative +stat arb methods alongside copula, thinning the potential alpha. It is also intuitive for human to think about relative pricing among 2 stocks, where as for higher dimensions it is not so easy, and left great chances for quantitative approaches. Copula itself is not limited to just 2 dimensions. You can expand it to arbitrarily large dimensions as you wish. @@ -218,7 +218,7 @@ The R-vine structure is mapped to the matrix as follows: 1. Find a diagonal term :math:`a`. For example :math:`M_{2, 2} = 4`. - 2. Follow that column downwards and stop somewhere :math:`b`, say we stop at :math:`M_{4, 5} = 1`. + 2. Follow that column downwards and stop somewhere :math:`b`, say we stop at :math:`M_{4, 2} = 1`. 3. The leftover terms below :math:`b` in that column are then conditions :math:`\{c_1, c_2, \cdots\}`. In this example we have :math:`\{2, 3\}` left. From 8af39d218ae2b1e4627d700efef6f1bacb1354a0 Mon Sep 17 00:00:00 2001 From: PanPip Date: Thu, 8 Apr 2021 13:46:54 +0200 Subject: [PATCH 087/103] Minor code style changes to the OU Stochastic Control Module --- .../ou_model_jurek.py | 309 +++++++++--------- .../ou_model_mudchanatongsuk.py | 124 +++---- tests/test_ou_model_jurek.py | 136 ++++---- tests/test_ou_model_mudchanatongsuk.py | 24 +- 4 files changed, 301 insertions(+), 292 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 98ff5b09..d6fadeac 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -9,8 +9,8 @@ `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. In EFA 2006 Meetings Paper. `__ """ - # pylint: disable=invalid-name, too-many-instance-attributes, too-many-locals + import warnings import cvxpy as cp import numpy as np @@ -39,27 +39,27 @@ def __init__(self): Initializes the parameters of the module. """ - # Characteristics of Training Data. - self.ticker_A = None # Ticker Symbol of first stock. - self.ticker_B = None # Ticker Symbol of second stock. - self.spread = None # Constructed spread from training data. - self.scaled_spread_weights = None # Scaled weights for the prices in spread. - self.time_array = None # Time indices of training data. - self.delta_t = None # Time difference between each index in data, calculated in years. + # Characteristics of Training Data + self.ticker_A = None # Ticker Symbol of first stock + self.ticker_B = None # Ticker Symbol of second stock + self.spread = None # Constructed spread from training data + self.scaled_spread_weights = None # Scaled weights for the prices in spread + self.time_array = None # Time indices of training data + self.delta_t = None # Time difference between each index in data, calculated in years - # Estimated params from training data. - self.sigma = None # Standard deviation of spread. - self.mu = None # Long run mean of spread. - self.k = None # Rate of mean reversion. + # Estimated params from training data + self.sigma = None # Standard deviation of spread + self.mu = None # Long run mean of spread + self.k = None # Rate of mean reversion - # Params inputted by user. - self.r = None # Rate of returns. - self.gamma = None # Coefficient of relative risk aversion. - self.beta = None # Rate of time preference. + # Params inputted by user + self.r = None # Rate of returns + self.gamma = None # Coefficient of relative risk aversion + self.beta = None # Rate of time preference @staticmethod - def _calc_total_return_indices(prices : pd.DataFrame) -> pd.DataFrame: + def _calc_total_return_indices(prices: pd.DataFrame) -> pd.DataFrame: """ This method calculates the total return indices from pricing data. This calculation follows Section IV A in Jurek (2007). @@ -68,7 +68,7 @@ def _calc_total_return_indices(prices : pd.DataFrame) -> pd.DataFrame: :return: (pd.DataFrame) Total return indices. """ - #Calculating the daily returns. + # Calculating the daily returns returns_df = prices.pct_change() returns_df = returns_df.replace([np.inf, -np.inf], np.nan).ffill().dropna() @@ -97,32 +97,32 @@ def fit(self, prices: pd.DataFrame, delta_t: float = 1 / 252, adf_test: bool = F warnings.warn("Please make sure length of training data is greater than 10 years. " "This is the time period used to fit the model in the original paper.") - # Setting instance attributes. + # Setting instance attributes self.delta_t = delta_t self.ticker_A, self.ticker_B = prices.columns[0], prices.columns[1] - #Calculating the total return indices from pricing data. + # Calculating the total return indices from pricing data total_return_indices = self._calc_total_return_indices(prices) self.time_array = np.arange(0, len(total_return_indices)) * self.delta_t - # As mentioned in the paper, the vector of linear weights are calculated using co-integrating regression. + # As mentioned in the paper, the vector of linear weights are calculated using co-integrating regression eg_portfolio = EngleGrangerPortfolio() - eg_portfolio.fit(total_return_indices, add_constant=True) # Fitting the total return indices. - eg_adf_statistics = eg_portfolio.adf_statistics # Stores the results of the ADF statistic test. - eg_cointegration_vectors = eg_portfolio.cointegration_vectors # Stores the calculated weights for the pair o stocks in the spread. + eg_portfolio.fit(total_return_indices, add_constant=True) # Fitting the total return indices + eg_adf_statistics = eg_portfolio.adf_statistics # Stores the results of the ADF statistic test + eg_cointegration_vectors = eg_portfolio.cointegration_vectors # Stores the calculated weights for the pair of stocks in the spread if adf_test is True and eg_adf_statistics.loc['statistic_value', 0] > eg_adf_statistics.loc[f'{int(significance_level * 100)}%', 0]: - # Making sure that the data passes the ADF statistic test. + # Making sure that the data passes the ADF statistic test print(eg_adf_statistics) warnings.warn("ADF statistic test failure.") - # Scaling the weights such that they sum to 1. + # Scaling the weights such that they sum to 1 self.scaled_spread_weights = eg_cointegration_vectors.loc[0] / abs(eg_cointegration_vectors.loc[0]).sum() - # Calculating the final spread value from the scaled weights. + # Calculating the final spread value from the scaled weights self.spread = (total_return_indices * self.scaled_spread_weights).sum(axis=1) - self.spread = self.spread.to_numpy() # This conversion seems to have changed the estimated values. + self.spread = self.spread.to_numpy() # This conversion seems to have changed the estimated values params = self._estimate_params(self.spread) self.mu, self.k, self.sigma = params @@ -139,18 +139,18 @@ def _estimate_params(self, spread: np.array) -> tuple: N = len(spread) - # Mean estimator. + # Mean estimator mu = spread.mean() - # Estimator for rate of mean reversion. + # Estimator for rate of mean reversion k = (-1 / self.delta_t) * np.log(np.multiply(spread[1:] - mu, spread[:-1] - mu).sum() / np.power(spread[1:] - mu, 2).sum()) - # Part of sigma estimation formula. + # Part of sigma estimation formula sigma_calc_sum = np.power((spread[1:] - mu - np.exp(-k * self.delta_t) * (spread[:-1] - mu)) / np.exp(-k * self.delta_t), 2).sum() - #Estimator for standard deviation. + # Estimator for standard deviation sigma = np.sqrt(2 * k * sigma_calc_sum / ((np.exp(2 * k * self.delta_t) - 1) * (N - 2))) return mu, k, sigma @@ -164,12 +164,12 @@ def _spread_calc(self, prices: pd.DataFrame) -> tuple: :return: (tuple) Consists of time remaining array and spread numpy array. """ - #Calculating the total return indices from pricing data. + # Calculating the total return indices from pricing data total_return_indices = self._calc_total_return_indices(prices) t = np.arange(0, len(total_return_indices)) * self.delta_t - tau = t[-1] - t # Stores time remaining till closure. (In years) + tau = t[-1] - t # Stores time remaining till closure (In years) - # Calculating the spread with weights calculated from training data. + # Calculating the spread with weights calculated from training data S = (total_return_indices * self.scaled_spread_weights).sum(axis=1) S = S.to_numpy() @@ -186,15 +186,19 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, utility_type: int = 1, The first type of investor is represented by utility_type = 1. This agent has constant relative risk aversion preferences(CRRA investor) with utility defined over terminal wealth. - For this type of investor, gamma = 1 implies log utility investor, and - gamma != 1 implies general CRRA investor. + For this type of investor, + + gamma = 1 implies log utility investor, and + gamma != 1 implies general CRRA investor. The second type of investor is represented by utility_type = 2. This agent has utility defined over intermediate consumption, with agent’s preferences described by Epstein-Zin recursive utility with psi(elasticity of intertemporal substitution) = 1. - For this type of investor, gamma = 1 reduces to standard log utility investor, and - gamma > 1 implies more risk averse investors, - whereas gamma < 1 implies more risk tolerance in comparison to investor with log utility. + For this type of investor, + + gamma = 1 reduces to standard log utility investor, and + gamma > 1 implies more risk averse investors, + whereas gamma < 1 implies more risk tolerance in comparison to investor with log utility. What is beta? Beta signifies the constant fraction of total wealth an investor chooses to consume. This is analogous to a hedge fund investor @@ -219,29 +223,29 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, utility_type: int = 1, if utility_type not in [1, 2]: raise Exception("Please make sure utility_type is either 1 or 2.") - # Setting instance attributes. + # Setting instance attributes self.r = r self.gamma = gamma self.beta = beta tau, S = self._spread_calc(prices) - W = np.ones(len(tau)) # Wealth is normalized to one. + W = np.ones(len(tau)) # Wealth is normalized to one N = None - # The optimal weights equation is the same for both types of utility functions. + # The optimal weights equation is the same for both types of utility functions # For gamma = 1, the outputs weights are identical for both types of utility functions, - # whereas for gamma != 1, the calculation of A and B functions in the equation are different. + # whereas for gamma != 1, the calculation of A and B functions in the equation are different if self.gamma == 1: N = ((self.k * (self.mu - S) - self.r * S) / (self.sigma ** 2)) * W else: # For the case of gamma = 1, A & B are not used in the final optimal portfolio calculation, - # so the corresponding calculations are skipped. + # so the corresponding calculations are skipped A = None B = None - # A and B functions are used in the final weights calculation. + # A and B functions are used in the final weights calculation if utility_type == 1: A, B = self._AB_calc_1(tau) @@ -250,7 +254,7 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, utility_type: int = 1, N = ((self.k * (self.mu - S) - self.r * S) / (self.gamma * self.sigma ** 2) + (2 * A * S + B) / self.gamma) * W - return N / W # We return the optimal allocation of spread asset scaled by wealth. + return N / W # We return the optimal allocation of spread asset scaled by wealth def optimal_portfolio_weights_fund_flows(self, prices: pd.DataFrame, f: float, gamma: float = 1, r: float = 0.05) -> np.array: @@ -278,7 +282,7 @@ def optimal_portfolio_weights_fund_flows(self, prices: pd.DataFrame, f: float, g :return: (np.array) Optimal weights with fund flows. """ - # Calculating the scaled optimal portfolio weights. + # Calculating the scaled optimal portfolio weights N = self.optimal_portfolio_weights(prices, utility_type=1, gamma=gamma, r=r) return (1 / (1 + f)) * N @@ -305,53 +309,53 @@ def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamm if utility_type not in [1, 2]: raise Exception("Please make sure utility_type is either 1 or 2.") - # Setting instance attributes. + # Setting instance attributes self.r = r self.gamma = gamma self.beta = beta - # Calculating the time left array and the spread. + # Calculating the time left array and the spread tau, S = self._spread_calc(prices) if self.gamma == 1: - # Calculation of A and B functions are not done in case of gamma = 1. (Refer Appendix A.1 and B.2). + # Calculation of A and B functions are not done in case of gamma = 1 (Refer Appendix A.1 and B.2) warnings.warn("Calculation of stabilization region is not implemented for gamma = 1.") return None A = None B = None - # A and B functions are used in the final weights calculation. + # A and B functions are used in the final weights calculation if utility_type == 1: A, B = self._AB_calc_1(tau) else: A, B = self._AB_calc_2(tau) - # Calculating phi (Refer Equation 17 in Jurek (2007)). + # Calculating phi (Refer Equation 17 in Jurek (2007)) phi = (2 * A / self.gamma) - ((self.k + self.r) / (self.gamma * self.sigma ** 2)) # Note : phi < 0. - # term_1 and term_2 calculations are part of the constraint equation calculation below. + # term_1 and term_2 calculations are part of the constraint equation calculation below term_1 = (self.k * self.mu + (self.sigma ** 2) * B) / (self.gamma * self.sigma ** 2) term_2 = np.sqrt(-phi) - # Initializing the upper bound and lower bound arrays. + # Initializing the upper bound and lower bound arrays max_bound = np.zeros(len(tau)) min_bound = np.zeros(len(tau)) - # Iterating over each time step in the array. + # Iterating over each time step in the array for ind in range(len(tau)): - s = cp.Variable() # Setting an optimization variable for spread. - # Defining the constraint equation involving spread. + s = cp.Variable() # Setting an optimization variable for spread + # Defining the constraint equation involving spread constraint = [cp.abs(phi[ind] * s + term_1[ind]) <= term_2[ind] - 1e-6] - # Solving the maximization problem to calculate the upper bound. + # Solving the maximization problem to calculate the upper bound prob_max = cp.Problem(cp.Maximize(s), constraint) prob_max.solve() max_bound[ind] = prob_max.value - # Solving the minimization problem to calculate the lower bound. + # Solving the minimization problem to calculate the lower bound prob_min = cp.Problem(cp.Minimize(s), constraint) prob_min.solve() min_bound[ind] = prob_min.value @@ -359,7 +363,7 @@ def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamm return S, min_bound, max_bound - def _AB_calc_1(self, tau) -> tuple: + def _AB_calc_1(self, tau: np.array) -> tuple: """ This helper function computes the A and B functions for investors with utility_type = 1. The implementation follows Appendix A.2 in the paper. @@ -368,31 +372,31 @@ def _AB_calc_1(self, tau) -> tuple: :return: (tuple) A and B arrays. """ - # Calculating value of variable c_1 in Appendix A.2.1. + # Calculating value of variable c_1 in Appendix A.2.1 c_1 = 2 * self.sigma ** 2 / self.gamma - # Calculating value of variable c_2 in Appendix A.2.1. + # Calculating value of variable c_2 in Appendix A.2.1 c_2 = -(self.k / self.gamma + self.r * (1 - self.gamma) / self.gamma) - # Calculating value of variable c_3 in Appendix A.2.1. + # Calculating value of variable c_3 in Appendix A.2.1 c_3 = 0.5 * ((1 - self.gamma) / self.gamma) * (((self.k + self.r) / self.sigma) ** 2) - # Calculating value of discriminant in Appendix A.2.1. + # Calculating value of discriminant in Appendix A.2.1 disc = 4 * (self.k ** 2 - self.r ** 2 * (1 - self.gamma)) / self.gamma - # Note: discriminant is always positive for gamma > 1. + # Note: discriminant is always positive for gamma > 1 - # Calculating value of variable gamma_0 in Appendix A.2.1. + # Calculating value of variable gamma_0 in Appendix A.2.1 gamma_0 = 1 - (self.k / self.r) ** 2 - # Note: gamma_0 is not always > 0. + # Note: gamma_0 is not always > 0 - A = self._A_calc_1(tau, c_1, c_2, disc, gamma_0) # Calculating value of function A. - B = self._B_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function B. + A = self._A_calc_1(tau, c_1, c_2, disc, gamma_0) # Calculating value of function A + B = self._B_calc_1(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function B return A, B - def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0) -> np.array: + def _A_calc_1(self, tau: np.array, c_1: float, c_2: float, disc: float, gamma_0: float) -> np.array: """ This method calculates the value of function A as described in the paper for investor with utility_type = 1. The implementation follows Appendix A.2.1 in the paper. @@ -408,7 +412,7 @@ def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0) -> np.array: """ A = None - error_margin = 1e-4 # Error margin around gamma_0. + error_margin = 1e-4 # Error margin around gamma_0 if 0 < self.gamma < gamma_0 - error_margin: @@ -425,14 +429,14 @@ def _A_calc_1(self, tau, c_1, c_2, disc, gamma_0) -> np.array: A = -c_2 / c_1 + (np.sqrt(disc) / (2 * c_1)) * (1 / np.tanh(-np.sqrt(disc) * tau / 2 + np.arctanh(np.sqrt(disc) / (2 * c_2)))) else: - # Case when self.gamma > 1. + # Case when self.gamma > 1 A = -c_2 / c_1 + (np.sqrt(disc) / (2 * c_1)) * np.tanh(-np.sqrt(disc) * tau / 2 + np.arctanh(2 * c_2 / np.sqrt(disc))) return A - def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: + def _B_calc_1(self, tau: np.array, c_1: float, c_2: float, c_3: float, disc: float, gamma_0: float) -> np.array: """ This method calculates the value of function B as described in the paper for investor with utility_type = 1. The implementation follows Appendix A.2.2 in the paper. @@ -448,21 +452,21 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: :return: (np.array) B array. """ - # Calculating value of variable c_4 in Appendix A.2.2. + # Calculating value of variable c_4 in Appendix A.2.2 c_4 = 2 * self.k * self.mu / self.gamma - # Calculating value of variable c_5 in Appendix A.2.2. + # Calculating value of variable c_5 in Appendix A.2.2 c_5 = -((self.k + self.r) / self.sigma ** 2) * ((1 - self.gamma) / self.gamma) * self.k * self.mu B = None - error_margin = 1e-4 # Error margin around gamma_0. + error_margin = 1e-4 # Error margin around gamma_0 if 0 < self.gamma < gamma_0 - error_margin: - # Calculating value of function phi_1 in Appendix A.2.2. + # Calculating value of function phi_1 in Appendix A.2.2 phi_1 = np.sqrt(-disc) * (np.cos(np.sqrt(-disc) * tau / 2) - 1) + 2 * c_2 * np.sin(np.sqrt(-disc) * tau / 2) - # Calculating value of function phi_2 in Appendix A.2.2. + # Calculating value of function phi_2 in Appendix A.2.2 phi_2 = np.arctanh(np.tan(0.25 * (np.sqrt(-disc) * tau - 2 * np.arctan(2 * c_2 / np.sqrt(-disc))))) + \ np.arctanh(np.tan(0.5 * np.arctan(2 * c_2 / np.sqrt(-disc)))) @@ -474,7 +478,7 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: B = (c_1 * c_5 * (c_2 * tau - 2) - (c_2 ** 2) * c_4) * tau / (2 * c_1 * (c_2 * tau - 1)) else: - # Case when self.gamma > gamma_0 + error_margin. + # Case when self.gamma > gamma_0 + error_margin B = (4 * (c_2 * c_5 - c_3 * c_4 + (c_3 * c_4 - c_2 * c_5) * np.cosh(np.sqrt(disc) * tau / 2)) + 2 * c_5 * np.sqrt(disc) * np.sinh(np.sqrt(disc) * tau / 2)) \ @@ -483,7 +487,7 @@ def _B_calc_1(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: return B - def _AB_calc_2(self, tau) -> tuple: + def _AB_calc_2(self, tau: np.array) -> tuple: """ This helper function computes the A and B functions for investors with utility_type = 2. The implementation follows Appendix B.1 in the paper. @@ -492,29 +496,29 @@ def _AB_calc_2(self, tau) -> tuple: :return: (tuple) A and B arrays. """ - # Calculating value of variable c_1 in Appendix B.1.1. + # Calculating value of variable c_1 in Appendix B.1.1 c_1 = 2 * self.sigma ** 2 / self.gamma - # Calculating value of variable c_2 in Appendix B.1.1. + # Calculating value of variable c_2 in Appendix B.1.1 c_2 = (self.gamma * (2 * self.r - self.beta) - 2 * (self.k + self.r)) / (2 * self.gamma) - # Calculating value of variable c_3 in Appendix B.1.1. + # Calculating value of variable c_3 in Appendix B.1.1 c_3 = ((self.k + self.r) ** 2) * (1 - self.gamma) / (2 * self.gamma * (self.sigma ** 2)) - # Calculating value of discriminant in Appendix B.1.1. + # Calculating value of discriminant in Appendix B.1.1 disc = ((2 * self.k + self.beta) ** 2 + (self.gamma - 1) * ((-2 * self.r + self.beta) ** 2)) / self.gamma - # Calculating value of variable gamma_0 in Appendix B.1.1. + # Calculating value of variable gamma_0 in Appendix B.1.1 gamma_0 = 4 * (self.k + self.r) * (self.r - self.beta - self.k) / ((2 * self.r - self.beta) ** 2) - A = self._A_calc_2(tau, c_1, c_2, disc, gamma_0) # Calculating value of function A. - B = self._B_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function B. + A = self._A_calc_2(tau, c_1, c_2, disc, gamma_0) # Calculating value of function A + B = self._B_calc_2(tau, c_1, c_2, c_3, disc, gamma_0) # Calculating value of function B return A, B - def _A_calc_2(self, tau, c_1, c_2, disc, gamma_0) -> np.array: + def _A_calc_2(self, tau: np.array, c_1: float, c_2: float, disc: float, gamma_0: float) -> np.array: """ This method calculates the value of function A as described in the paper for investor with utility_type = 2. The implementation follows Appendix B.1.1 in the paper. @@ -530,11 +534,11 @@ def _A_calc_2(self, tau, c_1, c_2, disc, gamma_0) -> np.array: :return: (np.array) A array. """ - # Same calculation as for general CRRA Investor. + # Same calculation as for general CRRA Investor return self._A_calc_1(tau, c_1, c_2, disc, gamma_0) - def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: + def _B_calc_2(self, tau: np.array, c_1: float, c_2: float, c_3: float, disc: float, gamma_0: float) -> np.array: """ This method calculates the value of function B as described in the paper for investor with utility_type = 2. The implementation follows Appendix B.1.2 in the paper. @@ -550,39 +554,39 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: :return: (np.array) B array. """ - # Calculating value of variable c_4 in Appendix B.1.2. + # Calculating value of variable c_4 in Appendix B.1.2 c_4 = 2 * self.k * self.mu / self.gamma - # Calculating value of variable c_5 in Appendix B.1.2. + # Calculating value of variable c_5 in Appendix B.1.2 c_5 = -(self.k + self.r * (1 - self.gamma) + self.beta * self.gamma) / (2 * self.gamma) - # Calculating value of variable c_6 in Appendix B.1.2. + # Calculating value of variable c_6 in Appendix B.1.2 c_6 = self.k * (self.k + self.r) * (self.gamma - 1) * self.mu / (self.gamma * self.sigma ** 2) B = None - error_margin = 1e-4 # Error margin around gamma_0. + error_margin = 1e-4 # Error margin around gamma_0 - rep_exp_1 = np.exp(tau * c_2) # Repeating Exponential Form with variable c_2. - rep_exp_2 = np.exp(tau * c_5) # Repeating Exponential Form with variable c_5. + rep_exp_1 = np.exp(tau * c_2) # Repeating Exponential Form with variable c_2 + rep_exp_2 = np.exp(tau * c_5) # Repeating Exponential Form with variable c_5 if 0 < self.gamma < gamma_0 - error_margin: - # Implementation of Case I in Appendix B.1.2. + # Implementation of Case I in Appendix B.1.2 B = self._B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau) elif gamma_0 - error_margin <= self.gamma <= gamma_0 + error_margin: - # Implementation of Case II in Appendix B.1.2. + # Implementation of Case II in Appendix B.1.2 B = self._B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau) elif gamma_0 + error_margin < self.gamma < 1: - # Implementation of Case III in Appendix B.1.2. + # Implementation of Case III in Appendix B.1.2 B = self._B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau) else: - # Case when self.gamma > 1. - # Implementation of Case IV in Appendix B.1.2. + # Case when self.gamma > 1 + # Implementation of Case IV in Appendix B.1.2 B = self._B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau) @@ -590,7 +594,8 @@ def _B_calc_2(self, tau, c_1, c_2, c_3, disc, gamma_0) -> np.array: @staticmethod - def _B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau): + def _B_calc_2_IV(c_1: float, c_2: float, c_3: float, c_4: float, c_5: float, c_6: float, disc: float, + rep_exp_1: np.array, rep_exp_2: np.array, tau: np.array) -> np.array: """ Method calculates value of function B according to Case IV in Appendix B.1.2. @@ -607,11 +612,11 @@ def _B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau): :return: (np.array) Final value of B. """ - rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1. - rep_phrase_2 = 0.5 * np.sqrt(disc) * tau - np.arctanh(2 * c_2 / np.sqrt(disc)) # Repeated Phrase 2. - denominator = 2 * c_1 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. + rep_phrase_1 = np.sqrt(-c_1 * c_3 / disc) # Repeated Phrase 1 + rep_phrase_2 = 0.5 * np.sqrt(disc) * tau - np.arctanh(2 * c_2 / np.sqrt(disc)) # Repeated Phrase 2 + denominator = 2 * c_1 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation - # The final equation for B is split into 5 terms. + # The final equation for B is split into 5 terms term_1 = 2 * rep_exp_1 * rep_phrase_1 * c_4 * c_5 * (c_2 + 0.5 * np.sqrt(disc) * np.tanh(rep_phrase_2)) term_2 = 2 * rep_exp_1 * rep_phrase_1 - 2 * rep_exp_2 * (1 / np.cosh(rep_phrase_2)) @@ -623,7 +628,7 @@ def _B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau): term_5 = -term_3 - # Calculating the final value of function B. + # Calculating the final value of function B B = np.exp(-tau * c_2) * (term_1 + c_1 * (c_6 * (c_2 * term_2 + term_3 * c_5 @@ -634,7 +639,8 @@ def _B_calc_2_IV(c_1, c_2, c_3, c_4, c_5, c_6, disc, rep_exp_1, rep_exp_2, tau): @staticmethod - def _B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): + def _B_calc_2_III(c_1: float, c_2: float, c_3: float, c_4: float, c_5: float, c_6: float, + rep_exp_1: np.array, rep_exp_2: np.array, tau: np.array) -> np.array: """ Method calculates value of function B according to Case III in Appendix B.1.2. @@ -650,13 +656,13 @@ def _B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): :return: (np.array) Final value of B. """ - rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) # Repeated Phrase 1. - rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) # Repeated Phrase 2. - rep_phrase_3 = np.arctanh(rep_phrase_2 / c_2) - tau * rep_phrase_2 # Repeated Phrase 3. + rep_phrase_1 = np.sqrt(c_1 * c_3 / c_2 ** 2) # Repeated Phrase 1 + rep_phrase_2 = np.sqrt(c_2 ** 2 - c_1 * c_3) # Repeated Phrase 2 + rep_phrase_3 = np.arctanh(rep_phrase_2 / c_2) - tau * rep_phrase_2 # Repeated Phrase 3 # arccoth(x) = arctanh(1/x) - denominator = c_2 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. + denominator = c_2 * rep_phrase_1 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation - # The final equation for B is split into 5 terms. + # The final equation for B is split into 5 terms term_1 = rep_exp_1 * rep_phrase_1 * c_6 * c_2 ** 2 term_2 = rep_exp_1 * c_3 * rep_phrase_1 * c_4 @@ -671,7 +677,7 @@ def _B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): + rep_exp_2 * rep_phrase_2 * c_5 * c_6) # csch = 1/sinh - # Calculating the final value of function B. + # Calculating the final value of function B B = np.exp(-tau * c_2) * (term_1 - (term_2 + (rep_phrase_2 * term_3 + term_4) * c_6) * c_2 + term_5) / denominator @@ -679,7 +685,8 @@ def _B_calc_2_III(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): @staticmethod - def _B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): + def _B_calc_2_II(c_1: float, c_2: float, c_4: float, c_5: float, c_6: float, + rep_exp_1: np.array, rep_exp_2: np.array, tau: np.array) -> np.array: """ Method calculates value of function B according to Case II in Appendix B.1.2. @@ -694,9 +701,9 @@ def _B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): :return: (np.array) Final value of B. """ - denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 # Denominator in final equation. + denominator = c_1 * rep_exp_1 * (tau * c_2 - 1) * (c_2 - c_5) ** 2 # Denominator in final equation - # The final equation for B is split into 4 terms. + # The final equation for B is split into 4 terms term_1 = rep_exp_1 * tau * c_4 * c_2 ** 3 term_2 = (c_4 * (rep_exp_1 * (tau * c_5 + 1) - rep_exp_2) + rep_exp_1 * tau * c_1 * c_6) * c_2 ** 2 @@ -705,7 +712,7 @@ def _B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): term_4 = (rep_exp_1 - rep_exp_2) * c_1 * c_5 * c_6 - # Calculating the final value of function B. + # Calculating the final value of function B B = (-term_1 + term_2 - term_3 + term_4) / denominator @@ -713,7 +720,8 @@ def _B_calc_2_II(c_1, c_2, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): @staticmethod - def _B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): + def _B_calc_2_I(c_1: float, c_2: float, c_3: float, c_4: float, c_5: float, c_6: float, + rep_exp_1: np.array, rep_exp_2: np.array, tau: np.array) -> np.array: """ Method calculates value of function B according to Case I in Appendix B.1.2. @@ -729,12 +737,12 @@ def _B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): :return: (np.array) Final value of B. """ - rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) # Repeating Phrase 1. - rep_phrase_2 = np.sqrt(c_1 * c_3) / rep_phrase_1 # Repeating Phrase 2. - rep_phrase_3 = rep_phrase_1 * tau + np.arctan(c_2 / rep_phrase_1) # Repeating Phrase 3. - denominator = c_1 * rep_phrase_2 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation. + rep_phrase_1 = np.sqrt(c_1 * c_3 - c_2 ** 2) # Repeating Phrase 1 + rep_phrase_2 = np.sqrt(c_1 * c_3) / rep_phrase_1 # Repeating Phrase 2 + rep_phrase_3 = rep_phrase_1 * tau + np.arctan(c_2 / rep_phrase_1) # Repeating Phrase 3 + denominator = c_1 * rep_phrase_2 * (c_1 * c_3 + c_5 * (c_5 - 2 * c_2)) # Denominator in final equation - # The final equation for B is split into 5 terms. + # The final equation for B is split into 5 terms term_1 = rep_exp_1 * rep_phrase_2 * c_4 * c_5 * (c_2 - rep_phrase_1 * np.tan(rep_phrase_3)) term_2 = rep_exp_1 * rep_phrase_2 - 2 * rep_exp_2 * (1 / np.cos(rep_phrase_3)) @@ -745,7 +753,7 @@ def _B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): term_5 = -term_3 - # Calculating the final value of function B. + # Calculating the final value of function B B = np.exp(-tau * c_2) * (term_1 + c_1 * (c_6 * (c_2 * term_2 + term_3 * c_5 @@ -759,37 +767,40 @@ def _B_calc_2_I(c_1, c_2, c_3, c_4, c_5, c_6, rep_exp_1, rep_exp_2, tau): def _calc_half_life(k: float) -> float: """ Function returns half life of mean reverting spread from rate of mean reversion. - :return: (float) half life. + + :param k: (float) K value. + :return: (float) Half life. """ - return np.log(2) / k # Half life of shocks. + return np.log(2) / k # Half life of shocks def describe(self) -> pd.Series: """ Method returns values of instance attributes calculated from training data. - :return: (pd.Series) series describing parameter values. + + :return: (pd.Series) Series describing parameter values. """ if self.sigma is None: raise Exception("Please run the fit method before calling describe.") - # List defines the indexes of the final pandas object. + # List defines the indexes of the final pandas object index = ['Ticker of first stock', 'Ticker of second stock', 'Scaled Spread weights', 'long-term mean', 'rate of mean reversion', 'standard deviation', 'half-life'] - # List defines the values of the final pandas object. + # List defines the values of the final pandas object data = [self.ticker_A, self.ticker_B, np.round(self.scaled_spread_weights.values, 3), self.mu, self.k, self.sigma, self._calc_half_life(self.k)] - # Combine data and indexes into the pandas Series. + # Combine data and indexes into the pandas Series output = pd.Series(data=data, index=index) return output - def plot_results(self, prices:pd.DataFrame, num_test_windows = 5, delta_t =1 / 252, utility_type = 1, gamma = 10, - beta = 0.1, r = 0.05, f = 0.1): + def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: float = 1 / 252, utility_type: int = 1, + gamma: float = 10, beta: float = 0.1, r: float = 0.05, f: float = 0.1): """ Method plots out of sample performance of the model on specified number of test windows. We use a backward looking rolling window as training data and its size depends on the number of test windows chosen. @@ -801,17 +812,17 @@ def plot_results(self, prices:pd.DataFrame, num_test_windows = 5, delta_t =1 / 2 :param prices: (pd.DataFrame) Contains price series of both stocks in spread with dates as index. :param num_test_windows: (int) Number of out of sample testing windows to plot. :param delta_t: (float) Time difference between each index of prices, calculated in years. - :param gamma: (float) coefficient of relative risk aversion. - :param f: (float) coefficient of proportionality (assumed to be positive). - :param r: (float) Rate of Returns. :param utility_type: (int) Flag signifies type of investor preferences. + :param gamma: (float) coefficient of relative risk aversion. :param beta: (float) Subjective rate of time preference. (Only required for utility_type = 2). + :param r: (float) Rate of Returns. + :param f: (float) Coefficient of proportionality (assumed to be positive). """ - # Setting font size of plots. + # Setting font size of plots plt.rcParams.update({'font.size': 8}) - # Price series preprocessing. + # Price series preprocessing prices = prices.ffill() if not np.issubdtype(prices.index.dtype, np.datetime64): @@ -821,24 +832,24 @@ def plot_results(self, prices:pd.DataFrame, num_test_windows = 5, delta_t =1 / 2 raise Exception("Please make sure length of input data is greater than 10 years. " "This is the time period used to fit the model in the paper.") - # Getting the list of years in input data. + # Getting the list of years in input data years = prices.index.year.unique() - # Initializing a dataframe which stores stabilization region results. + # Initializing a dataframe which stores stabilization region results stab_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, columns=['Spread', 'lower bound', 'upper bound']) - # Initializing a dataframe which stores optimal weights. + # Initializing a dataframe which stores optimal weights optimal_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, columns=['Weights']) - # Initializing a dataframe which stores optimal weights in the case with fund flows. + # Initializing a dataframe which stores optimal weights in the case with fund flows optimal_fund_flows_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]): str(years[-1])].index, columns=['Weights']) ind = 0 - # Iterating over the test windows. + # Iterating over the test windows for year in np.arange(years[-(num_test_windows + 1)], years[-1], 1): - # Setting the train and test data. + # Setting the train and test data data_train_dataframe = prices.loc[str(year - (len(years) - (num_test_windows + 1))):str(year - 1)] data_test_dataframe = prices.loc[str(year)] @@ -851,27 +862,27 @@ def plot_results(self, prices:pd.DataFrame, num_test_windows = 5, delta_t =1 / 2 S, min_bound, max_bound = self.stabilization_region(data_test_dataframe, gamma=gamma, utility_type=utility_type, beta=beta, r=r) - # Adding the final results to their corresponding dataframes for each test window. + # Adding the final results to their corresponding dataframes for each test window stab_result_dataframe.iloc[ind:ind + len(S), :] = np.array([S, min_bound, max_bound]).T optimal_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_weights]).T optimal_fund_flows_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_fund_flow_weights]).T ind += len(S) - # Plotting the stabilization bound plot. + # Plotting the stabilization bound plot ax = stab_result_dataframe.plot(style=['c-', 'r:', 'r:'], legend=False, linewidth=1.0, figsize=(8, 4)) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Spread') ax.set_title("Evolution of spread with stabilization bound") plt.show() - # Plotting the optimal weights allocation plot. + # Plotting the optimal weights allocation plot ax = optimal_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=(8, 4)) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Optimal Weights') ax.set_title('Optimal allocation to the spread asset scaled by wealth') plt.show() - # Plotting the optimal weights allocation plot in the case with fund flows. + # Plotting the optimal weights allocation plot in the case with fund flows ax = optimal_fund_flows_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=(8, 4)) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Optimal Weights with fund flows') diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 3aca169c..18de355e 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -9,8 +9,8 @@ `Mudchanatongsuk, S., Primbs, J.A. and Wong, W., 2008, June. Optimal pairs trading: A stochastic control approach. `__ """ - # pylint: disable=invalid-name, too-many-instance-attributes + import math import numpy as np import pandas as pd @@ -34,33 +34,33 @@ def __init__(self): Initializes the parameters of the module. """ - # Characteristics of Training Data. - self.ticker_A = None # Ticker Symbol of first stock. - self.ticker_B = None # Ticker Symbol of second stock. - self.S = None # Log price of stock B in spread. - self.spread = None # Constructed spread from training data. - self.time_array = None # Time indices of training data. - self.delta_t = 1 / 251 # Time difference between each index in data, calculated in years. + # Characteristics of Training Data + self.ticker_A = None # Ticker Symbol of first stock + self.ticker_B = None # Ticker Symbol of second stock + self.S = None # Log price of stock B in spread + self.spread = None # Constructed spread from training data + self.time_array = None # Time indices of training data + self.delta_t = 1 / 251 # Time difference between each index in data, calculated in years - # Estimated params from training data. - self.sigma = None # Standard deviation of stock B. - self.mu = None # Drift of stock B. - self.k = None # Rate of mean reversion of spread. - self.theta = None # Long run mean of spread. - self.eta = None # Standard deviation of spread. - self.rho = None # Instantaneous correlation coefficient between two standard brownian motions. + # Estimated params from training data + self.sigma = None # Standard deviation of stock B + self.mu = None # Drift of stock B + self.k = None # Rate of mean reversion of spread + self.theta = None # Long run mean of spread + self.eta = None # Standard deviation of spread + self.rho = None # Instantaneous correlation coefficient between two standard brownian motions - # Params inputted by user. - self.gamma = None # Parameter of utility function (self.gamma < 1) + # Params inputted by user + self.gamma = None # Parameter of utility function (self.gamma < 1) @staticmethod - def _data_preprocessing(prices) -> pd.DataFrame: + def _data_preprocessing(prices: pd.DataFrame) -> pd.DataFrame: """ Helper function for input data preprocessing. :param prices: (pd.DataFrame) Pricing data of both stocks in spread. - :return: (pd.DataFrame) processed dataframe. + :return: (pd.DataFrame) Processed dataframe. """ return prices.ffill() @@ -79,22 +79,22 @@ def fit(self, prices: pd.DataFrame): # Preprocessing prices = self._data_preprocessing(prices) - # Setting instance attributes. + # Setting instance attributes self.time_array = np.arange(0, len(prices)) * self.delta_t self.ticker_A, self.ticker_B = prices.columns[0], prices.columns[1] - # Calculating the spread. + # Calculating the spread self.S = np.log(prices.loc[:, self.ticker_B]) self.spread = np.log(prices.loc[:, self.ticker_A]) - self.S - self.spread = self.spread.to_numpy() # Converting from pd.Series to numpy array. - self.S = self.S.to_numpy() # Converting from pd.Series to numpy array. + self.spread = self.spread.to_numpy() # Converting from pd.Series to numpy array + self.S = self.S.to_numpy() # Converting from pd.Series to numpy array params = self._estimate_params_log_likelihood() - self.sigma, self.mu, self.k,self.theta, self.eta, self.rho = params[:-1] + self.sigma, self.mu, self.k, self.theta, self.eta, self.rho = params[:-1] - def optimal_portfolio_weights(self, prices: pd.DataFrame, gamma = -100) -> np.array: + def optimal_portfolio_weights(self, prices: pd.DataFrame, gamma: float = -100) -> np.array: """ This method calculates the final optimal portfolio weights for the calculated spread. @@ -114,19 +114,19 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, gamma = -100) -> np.ar # Preprocessing prices = self._data_preprocessing(prices) - # Setting instance attributes. + # Setting instance attributes self.gamma = gamma t = np.arange(0, len(prices)) * self.delta_t tau = t[-1] - t - # Calculating spread. + # Calculating spread x = np.log(prices.iloc[:, 0]) - np.log(prices.iloc[:, 1]) - x = x.to_numpy() # Converting from pd.Series to numpy array. + x = x.to_numpy() # Converting from pd.Series to numpy array - # Calculating the alpha and beta functions. + # Calculating the alpha and beta functions alpha_t, beta_t = self._alpha_beta_calc(tau) - # Calculating the final optimal portfolio weights. + # Calculating the final optimal portfolio weights h = (1 / (1 - self.gamma)) * (beta_t + 2 * np.multiply(x, alpha_t) - self.k * (x - self.theta) / self.eta ** 2 + self.rho * self.theta / self.eta + 0.5) @@ -134,36 +134,36 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, gamma = -100) -> np.ar return h - def _alpha_beta_calc(self, tau) -> tuple: + def _alpha_beta_calc(self, tau: np.array) -> tuple: """ This helper function computes the alpha and beta functions as given in equation 24 and 25 of Mudchanatongsuk (2008). :param tau: (np.array) Array with time till completion in years. - :return: (tuple) alpha and beta arrays. + :return: (tuple) Alpha and beta arrays. """ - sqrt_gamma = np.sqrt(1 - self.gamma) # Repeating Calculation involving gamma. - exp_calc = np.exp(2 * self.k * tau / sqrt_gamma) # Repeating Calculation involving gamma and tau series. + sqrt_gamma = np.sqrt(1 - self.gamma) # Repeating Calculation involving gamma + exp_calc = np.exp(2 * self.k * tau / sqrt_gamma) # Repeating Calculation involving gamma and tau series - # Calculating the alpha function output. + # Calculating the alpha function output alpha_t = self._alpha_calc(sqrt_gamma, exp_calc) - # Calculating the beta function output. + # Calculating the beta function output beta_t = self._beta_calc(sqrt_gamma, exp_calc) return alpha_t, beta_t - def _alpha_calc(self, sqrt_gamma, exp_calc) -> np.array: + def _alpha_calc(self, sqrt_gamma: float, exp_calc: np.array) -> np.array: """ This helper function computes the alpha function in equation 24. :param sqrt_gamma: (float) Repeating value. :param exp_calc: (np.array) Repeating series of values. - :return: (np.array) alpha array. + :return: (np.array) Alpha array. """ - # The equation for calculation of alpha is split into two parts. + # The equation for calculation of alpha is split into two parts left_calc = self.k * (1 - sqrt_gamma) / (2 * (self.eta ** 2)) right_calc = 2 * sqrt_gamma / (1 - sqrt_gamma - (1 + sqrt_gamma) * exp_calc) @@ -171,16 +171,16 @@ def _alpha_calc(self, sqrt_gamma, exp_calc) -> np.array: return left_calc * (1 + right_calc) - def _beta_calc(self, sqrt_gamma, exp_calc) -> np.array: + def _beta_calc(self, sqrt_gamma: float, exp_calc: np.array) -> np.array: """ This helper function computes the beta function in equation 25. :param sqrt_gamma: (float) Repeating value. :param exp_calc: (np.array) Repeating series of values. - :return: (np.array) beta array. + :return: (np.array) Beta array. """ - # The equation for calculation of beta is split into two parts. + # The equation for calculation of beta is split into two parts left_calc = 1/(2 * (self.eta ** 2) * ((1 - sqrt_gamma) - (1 + sqrt_gamma) * exp_calc)) right_calc = self.gamma * sqrt_gamma * (self.eta ** 2 + 2 * self.rho * self.sigma * self.eta) * ((1 - exp_calc) ** 2) - \ @@ -192,6 +192,7 @@ def _beta_calc(self, sqrt_gamma, exp_calc) -> np.array: def _estimate_params_log_likelihood(self) -> tuple: """ Estimates parameters of model based on log likelihood maximization. + :return: (tuple) Consists of final estimated params. """ @@ -199,13 +200,13 @@ def _estimate_params_log_likelihood(self) -> tuple: # sigma, mu, k, theta, eta, rho bounds = ((1e-5, None), (None, None), (1e-5, None), (None, None), (1e-5, None), (-1 + 1e-5, 1 - 1e-5)) - # Setting initial value of theta to the mean of the spread. + # Setting initial value of theta to the mean of the spread theta_init = np.mean(self.spread) # Initial guesses for sigma, mu, k, theta, eta, rho initial_guess = np.array((1, 0, 1, theta_init, 1, 0.5)) - # Using scipy minimize to calculate the max log likelihood. + # Using scipy minimize to calculate the max log likelihood result = so.minimize(self._compute_log_likelihood, initial_guess, args=(self.spread, self.S, self.delta_t), bounds=bounds, options={'maxiter': 100000}) @@ -219,42 +220,42 @@ def _estimate_params_log_likelihood(self) -> tuple: @staticmethod - def _compute_log_likelihood(params, *args) -> float: + def _compute_log_likelihood(params: tuple, *args) -> float: """ Helper function computes log likelihood function for a set of params. This implementation follows Appendix of Mudchanatongsuk (2008). - param params: (tuple) Contains values of set params. + :param params: (tuple) Contains values of set params. :return: (float) negation of log likelihood. """ # Setting given parameters - sigma, mu, k ,theta, eta, rho = params - X,S, dt = args + sigma, mu, k, theta, eta, rho = params + X, S, dt = args - # Setting y as given in Appendix. + # Setting y as given in Appendix y = np.array([X, S]) - # Calculating matrix as given in equation (41) in the paper. - matrix = np.zeros((2,2)) + # Calculating matrix as given in equation (41) in the paper + matrix = np.zeros((2, 2)) matrix[0, 0] = (eta ** 2) * (1 - np.exp(-2 * k * dt)) / (2 * k) matrix[0, 1] = rho * eta * sigma * (1 - np.exp(k * dt)) / k - matrix[1, 0] = matrix[0 ,1] + matrix[1, 0] = matrix[0, 1] matrix[1, 1] = sigma ** 2 * dt X = X[:-1] S = S[:-1] y = y[:, 1:] - # Calculation follows equation (40) in the paper. + # Calculation follows equation (40) in the paper E_y = np.zeros((2, len(X))) E_y[0, :] = X * np.exp(-k * dt) + theta * (1 - np.exp(-k * dt)) E_y[1, :] = S + (mu - 0.5 * sigma ** 2) * dt vec = y - E_y - # Calculating the joint density function given in equation (39) in the paper. - with np.errstate(all='raise'): # This was done due to np.nan's outputted in final result of scipy minimize. + # Calculating the joint density function given in equation (39) in the paper + with np.errstate(all='raise'): # This was done due to np.nan's outputted in final result of scipy minimize try: f_y_denm = (2 * math.pi * np.sqrt(np.linalg.det(matrix))) @@ -262,10 +263,10 @@ def _compute_log_likelihood(params, *args) -> float: except FloatingPointError: return 0 - # Calculating the final log likelihood given in equation (38) in the paper. + # Calculating the final log likelihood given in equation (38) in the paper log_likelihood = np.log(f_y).sum() - # Returning the negation as we are using scipy minimize. + # Returning the negation as we are using scipy minimize return -log_likelihood @@ -273,27 +274,30 @@ def _compute_log_likelihood(params, *args) -> float: def _calc_half_life(k: float) -> float: """ Function returns half life of mean reverting spread from rate of mean reversion. + + :param k: (float) K value. :return: (float) Half life. """ - return np.log(2) / k # Half life of shocks. + return np.log(2) / k # Half life of shocks. def describe(self) -> pd.Series: """ Method returns values of instance attributes calculated from training data. + :return: (pd.Series) series describing parameter values. """ if self.sigma is None: raise Exception("Please run the fit method before calling describe.") - # List defines the indexes of the final pandas object. + # List defines the indexes of the final pandas object index = ['Ticker of first stock', 'Ticker of second stock', 'long-term mean of spread', 'rate of mean reversion of spread', 'standard deviation of spread', 'half-life of spread', 'Drift of stock B', 'standard deviation of stock B'] - # List defines the values of the final pandas object. + # List defines the values of the final pandas object data = [self.ticker_A, self.ticker_B, self.theta, self.k, self.eta, self._calc_half_life(self.k), self.mu, self.sigma] diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index 0ada39cd..83e04428 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -5,39 +5,40 @@ """ Test functions for the Jurek OU model in the Stochastic Control Approach module. """ +# pylint: disable=protected-access + import warnings import unittest import os from unittest import mock + import numpy as np import pandas as pd from arbitragelab.stochastic_control_approach.ou_model_jurek import OUModelJurek -# pylint: disable=protected-access - class TestOUModelJurek(unittest.TestCase): """ - Test Jurek OU model in Stochastic Control Approach module. + Test Jurek OU model in Stochastic Control Approach module """ @classmethod - def setUpClass(cls) -> None: + def setUpClass(cls): """ - Set up data and parameters. + Set up data and parameters """ np.random.seed(0) project_path = os.path.dirname(__file__) - # Setting up the first dataset. + # Setting up the first dataset path = project_path + '/test_data/gld_gdx_data.csv' data = pd.read_csv(path) data = data.set_index('Date') cls.dataframe = data[['GLD', 'GDX']] - # Setting up the second dataset. + # Setting up the second dataset path = project_path + '/test_data/shell-rdp-close_USD.csv' data = pd.read_csv(path, index_col='Date').ffill() data.index = pd.to_datetime(data.index, format="%d/%m/%Y") @@ -49,27 +50,26 @@ def test_fit(self): Tests the fit method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_jurek = OUModelJurek() - # Testing for the adf test statistic warning. - with warnings.catch_warnings(): - warnings.simplefilter("ignore", UserWarning) + # Testing for the adf test statistic warning + with self.assertWarns(UserWarning): sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=True, significance_level=0.95) - # Checking parameter values for spread calculation. + # Checking parameter values for spread calculation self.assertAlmostEqual(np.mean(sc_jurek.spread), 0.5328233514, delta=1e-7) self.assertAlmostEqual(sc_jurek.spread[7], 0.5532053519, delta=1e-7) self.assertAlmostEqual(sc_jurek.spread[28], 0.5423901587, delta=1e-7) self.assertAlmostEqual(sc_jurek.spread[-1], 0.5054215932, delta=1e-7) - # Checking other parameter values. + # Checking other parameter values self.assertAlmostEqual(sc_jurek.mu, 0.532823, delta=1e-4) self.assertAlmostEqual(sc_jurek.k, 10.2728, delta=1e-4) self.assertAlmostEqual(sc_jurek.sigma, 0.0743999, delta=1e-4) - # Testing for the adf_test=False flag. - sc_jurek.fit(self.shell_rdp_data, delta_t=1 / 252, adf_test=False) + # Testing for the adf_test=False flag + sc_jurek.fit(self.shell_rdp_data, delta_t=1/252, adf_test=False) def test_describe(self): @@ -77,15 +77,14 @@ def test_describe(self): Tests the describe method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_jurek = OUModelJurek() - # Testing for the run fit before this method exception. + # Testing for the run fit before this method exception with self.assertRaises(Exception): sc_jurek.describe() - with warnings.catch_warnings(): - warnings.simplefilter("ignore", UserWarning) + with self.assertWarns(UserWarning): sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) index = ['Ticker of first stock', 'Ticker of second stock', 'Scaled Spread weights', @@ -93,7 +92,7 @@ def test_describe(self): data = ['GLD', 'GDX', [0.779, -0.221], 0.532823, 10.2728, 0.0743999, 0.067474] - # Testing the output of describe method. + # Testing the output of describe method pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_jurek.describe(), check_exact=False, atol=1e-4) @@ -102,56 +101,55 @@ def test_optimal_weights(self): Tests the optimal portfolio weights method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_jurek = OUModelJurek() - # Testing for the run fit before this method exception. + # Testing for the run fit before this method exception with self.assertRaises(Exception): sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) - with warnings.catch_warnings(): - warnings.simplefilter("ignore", UserWarning) + with self.assertWarns(UserWarning): sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) - # Testing for the invalid utility_type exception. + # Testing for the invalid utility_type exception with self.assertRaises(Exception): - sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=10) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=10) - # Testing for the invalid gamma exception. + # Testing for the invalid gamma exception with self.assertRaises(Exception): - sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = -1) + sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=-1) - weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) - # Checking the values of weights for gamma = 0.5 and utility_type=1. + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + # Checking the values of weights for gamma = 0.5 and utility_type=1 self.assertAlmostEqual(np.mean(weights), -2.7252320178, delta=1e-7) self.assertAlmostEqual(weights[7], -58.5665057992, delta=1e-7) self.assertAlmostEqual(weights[28], -30.3169549896, delta=1e-7) self.assertAlmostEqual(weights[-1], 92.5766316230, delta=1e-7) - weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 1, utility_type=1) - # Checking the values of weights for gamma = 1 and utility_type=1. + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=1, utility_type=1) + # Checking the values of weights for gamma = 1 and utility_type=1 self.assertAlmostEqual(np.mean(weights), -4.8129160068, delta=1e-7) self.assertAlmostEqual(weights[7], -42.82308043, delta=1e-7) self.assertAlmostEqual(weights[28], -22.6539479, delta=1e-7) self.assertAlmostEqual(weights[-1], 46.28831581, delta=1e-7) - weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=2) - # Checking the values of weights for gamma = 0.5 and utility_type=2. + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=2) + # Checking the values of weights for gamma = 0.5 and utility_type=2 self.assertAlmostEqual(np.mean(weights), -2947786.5697284327, delta=1e-7) self.assertAlmostEqual(weights[7], -9803080.87074925, delta=1e-7) self.assertAlmostEqual(weights[28], -1762115.70956469, delta=1e-7) self.assertAlmostEqual(weights[-1], -54007.10111104, delta=1e-7) - weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=1) - # Checking the values of weights for gamma = 2 and utility_type=1. + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=2, utility_type=1) + # Checking the values of weights for gamma = 2 and utility_type=1 self.assertAlmostEqual(np.mean(weights), -5.3267767287, delta=1e-7) self.assertAlmostEqual(weights[7], -31.15603589, delta=1e-7) self.assertAlmostEqual(weights[28], -16.4211391034, delta=1e-7) self.assertAlmostEqual(weights[-1], 23.14415791, delta=1e-7) - weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta = 0.01, gamma = 2, utility_type=2) - # Checking the values of weights for gamma = 2 and utility_type=2. + weights = sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=2, utility_type=2) + # Checking the values of weights for gamma = 2 and utility_type=2 self.assertAlmostEqual(np.mean(weights), 28.7539986245, delta=1e-7) self.assertAlmostEqual(weights[7], 34.13526822, delta=1e-7) self.assertAlmostEqual(weights[28], 28.56326627, delta=1e-7) @@ -163,60 +161,58 @@ def test_stabilization_region(self): Tests the stabilization region method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_jurek = OUModelJurek() - # Testing for the run fit before this method exception. + # Testing for the run fit before this method exception with self.assertRaises(Exception): sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) - with warnings.catch_warnings(): - warnings.simplefilter("ignore", UserWarning) + with self.assertWarns(UserWarning): sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) - # Testing for the invalid utility_type exception. + # Testing for the invalid utility_type exception with self.assertRaises(Exception): sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=0.5, utility_type=10) - # Testing for the invalid gamma exception. + # Testing for the invalid gamma exception with self.assertRaises(Exception): - sc_jurek.stabilization_region(self.dataframe, beta = 0.01, gamma = -1) + sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=-1) - # Testing for gamma = 1 warning. - with warnings.catch_warnings(): - warnings.simplefilter("ignore", UserWarning) + # Testing for gamma = 1 warning + with self.assertWarns(UserWarning): sc_jurek.stabilization_region(self.dataframe, gamma=1, utility_type=1) - spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta = 0.01, gamma = 0.5, utility_type=1) - # Checking the mean value of spread, min_bound and max_bound. + spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) + # Checking the mean value of spread, min_bound and max_bound self.assertAlmostEqual(np.mean(spread), 0.5328233514, delta=1e-7) self.assertAlmostEqual(np.mean(min_bound), 0.511643929, delta=1e-7) self.assertAlmostEqual(np.mean(max_bound), 0.549827869, delta=1e-7) - # Checking the min value of spread, min_bound and max_bound. + # Checking the min value of spread, min_bound and max_bound self.assertAlmostEqual(np.min(spread), 0.494787089, delta=1e-7) self.assertAlmostEqual(np.min(min_bound), 0.511372451, delta=1e-7) self.assertAlmostEqual(np.min(max_bound), 0.546616686, delta=1e-7) - # Checking the max value of spread, min_bound and max_bound. + # Checking the max value of spread, min_bound and max_bound self.assertAlmostEqual(np.max(spread), 0.558869423, delta=1e-7) self.assertAlmostEqual(np.max(min_bound), 0.513868404, delta=1e-7) self.assertAlmostEqual(np.max(max_bound), 0.550466393, delta=1e-7) spread, min_bound, max_bound = sc_jurek.stabilization_region(self.dataframe, beta=0.01, gamma=2, utility_type=2) - # Checking the mean value of spread, min_bound and max_bound. + # Checking the mean value of spread, min_bound and max_bound self.assertAlmostEqual(np.mean(spread), 0.5328233514, delta=1e-7) self.assertAlmostEqual(np.mean(min_bound), 0.5276749084, delta=1e-7) self.assertAlmostEqual(np.mean(max_bound), 0.5850429718, delta=1e-7) - # Checking the min value of spread, min_bound and max_bound. + # Checking the min value of spread, min_bound and max_bound self.assertAlmostEqual(np.min(spread), 0.494787089, delta=1e-7) self.assertAlmostEqual(np.min(min_bound), 0.4974942641, delta=1e-7) self.assertAlmostEqual(np.min(max_bound), 0.5625208403, delta=1e-7) - # Checking the max value of spread, min_bound and max_bound. + # Checking the max value of spread, min_bound and max_bound self.assertAlmostEqual(np.max(spread), 0.558869423, delta=1e-7) self.assertAlmostEqual(np.max(min_bound), 0.5556367547, delta=1e-7) self.assertAlmostEqual(np.max(max_bound), 0.6107958587, delta=1e-7) @@ -227,14 +223,13 @@ def test_optimal_weights_fund_flows(self): Tests the optimal weights with fund flows method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_jurek = OUModelJurek() - with warnings.catch_warnings(): - warnings.simplefilter("ignore", UserWarning) + with self.assertWarns(UserWarning): sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) - weights = sc_jurek.optimal_portfolio_weights_fund_flows(self.dataframe, f=0.2, gamma = 0.5) + weights = sc_jurek.optimal_portfolio_weights_fund_flows(self.dataframe, f=0.2, gamma=0.5) self.assertAlmostEqual(np.mean(weights), -2.2710266815, delta=1e-7) self.assertAlmostEqual(weights[7], -48.8054214993, delta=1e-7) @@ -247,14 +242,13 @@ def test_private_methods(self): Function tests special cases for code coverage. """ - # Creating an object of the class. + # Creating an object of the class sc_jurek = OUModelJurek() - with warnings.catch_warnings(): - warnings.simplefilter("ignore", UserWarning) + with self.assertWarns(UserWarning): sc_jurek.fit(self.dataframe, delta_t=1/252, adf_test=False) - # Representative values of parameters. + # Representative values of parameters time_array = np.arange(0, len(self.dataframe)) * (1/252) tau = time_array[-1] - time_array c_1 = 0.0221413 @@ -262,10 +256,10 @@ def test_private_methods(self): c_3 = 9625.4458424 disc = -844.234913 - # For utility_type=1. + # For utility_type=1 sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=1) - # Running below cases with gamma values for code coverage. + # Running below cases with gamma values for code coverage with warnings.catch_warnings(): warnings.simplefilter("ignore") sc_jurek._A_calc_1(tau, c_1, c_2, disc, 0.5) @@ -273,10 +267,10 @@ def test_private_methods(self): sc_jurek._B_calc_1(tau, c_1, c_2, c_3, disc, 0.5) sc_jurek._B_calc_1(tau, c_1, c_2, c_3, disc, 0.9) - # For utility_type = 2. + # For utility_type = 2 sc_jurek.optimal_portfolio_weights(self.dataframe, beta=0.01, gamma=0.5, utility_type=2) - # Running below cases with gamma values for code coverage. + # Running below cases with gamma values for code coverage with warnings.catch_warnings(): warnings.simplefilter("ignore") sc_jurek._B_calc_2(tau, c_1, c_2, c_3, disc, 0.5) @@ -289,20 +283,20 @@ def test_plotting(self, mock_plt): Tests the plot_results method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_jurek = OUModelJurek() - # Tests not datetime index exception. + # Tests not datetime index exception with self.assertRaises(Exception): sc_jurek.plot_results(self.dataframe) self.dataframe.index = pd.to_datetime(self.dataframe.index) - # Tests length of dataframe exception. + # Tests length of dataframe exception with self.assertRaises(Exception): sc_jurek.plot_results(self.dataframe) - # Using a different dataset with atleast 10 years of data. + # Using a different dataset with at least 10 years of data sc_jurek.plot_results(self.shell_rdp_data) # Assert plt.figure got called diff --git a/tests/test_ou_model_mudchanatongsuk.py b/tests/test_ou_model_mudchanatongsuk.py index 46c3ad32..3a8e36d3 100644 --- a/tests/test_ou_model_mudchanatongsuk.py +++ b/tests/test_ou_model_mudchanatongsuk.py @@ -40,12 +40,12 @@ def test_fit(self): Tests the fit method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_mudchana = OUModelMudchanatongsuk() sc_mudchana.fit(self.dataframe) - # Checking parameter values for spread calculation. + # Checking parameter values for spread calculation self.assertAlmostEqual(np.mean(sc_mudchana.spread), 2.0465361303, delta=1e-7) self.assertAlmostEqual(sc_mudchana.spread[7], 2.1073878043, delta=1e-7) self.assertAlmostEqual(sc_mudchana.spread[28], 2.0496029865, delta=1e-7) @@ -65,10 +65,10 @@ def test_describe(self): Tests the describe method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_mudchana = OUModelMudchanatongsuk() - # Testing for the run fit before this method exception. + # Testing for the run fit before this method exception with self.assertRaises(Exception): sc_mudchana.describe() @@ -80,7 +80,7 @@ def test_describe(self): data = ['GLD', 'GDX', 1.98816, 3.99205, 0.404292, 0.173632, 0.114877, 0.503695] - # Testing the output of describe method. + # Testing the output of describe method pd.testing.assert_series_equal(pd.Series(index=index,data=data), sc_mudchana.describe(), check_exact=False, atol=1e-3) @@ -89,21 +89,21 @@ def test_optimal_weights(self): Tests the optimal portfolio weights method in the class. """ - # Creating an object of the class. + # Creating an object of the class sc_mudchana = OUModelMudchanatongsuk() - # Testing for the run fit before this method exception. + # Testing for the run fit before this method exception with self.assertRaises(Exception): - sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = -10) + sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma=-10) sc_mudchana.fit(self.dataframe) - # Testing for invalid value of gamma exception. + # Testing for invalid value of gamma exception with self.assertRaises(Exception): - sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = 10) + sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma=10) - weights = sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma = -10) - # Checking the values of weights. + weights = sc_mudchana.optimal_portfolio_weights(self.dataframe, gamma=-10) + # Checking the values of weights self.assertAlmostEqual(np.mean(weights), 0.4986890920, delta=1e-5) self.assertAlmostEqual(weights[7], 0.5117099817, delta=1e-4) self.assertAlmostEqual(weights[28], 0.5246204647, delta=1e-4) From a366e86cc426154ec68f4db8c05423b530c35615 Mon Sep 17 00:00:00 2001 From: PanPip Date: Thu, 8 Apr 2021 13:48:25 +0200 Subject: [PATCH 088/103] Docs changes for the OU Stochastic Control Module --- .../introduction.rst | 18 +++++++++--------- .../ou_model_jurek.rst | 16 +++++++++------- .../ou_model_mudchanatongsuk.rst | 15 +++++++-------- 3 files changed, 25 insertions(+), 24 deletions(-) diff --git a/docs/source/stochastic_control_approach/introduction.rst b/docs/source/stochastic_control_approach/introduction.rst index 946aaf0f..99f5e4ac 100644 --- a/docs/source/stochastic_control_approach/introduction.rst +++ b/docs/source/stochastic_control_approach/introduction.rst @@ -1,14 +1,14 @@ -.. _stochastic_control_approach_strategies-introduction: +.. _stochastic_control_approach-introduction: .. note:: - The following documentation appears in Section 5 of the following work: + The following documentation appears in Section 5 of the following work: - `Krauss (2015), Statistical arbitrage pairs trading strategies:Review and outlook `__ + `Krauss (2015), Statistical arbitrage pairs trading strategies: Review and outlook `__ -====================================================== -Introduction to Stochastic Control Approach Strategies -====================================================== +============ +Introduction +============ Modeling asset pricing dynamics with the Ornstein-Uhlenbeck process ################################################################### @@ -18,8 +18,8 @@ OU Model Jurek `Jurek and Yang (2007) `__ provide the paper with the highest impact in this domain. In their setup, they allow non-myopic arbitrageurs to allocate their capital -to a mean-reverting spread or to a risk free asset. The former evolves according to an Ornstein-Uhlenbeck process -and the latter is compounded continuously with the riskfree rate. Two scenarios for investor preferences are considered +to a mean-reverting spread or to a risk-free asset. The former evolves according to an Ornstein-Uhlenbeck process, +and the latter is compounded continuously with the risk-free rate. Two scenarios for investor preferences are considered over a finite time horizon: constant relative risk aversion and the recursive Epstein-Zinutility function. Utilizing the asset price dynamics, Jurek and Yang develop the budget constraints and the wealth dynamics of the arbitrageurs’ assets. @@ -32,7 +32,7 @@ the most comprehensive discussion of the stochastic control approach applied to OU Model Mudchanatongsuk ************************ -`Mudchanatongsuk et al.(2008) `__ also solves +`Mudchanatongsuk et al.(2008) `__ also solve the stochastic control problem for pairs trading under power utility for terminal wealth. Their ansatz mostly differs in the assumed asset pricing dynamics, but the spread also relies on an OU-process. diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 3254608f..048d8e70 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -1,7 +1,7 @@ -.. _stochastic_control_approach_strategies-ou_model_jurek: +.. _stochastic_control_approach-ou_model_jurek: .. note:: - The following implementations and documentation closely following work: + The following implementations and documentation closely following work: `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. `__ @@ -385,6 +385,8 @@ We use GLD and GDX tickers from Yahoo Finance as the dataset for this example. .. code-block:: + import yfinance as yf + data1 = yf.download("GLD GDX", start="2009-03-25", end="2019-03-25") data2 = yf.download("GLD GDX", start="2019-03-27", end="2020-03-27") @@ -392,7 +394,7 @@ We use GLD and GDX tickers from Yahoo Finance as the dataset for this example. data_test_dataframe = data2["Adj Close"][["GLD", "GDX"]] .. Note:: - To get good results for the estimated parameters, using atleast 10 years of training data is recommended. + To get good results for the estimated parameters, using t 10 years of training data is recommended. Example 1 ********* @@ -412,11 +414,11 @@ Finally, we use the out-of-sample test data to calculate the optimal portfolio w print(sc.describe()) - plt.plot(sc.optimal_portfolio_weights(data_test_dataframe, beta = 0.01, gamma = 0.5, utility_type=1)) + plt.plot(sc.optimal_portfolio_weights(data_test_dataframe, beta=0.01, gamma=0.5, utility_type=1)) plt.show() -.. Note:: +.. warning:: For utility_type = 2 and low values of :math:`\gamma (< 1)`, the model becomes unstable with respect to the value of :math:`k`. Example 2 @@ -437,7 +439,7 @@ Finally, on the out-of-sample test data we calculate the stabilization region fo print(sc.describe()) - S, min_bound, max_bound = sc.stabilization_region(data_test_dataframe, beta = 0.01, gamma = 0.5, utility_type=1) + S, min_bound, max_bound = sc.stabilization_region(data_test_dataframe, beta=0.01, gamma=0.5, utility_type=1) plt.plot(S, label='Spread') plt.plot(min_bound, color='red', linestyle='dashed') @@ -466,7 +468,7 @@ using the fitted model. print(sc.describe()) - plt.plot(sc.optimal_portfolio_weights_fund_flows(data_test_dataframe, f=0.05, gamma = 0.5)) + plt.plot(sc.optimal_portfolio_weights_fund_flows(data_test_dataframe, f=0.05, gamma=0.5)) plt.show() diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index 8b4aad64..d2697c7d 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -1,13 +1,12 @@ -.. _stochastic_control_approach_strategies-ou_model_mudchanatongsuk: +.. _stochastic_control_approach-ou_model_mudchanatongsuk: .. note:: - The following implementations and documentation closely following work: + The following implementations and documentation closely following work: `Mudchanatongsuk, S., Primbs, J.A. and Wong, W., 2008, June. Optimal pairs trading: A stochastic control approach. `__ - ======================== OU Model Mudchanatongsuk ======================== @@ -15,12 +14,12 @@ OU Model Mudchanatongsuk Introduction ############ -In the paper corresponding to this module, the authors implement a stochastic control based approach to the problem of pairs trading. +In the paper corresponding to this module, the authors implement a stochastic control-based approach to the problem of pairs trading. The paper models the log-relationship between a pair of stock prices as an Ornstein-Uhlenbeck process and use this to formulate a portfolio optimization based stochastic control problem. This problem is constructed in such a way that one may either trade based on the spread (by buying and selling equal amounts of the stocks in the pair) or -place money in a risk free asset. Then the optimal solution to this control problem +place money in a risk-free asset. Then the optimal solution to this control problem is obtained in closed form via the corresponding Hamilton-Jacobi-Bellman equation under a power utility on terminal wealth. Modelling @@ -145,7 +144,7 @@ Step 2: Getting the Optimal Portfolio Weights In this step we input the evaluation data and specify the utility function parameter :math:`\gamma`. -.. note:: +.. warning:: As noted in the paper, please make sure the value of gamma is less than 1. @@ -162,6 +161,8 @@ We use GLD and GDX tickers from Yahoo Finance as the dataset for this example. .. code-block:: + import yfinance as yf + data1 = yf.download("GLD GDX", start="2012-03-25", end="2016-01-09") data2 = yf.download("GLD GDX", start="2016-02-21", end="2020-08-15") @@ -198,9 +199,7 @@ The following research notebook can be used to better understand the approach de .. _`Optimal Pairs Trading A Stochastic Control Approach`: - References ########## * `Mudchanatongsuk, S., Primbs, J.A. and Wong, W., 2008, June. Optimal pairs trading: A stochastic control approach. `__ - From ab77ddecfcbaed9ff7c41e336e1e135212b3d0cf Mon Sep 17 00:00:00 2001 From: PanPip Date: Thu, 8 Apr 2021 13:49:31 +0200 Subject: [PATCH 089/103] Added OU Stochastic Control Module to the changelog --- docs/source/changelog.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/source/changelog.rst b/docs/source/changelog.rst index 9697afec..23d92668 100644 --- a/docs/source/changelog.rst +++ b/docs/source/changelog.rst @@ -12,6 +12,8 @@ Changelog .. For Help: https://releases.readthedocs.io/en/latest/index.html +* :feature:`43` OU Model Jurek and OU Model Mudchanatongsuk added to the Stochastic Control Approach Module. +* :support:`43` OU Model Jurek and OU Model Mudchanatongsuk documentation. * :feature:`42` Options to sort pairs by zero-crossings, variance, same industry group added to the Basic Distance Strategy. * :support:`42` Updated Basic Distance Strategy documentation. * :feature:`40` Vine Copula Partner Selection Approaches added to the Copula Approach Module. From 6aaf4379e55906923a29c9777494f8fcc4f7316c Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Thu, 8 Apr 2021 21:32:46 +0530 Subject: [PATCH 090/103] Minor fix to sphinx docs. --- docs/source/stochastic_control_approach/ou_model_jurek.rst | 2 +- .../stochastic_control_approach/ou_model_mudchanatongsuk.rst | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 048d8e70..85863dba 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -1,7 +1,7 @@ .. _stochastic_control_approach-ou_model_jurek: .. note:: - The following implementations and documentation closely following work: + The following implementations and documentation closely follow the below work: `Jurek, J.W. and Yang, H., 2007, April. Dynamic portfolio selection in arbitrage. `__ diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index d2697c7d..bf0eec26 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -1,7 +1,7 @@ .. _stochastic_control_approach-ou_model_mudchanatongsuk: .. note:: - The following implementations and documentation closely following work: + The following implementations and documentation closely follow the below work: `Mudchanatongsuk, S., Primbs, J.A. and Wong, W., 2008, June. Optimal pairs trading: A stochastic control approach. `__ From 05cebc448788db49d0052d8e0a90677ab62ce29b Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 12 Apr 2021 15:07:11 +0530 Subject: [PATCH 091/103] Minor change to default param values in Jurek class. --- arbitragelab/stochastic_control_approach/ou_model_jurek.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index d6fadeac..5d7f8a6c 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -178,7 +178,7 @@ def _spread_calc(self, prices: pd.DataFrame) -> tuple: def optimal_portfolio_weights(self, prices: pd.DataFrame, utility_type: int = 1, gamma: float = 1, - beta: float = 0.1, r: float = 0.05) -> np.array: + beta: float = 0.01, r: float = 0.05) -> np.array: """ Implementation of Theorem 1 and Theorem 2 in Jurek (2007). @@ -288,7 +288,7 @@ def optimal_portfolio_weights_fund_flows(self, prices: pd.DataFrame, f: float, g return (1 / (1 + f)) * N - def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamma: float = 1, beta: float = 0.1, r: float = 0.05) -> tuple: + def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamma: float = 1, beta: float = 0.01, r: float = 0.05) -> tuple: """ Implementation of Theorem 3 in Jurek (2007). @@ -800,7 +800,7 @@ def describe(self) -> pd.Series: def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: float = 1 / 252, utility_type: int = 1, - gamma: float = 10, beta: float = 0.1, r: float = 0.05, f: float = 0.1): + gamma: float = 10, beta: float = 0.01, r: float = 0.05, f: float = 0.1): """ Method plots out of sample performance of the model on specified number of test windows. We use a backward looking rolling window as training data and its size depends on the number of test windows chosen. From ac3be7ef1b4ab2500d46f66fa354db4c06d1e29f Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 12 Apr 2021 15:48:17 +0530 Subject: [PATCH 092/103] Added new params to plot_results method. --- .../stochastic_control_approach/ou_model_jurek.py | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 5d7f8a6c..84b74da3 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -800,7 +800,7 @@ def describe(self) -> pd.Series: def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: float = 1 / 252, utility_type: int = 1, - gamma: float = 10, beta: float = 0.01, r: float = 0.05, f: float = 0.1): + gamma: float = 10, beta: float = 0.01, r: float = 0.05, f: float = 0.1, figsize: tuple = (8, 4), fontsize: int = 8): """ Method plots out of sample performance of the model on specified number of test windows. We use a backward looking rolling window as training data and its size depends on the number of test windows chosen. @@ -817,10 +817,12 @@ def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: :param beta: (float) Subjective rate of time preference. (Only required for utility_type = 2). :param r: (float) Rate of Returns. :param f: (float) Coefficient of proportionality (assumed to be positive). + :param figsize: (tuple) Input to matplotlib figsize parameter for plotting. + :param fontsize: (int) general matplotlib font size for plotting. """ # Setting font size of plots - plt.rcParams.update({'font.size': 8}) + plt.rcParams.update({'font.size': fontsize}) # Price series preprocessing prices = prices.ffill() @@ -869,21 +871,21 @@ def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: ind += len(S) # Plotting the stabilization bound plot - ax = stab_result_dataframe.plot(style=['c-', 'r:', 'r:'], legend=False, linewidth=1.0, figsize=(8, 4)) + ax = stab_result_dataframe.plot(style=['c-', 'r:', 'r:'], legend=False, linewidth=1.0, figsize=figsize) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Spread') ax.set_title("Evolution of spread with stabilization bound") plt.show() # Plotting the optimal weights allocation plot - ax = optimal_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=(8, 4)) + ax = optimal_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=figsize) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Optimal Weights') ax.set_title('Optimal allocation to the spread asset scaled by wealth') plt.show() # Plotting the optimal weights allocation plot in the case with fund flows - ax = optimal_fund_flows_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=(8, 4)) + ax = optimal_fund_flows_result_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=figsize) ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) ax.set_ylabel('Optimal Weights with fund flows') ax.set_title('Optimal allocation to the spread asset with fund flows scaled by wealth') From 7bedc6e0550cf828aaffb54ed6b30e7ee2509fe1 Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 12 Apr 2021 20:29:03 +0530 Subject: [PATCH 093/103] Minor addition to docs. --- .../source/stochastic_control_approach/ou_model_jurek.rst | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 85863dba..608d69e6 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -327,6 +327,10 @@ Implementation .. automethod:: OUModelJurek.optimal_portfolio_weights +.. note:: + The output of the `optimal_portfolio_weights` method is the portfolio weights of the spread scaled w.r.t initial wealth. + + Step 3: Stabilization Region **************************** @@ -358,6 +362,10 @@ Implementation .. automethod:: OUModelJurek.optimal_portfolio_weights_fund_flows +.. note:: + The output of the `optimal_portfolio_weights_fund_flows` is the portfolio weights of the spread scaled w.r.t initial wealth. + + .. figure:: images/optimal_weights_fund_flows.png :scale: 100 % :align: center From 1b474fc3e58a6331044e86b84404f7ee54ff122b Mon Sep 17 00:00:00 2001 From: "Vijay Nadimpalli (Pycharm-Linux)" Date: Mon, 12 Apr 2021 23:28:04 +0530 Subject: [PATCH 094/103] Added wealth process plots to Jurek class, and made spread_calc public. Made minor changes to docs. --- .../ou_model_jurek.py | 40 +++++++++++++++++-- .../ou_model_mudchanatongsuk.py | 28 +++++++++---- .../ou_model_jurek.rst | 13 ++++-- .../ou_model_mudchanatongsuk.rst | 8 +++- tests/test_ou_model_jurek.py | 1 + 5 files changed, 75 insertions(+), 15 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 84b74da3..41a2ebc1 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -156,7 +156,7 @@ def _estimate_params(self, spread: np.array) -> tuple: return mu, k, sigma - def _spread_calc(self, prices: pd.DataFrame) -> tuple: + def spread_calc(self, prices: pd.DataFrame) -> tuple: """ This method calculates the spread on test data using the scaled weights from training data. @@ -228,7 +228,7 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, utility_type: int = 1, self.gamma = gamma self.beta = beta - tau, S = self._spread_calc(prices) + tau, S = self.spread_calc(prices) W = np.ones(len(tau)) # Wealth is normalized to one @@ -315,7 +315,7 @@ def stabilization_region(self, prices: pd.DataFrame, utility_type: int = 1, gamm self.beta = beta # Calculating the time left array and the spread - tau, S = self._spread_calc(prices) + tau, S = self.spread_calc(prices) if self.gamma == 1: # Calculation of A and B functions are not done in case of gamma = 1 (Refer Appendix A.1 and B.2) @@ -799,6 +799,7 @@ def describe(self) -> pd.Series: return output +# pylint: disable=too-many-arguments, too-many-statements def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: float = 1 / 252, utility_type: int = 1, gamma: float = 10, beta: float = 0.01, r: float = 0.05, f: float = 0.1, figsize: tuple = (8, 4), fontsize: int = 8): """ @@ -809,6 +810,9 @@ def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: For example, if the total data is of length 16 years, with the number of test windows set to 5, the length of training data would be 16 - (5 + 1) = 10. (The last year is not considered for testing). + This method plots the stabilization region, optimal portfolio weights with and without fund flows, and the + evolution of the wealth process with initial wealth normalized to 1. + :param prices: (pd.DataFrame) Contains price series of both stocks in spread with dates as index. :param num_test_windows: (int) Number of out of sample testing windows to plot. :param delta_t: (float) Time difference between each index of prices, calculated in years. @@ -846,8 +850,12 @@ def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: # Initializing a dataframe which stores optimal weights in the case with fund flows optimal_fund_flows_result_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]): str(years[-1])].index, columns=['Weights']) + # Initializing a dataframe which stores wealth + wealth_dataframe = pd.DataFrame(index=prices.loc[str(years[-(num_test_windows + 1)]):str(years[-1])].index, + columns=['Wealth']) ind = 0 + W_initial = 1 # Initial wealth normalized to 1 # Iterating over the test windows for year in np.arange(years[-(num_test_windows + 1)], years[-1], 1): @@ -864,10 +872,29 @@ def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: S, min_bound, max_bound = self.stabilization_region(data_test_dataframe, gamma=gamma, utility_type=utility_type, beta=beta, r=r) + W = np.zeros(len(data_test_dataframe)) + W[0] = W_initial + + if utility_type == 1: + for i in range(len(data_test_dataframe) - 1): + # Calculating the wealth process for CRRA investor. Follows equation (3) in Appendix A + W[i + 1] = W[i] + W[i] * optimal_weights[i] * (S[i + 1] - S[i]) + r * W[i] * ( + 1 - optimal_weights[i] * S[i]) * delta_t + else: + for i in range(len(data_test_dataframe) - 1): + # Calculating the wealth process for investor with intermediate consumption + # Follows equation (39) in Appendix A + # Here we add an extra term which denotes consumption + W[i + 1] = W[i] + W[i] * optimal_weights[i] * (S[i + 1] - S[i]) + r * W[i] * ( + 1 - optimal_weights[i] * S[i]) * delta_t - beta * W[i] * delta_t + + W_initial = W[-1] + # Adding the final results to their corresponding dataframes for each test window stab_result_dataframe.iloc[ind:ind + len(S), :] = np.array([S, min_bound, max_bound]).T optimal_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_weights]).T optimal_fund_flows_result_dataframe.iloc[ind:ind + len(S), :] = np.array([optimal_fund_flow_weights]).T + wealth_dataframe.iloc[ind:ind + len(S), :] = np.array([W]).T ind += len(S) # Plotting the stabilization bound plot @@ -890,3 +917,10 @@ def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: ax.set_ylabel('Optimal Weights with fund flows') ax.set_title('Optimal allocation to the spread asset with fund flows scaled by wealth') plt.show() + + # Plotting the wealth plot + ax = wealth_dataframe.plot(style=['c-'], legend=False, linewidth=1.0, figsize=figsize) + ax.xaxis.grid(color='grey', linestyle=':', linewidth=0.6) + ax.set_ylabel('Wealth') + ax.set_title('Evolution of wealth over lifetime of simulation, with initial wealth normalized to 1') + plt.show() diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 18de355e..97d60d58 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -94,6 +94,26 @@ def fit(self, prices: pd.DataFrame): self.sigma, self.mu, self.k, self.theta, self.eta, self.rho = params[:-1] + def spread_calc(self, prices: pd.DataFrame) -> tuple: + """ + This method calculates the spread on test data. + + :param prices: (pd.DataFrame) Contains price series of both stocks in spread. + :return: (tuple) Consists of time remaining array and spread numpy array. + """ + + # Preprocessing + prices = self._data_preprocessing(prices) + t = np.arange(0, len(prices)) * self.delta_t + tau = t[-1] - t + + # Calculating spread + x = np.log(prices.iloc[:, 0]) - np.log(prices.iloc[:, 1]) + x = x.to_numpy() # Converting from pd.Series to numpy array + + return tau, x + + def optimal_portfolio_weights(self, prices: pd.DataFrame, gamma: float = -100) -> np.array: """ This method calculates the final optimal portfolio weights for the calculated spread. @@ -111,17 +131,11 @@ def optimal_portfolio_weights(self, prices: pd.DataFrame, gamma: float = -100) - if gamma >= 1: raise Exception("Please make sure value of gamma is less than 1.") - # Preprocessing - prices = self._data_preprocessing(prices) - # Setting instance attributes self.gamma = gamma - t = np.arange(0, len(prices)) * self.delta_t - tau = t[-1] - t # Calculating spread - x = np.log(prices.iloc[:, 0]) - np.log(prices.iloc[:, 1]) - x = x.to_numpy() # Converting from pd.Series to numpy array + tau, x = self.spread_calc(prices) # Calculating the alpha and beta functions alpha_t, beta_t = self._alpha_beta_calc(tau) diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 608d69e6..4133e149 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -263,7 +263,7 @@ this flow to commensurately decrease the amount of risk taken on by the underlyi How to use this submodule ######################### -This submodule contains five public methods, of which two methods are necessary to calculate the optimal weights. +This submodule contains seven public methods, of which two methods are necessary to calculate the optimal weights. The first method is for estimating the parameters of the model using training data, and the second method is for calculating the final optimal portfolio weights using evaluation data. @@ -328,9 +328,14 @@ Implementation .. automethod:: OUModelJurek.optimal_portfolio_weights .. note:: - The output of the `optimal_portfolio_weights` method is the portfolio weights of the spread scaled w.r.t initial wealth. + The output of the ``optimal_portfolio_weights`` method is the portfolio weights of the spread scaled w.r.t wealth. +.. tip:: + The ``spread_calc`` method can be used to calculate the spread on the test data. + + .. automethod:: OUModelJurek.spread_calc + Step 3: Stabilization Region **************************** @@ -363,7 +368,7 @@ Implementation .. note:: - The output of the `optimal_portfolio_weights_fund_flows` is the portfolio weights of the spread scaled w.r.t initial wealth. + The output of the ``optimal_portfolio_weights_fund_flows`` method is the portfolio weights of the spread scaled w.r.t wealth. .. figure:: images/optimal_weights_fund_flows.png @@ -378,7 +383,7 @@ Implementation Step 5: Plotting **************** -In this optional step, we can plot the stabilization regions and optimal portfolio weights. +In this optional step, we can plot the stabilization region, optimal portfolio weights and the evolution of wealth. Implementation ============== diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index bf0eec26..887114e0 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -102,7 +102,7 @@ Finally, the optimal weights are given by, How to use this submodule ######################### -This submodule contains two public methods. One for estimating the parameters of the model using training data, +This submodule contains three public methods. One for estimating the parameters of the model using training data, and the second method is for calculating the final optimal portfolio weights using evaluation data. Step 1: Model fitting @@ -154,6 +154,12 @@ Implementation .. automethod:: OUModelMudchanatongsuk.optimal_portfolio_weights +.. tip:: + The ``spread_calc`` method can be used to calculate the spread on the test data. + + .. automethod:: OUModelMudchanatongsuk.spread_calc + + Example ####### diff --git a/tests/test_ou_model_jurek.py b/tests/test_ou_model_jurek.py index 83e04428..2c610252 100644 --- a/tests/test_ou_model_jurek.py +++ b/tests/test_ou_model_jurek.py @@ -298,6 +298,7 @@ def test_plotting(self, mock_plt): # Using a different dataset with at least 10 years of data sc_jurek.plot_results(self.shell_rdp_data) + sc_jurek.plot_results(self.shell_rdp_data, utility_type=2) # Assert plt.figure got called assert mock_plt.show.called From 2e69caddcc501f360f452458982b3098dbb5abb1 Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 10:46:46 +0200 Subject: [PATCH 095/103] Minor code style adjustments to Stochastic Control Module --- arbitragelab/stochastic_control_approach/ou_model_jurek.py | 4 ++-- .../stochastic_control_approach/ou_model_mudchanatongsuk.py | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index 41a2ebc1..e2786b6c 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -799,9 +799,9 @@ def describe(self) -> pd.Series: return output -# pylint: disable=too-many-arguments, too-many-statements def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: float = 1 / 252, utility_type: int = 1, gamma: float = 10, beta: float = 0.01, r: float = 0.05, f: float = 0.1, figsize: tuple = (8, 4), fontsize: int = 8): + # pylint: disable=too-many-arguments, too-many-statements """ Method plots out of sample performance of the model on specified number of test windows. We use a backward looking rolling window as training data and its size depends on the number of test windows chosen. @@ -855,7 +855,7 @@ def plot_results(self, prices: pd.DataFrame, num_test_windows: int = 5, delta_t: columns=['Wealth']) ind = 0 - W_initial = 1 # Initial wealth normalized to 1 + W_initial = 1 # Initial wealth normalized to 1 # Iterating over the test windows for year in np.arange(years[-(num_test_windows + 1)], years[-1], 1): diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 97d60d58..61cd23c3 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -293,7 +293,7 @@ def _calc_half_life(k: float) -> float: :return: (float) Half life. """ - return np.log(2) / k # Half life of shocks. + return np.log(2) / k # Half life of shocks def describe(self) -> pd.Series: From 38280ac94846d9941c108ea044fe1a85a1212e58 Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 12:48:25 +0200 Subject: [PATCH 096/103] Fixed notebook links in Copula and Stochastic Control docs --- docs/source/copula_approach/mispricing_index_strategy.rst | 2 +- docs/source/copula_approach/partner_selection.rst | 2 +- docs/source/stochastic_control_approach/ou_model_jurek.rst | 2 +- .../stochastic_control_approach/ou_model_mudchanatongsuk.rst | 3 +-- 4 files changed, 4 insertions(+), 5 deletions(-) diff --git a/docs/source/copula_approach/mispricing_index_strategy.rst b/docs/source/copula_approach/mispricing_index_strategy.rst index 4d449c87..2c2cc0ef 100644 --- a/docs/source/copula_approach/mispricing_index_strategy.rst +++ b/docs/source/copula_approach/mispricing_index_strategy.rst @@ -315,7 +315,7 @@ The following research notebook can be used to better understand the copula stra * `Mispricing Index Copula Strategy`_ -.. _`Mispricing Index Copula Strategy`: https://github.com/hudson-and-thames/arbitrage_research/blob/copula_approach/Copula%20Approach/Copula_Strategy_Mispricing_Index.ipynb +.. _`Mispricing Index Copula Strategy`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Copula%20Approach/Copula_Strategy_Mispricing_Index.ipynb References ########## diff --git a/docs/source/copula_approach/partner_selection.rst b/docs/source/copula_approach/partner_selection.rst index 91b094fc..225cf0d1 100644 --- a/docs/source/copula_approach/partner_selection.rst +++ b/docs/source/copula_approach/partner_selection.rst @@ -342,7 +342,7 @@ The following research notebook can be used to better understand the partner sel * `Vine Copula Partner Selection Approaches`_ -.. _`Vine Copula Partner Selection Approaches`: https://github.com/hudson-and-thames/arbitrage_research/blob/partner_selection_vine_copula/Copula%20Approach/vine_copula_partner_selection.ipynb +.. _`Vine Copula Partner Selection Approaches`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Copula%20Approach/Vine_copula_partner_selection.ipynb References ########## diff --git a/docs/source/stochastic_control_approach/ou_model_jurek.rst b/docs/source/stochastic_control_approach/ou_model_jurek.rst index 4133e149..627a321c 100644 --- a/docs/source/stochastic_control_approach/ou_model_jurek.rst +++ b/docs/source/stochastic_control_approach/ou_model_jurek.rst @@ -493,7 +493,7 @@ The following research notebook can be used to better understand the approach de * `Dynamic Portfolio Selection in Arbitrage`_ -.. _`Dynamic Portfolio Selection in Arbitrage`: +.. _`Dynamic Portfolio Selection in Arbitrage`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Stochastic%20Control%20Approach/OU_Model_Jurek.ipynb References ########## diff --git a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst index 887114e0..05f4f730 100644 --- a/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst +++ b/docs/source/stochastic_control_approach/ou_model_mudchanatongsuk.rst @@ -202,8 +202,7 @@ The following research notebook can be used to better understand the approach de * `Optimal Pairs Trading A Stochastic Control Approach`_ -.. _`Optimal Pairs Trading A Stochastic Control Approach`: - +.. _`Optimal Pairs Trading A Stochastic Control Approach`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Stochastic%20Control%20Approach/OU_Model_Mudchanatongsuk.ipynb References ########## From b117236a331ef382dcf04b2ccb7ad7edcf39ca06 Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 13:31:31 +0200 Subject: [PATCH 097/103] Added tracking to other ArbitrageLab modules --- arbitragelab/codependence/codependence_matrix.py | 7 +++++++ arbitragelab/cointegration_approach/coint_sim.py | 1 + arbitragelab/cointegration_approach/multi_coint.py | 3 +++ arbitragelab/cointegration_approach/signals.py | 7 +++++++ .../cointegration_approach/sparse_mr_portfolio.py | 3 +++ .../copula_approach/copula_generate_mixedcopula.py | 6 ++++++ .../copula_approach/copula_strategy_basic.py | 4 ++++ arbitragelab/copula_approach/copula_strategy_mpi.py | 4 ++++ arbitragelab/copula_approach/pairs_selection.py | 4 ++++ .../vine_copula_partner_selection.py | 3 +++ arbitragelab/ml_approach/feature_expander.py | 4 ++++ arbitragelab/ml_approach/filters.py | 8 ++++++++ arbitragelab/ml_approach/neural_networks.py | 8 ++++++++ arbitragelab/ml_approach/regressor_committee.py | 3 +++ arbitragelab/ml_approach/tar.py | 4 ++++ arbitragelab/optimal_mean_reversion/cir_model.py | 1 + arbitragelab/optimal_mean_reversion/xou_model.py | 1 + arbitragelab/other_approaches/kalman_filter.py | 1 + arbitragelab/other_approaches/pca_approach.py | 1 + .../stochastic_control_approach/ou_model_jurek.py | 3 +++ .../ou_model_mudchanatongsuk.py | 4 ++++ arbitragelab/util/data_importer.py | 8 ++++++++ arbitragelab/util/indexed_highlight.py | 4 ++++ arbitragelab/util/rollers.py | 13 +++++++++++++ 24 files changed, 105 insertions(+) diff --git a/arbitragelab/codependence/codependence_matrix.py b/arbitragelab/codependence/codependence_matrix.py index 68ab8bb1..ec0258ed 100644 --- a/arbitragelab/codependence/codependence_matrix.py +++ b/arbitragelab/codependence/codependence_matrix.py @@ -15,6 +15,7 @@ from arbitragelab.codependence.correlation import distance_correlation from arbitragelab.codependence.gnpr_distance import spearmans_rho, gpr_distance, gnpr_distance from arbitragelab.codependence.optimal_transport import optimal_transport_dependence +from arbitragelab.util import devadarsh # pylint: disable=invalid-name @@ -49,6 +50,9 @@ def get_dependence_matrix(df: pd.DataFrame, dependence_method: str, theta: float Sets the relative area of correlation in a copula. [from 0 to 1] (0.2 by default) :return: (pd.DataFrame) Dependence matrix. """ + + devadarsh.track('get_dependence_matrix') + # Get the feature names. features_cols = df.columns.values n = df.shape[1] @@ -110,6 +114,9 @@ def get_distance_matrix(X: pd.DataFrame, distance_metric: str = 'angular') -> pd :param distance_metric: (str) The distance metric to be used for generating the distance matrix. :return: (pd.DataFrame) Distance matrix. """ + + devadarsh.track('get_distance_matrix') + if distance_metric == 'angular': distfun = lambda x: ((1 - x).round(5) / 2.) ** .5 elif distance_metric == 'abs_angular': diff --git a/arbitragelab/cointegration_approach/coint_sim.py b/arbitragelab/cointegration_approach/coint_sim.py index 805433e8..5c20602d 100644 --- a/arbitragelab/cointegration_approach/coint_sim.py +++ b/arbitragelab/cointegration_approach/coint_sim.py @@ -41,6 +41,7 @@ def __init__(self, ts_num: int, ts_length: int): self.ts_num = ts_num self.ts_length = ts_length self.__price_params, self.__coint_params = self.initialize_params() + devadarsh.track('CointegrationSimulation') @staticmethod diff --git a/arbitragelab/cointegration_approach/multi_coint.py b/arbitragelab/cointegration_approach/multi_coint.py index e7831813..5e0e918a 100644 --- a/arbitragelab/cointegration_approach/multi_coint.py +++ b/arbitragelab/cointegration_approach/multi_coint.py @@ -15,6 +15,7 @@ import pandas as pd from arbitragelab.cointegration_approach.johansen import JohansenPortfolio +from arbitragelab.util import devadarsh class MultivariateCointegration: @@ -38,6 +39,8 @@ def __init__(self, asset_df: pd.DataFrame, trade_df: pd.DataFrame): self.__trade_df = trade_df self.__coint_vec = None + devadarsh.track('MultivariateCointegration') + @staticmethod def _missing_impute(price_df: pd.DataFrame, nan_method: str = 'ffill', order: int = 3) -> pd.DataFrame: """ diff --git a/arbitragelab/cointegration_approach/signals.py b/arbitragelab/cointegration_approach/signals.py index b5eb03bc..5c76f44d 100644 --- a/arbitragelab/cointegration_approach/signals.py +++ b/arbitragelab/cointegration_approach/signals.py @@ -10,6 +10,7 @@ import pandas as pd from sklearn.linear_model import LinearRegression +from arbitragelab.util import devadarsh def get_half_life_of_mean_reversion(data: pd.Series) -> float: """ @@ -19,6 +20,8 @@ def get_half_life_of_mean_reversion(data: pd.Series) -> float: :return: (float) Half-life of mean reversion """ + devadarsh.track('get_half_life_of_mean_reversion') + reg = LinearRegression(fit_intercept=True) training_data = data.shift(1).dropna().values.reshape(-1, 1) @@ -46,6 +49,8 @@ def linear_trading_strategy(portfolio_series: pd.Series, sma_window: int = None, :return: (pd.DataFrame) Mean-reverting portfolio series and target allocation on each day. """ + devadarsh.track('linear_trading_strategy') + if sma_window is None: # The book suggests to use window = speed of reversion sma_window = int(get_half_life_of_mean_reversion(portfolio_series)) @@ -83,6 +88,8 @@ def bollinger_bands_trading_strategy(portfolio_series: pd.Series, sma_window: in :return: (pd.DataFrame) Mean-reverting portfolio series and target allocation on each day. """ + devadarsh.track('bollinger_bands_trading_strategy') + if exit_z_score >= entry_z_score: raise ValueError('Exit Z-score can not be bigger than entry Z-Score.') diff --git a/arbitragelab/cointegration_approach/sparse_mr_portfolio.py b/arbitragelab/cointegration_approach/sparse_mr_portfolio.py index ba595b63..30b080aa 100644 --- a/arbitragelab/cointegration_approach/sparse_mr_portfolio.py +++ b/arbitragelab/cointegration_approach/sparse_mr_portfolio.py @@ -31,6 +31,7 @@ from sklearn.preprocessing import normalize, StandardScaler from arbitragelab.optimal_mean_reversion import OrnsteinUhlenbeck +from arbitragelab.util import devadarsh class SparseMeanReversionPortfolio: @@ -58,6 +59,8 @@ def __init__(self, assets: pd.DataFrame): self._standardized = standard_data self._standardized.columns = self._assets.columns + devadarsh.track('SparseMeanReversionPortfolio') + @property def assets(self) -> pd.DataFrame: """ diff --git a/arbitragelab/copula_approach/copula_generate_mixedcopula.py b/arbitragelab/copula_approach/copula_generate_mixedcopula.py index ddbcfa24..59488195 100644 --- a/arbitragelab/copula_approach/copula_generate_mixedcopula.py +++ b/arbitragelab/copula_approach/copula_generate_mixedcopula.py @@ -21,8 +21,10 @@ import numpy as np import pandas as pd import matplotlib.pyplot as plt + import arbitragelab.copula_approach.copula_generate as cg import arbitragelab.copula_approach.copula_calculation as ccalc +from arbitragelab.util import devadarsh class MixedCopula(ABC): @@ -225,6 +227,8 @@ def __init__(self, cop_params: tuple = None, weights: tuple = None): self.copulas = [self.clayton_cop, self.t_cop, self.gumbel_cop] + devadarsh.track('CTGMixCop') + def fit(self, data: pd.DataFrame, max_iter: int = 25, gamma_scad: float = 0.6, a_scad: float = 6, weight_margin: float = 1e-2) -> float: """ @@ -631,6 +635,8 @@ def __init__(self, cop_params: list = None, weights: list = None): self.copulas = [self.clayton_cop, self.frank_cop, self.gumbel_cop] + devadarsh.track('CFGMixCop') + def fit(self, data: pd.DataFrame, max_iter: int = 25, gamma_scad: float = 0.6, a_scad: float = 6, weight_margin: float = 1e-2) -> float: """ diff --git a/arbitragelab/copula_approach/copula_strategy_basic.py b/arbitragelab/copula_approach/copula_strategy_basic.py index 73fa6fce..9f312579 100644 --- a/arbitragelab/copula_approach/copula_strategy_basic.py +++ b/arbitragelab/copula_approach/copula_strategy_basic.py @@ -19,9 +19,11 @@ import numpy as np import pandas as pd import scipy.stats as ss + import arbitragelab.copula_approach.copula_generate as cg import arbitragelab.copula_approach.copula_calculation as ccalc import arbitragelab.copula_approach.copula_generate_mixedcopula as cgmix +from arbitragelab.util import devadarsh class BasicCopulaStrategy: @@ -73,6 +75,8 @@ def __init__(self, copula: Union[cg.Copula, cgmix.MixedCopula] = None, open_thre self._short_count = 0 self._exit_count = 0 + devadarsh.track('BasicCopulaStrategy') + @staticmethod def to_quantile(data: pd.DataFrame) -> Tuple[pd.DataFrame, list]: """ diff --git a/arbitragelab/copula_approach/copula_strategy_mpi.py b/arbitragelab/copula_approach/copula_strategy_mpi.py index 688d4bdd..b4249c3d 100644 --- a/arbitragelab/copula_approach/copula_strategy_mpi.py +++ b/arbitragelab/copula_approach/copula_strategy_mpi.py @@ -12,9 +12,11 @@ from typing import Callable, Sequence, Union import numpy as np import pandas as pd + from arbitragelab.copula_approach.copula_strategy_basic import BasicCopulaStrategy import arbitragelab.copula_approach.copula_generate as cg import arbitragelab.copula_approach.copula_generate_mixedcopula as cgmix +from arbitragelab.util import devadarsh class CopulaStrategyMPI(BasicCopulaStrategy): @@ -62,6 +64,8 @@ def __init__(self, copula: Union[cg.Copula, cgmix.MixedCopula] = None, self._short_count = 0 self._exit_count = 0 + devadarsh.track('CopulaStrategyMPI') + @staticmethod def to_returns(pair_prices: pd.DataFrame, fill_init_nan: Sequence[float] = (0, 0)) -> pd.DataFrame: r""" diff --git a/arbitragelab/copula_approach/pairs_selection.py b/arbitragelab/copula_approach/pairs_selection.py index 5c90b77f..be6c5887 100644 --- a/arbitragelab/copula_approach/pairs_selection.py +++ b/arbitragelab/copula_approach/pairs_selection.py @@ -11,6 +11,8 @@ import scipy.stats as ss import pandas as pd +from arbitragelab.util import devadarsh + class PairsSelector: r""" @@ -27,6 +29,8 @@ def __init__(self): Class initiation. """ + devadarsh.track('PairsSelector') + def rank_pairs(self, stocks_universe: pd.DataFrame, method: str = 'kendall tau', nan_option: Union[str, None] = 'forward fill', keep_num_pairs: Union[int, None] = None) -> pd.Series: diff --git a/arbitragelab/copula_approach/vine_copula_partner_selection.py b/arbitragelab/copula_approach/vine_copula_partner_selection.py index eebc9e38..adbe1f9d 100644 --- a/arbitragelab/copula_approach/vine_copula_partner_selection.py +++ b/arbitragelab/copula_approach/vine_copula_partner_selection.py @@ -14,6 +14,7 @@ from arbitragelab.copula_approach.vine_copula_partner_selection_utils import extremal_measure, get_quantiles_data ,\ get_co_variance_matrix, get_sum_correlations_vectorized, diagonal_measure_vectorized, multivariate_rho_vectorized +from arbitragelab.util import devadarsh class PartnerSelection: @@ -60,6 +61,8 @@ def __init__(self, prices: pd.DataFrame, n: int = 50): # Quadruple combinations for all stocks in universe self.all_quadruples = self._generate_all_combinations() + devadarsh.track('PartnerSelection') + def _correlation(self) -> pd.DataFrame: """ Calculates correlation between all stocks in the universe. diff --git a/arbitragelab/ml_approach/feature_expander.py b/arbitragelab/ml_approach/feature_expander.py index 74acd760..5ce4f71b 100644 --- a/arbitragelab/ml_approach/feature_expander.py +++ b/arbitragelab/ml_approach/feature_expander.py @@ -9,6 +9,8 @@ import numpy as np import pandas as pd +from arbitragelab.util import devadarsh + # This silencer is related to dangerous-default-value in __init__ # pylint: disable=W0102 @@ -36,6 +38,8 @@ def __init__(self, methods: list = [], n_orders: int = 1): self.n_orders = n_orders self.dataset = None + devadarsh.track('FeatureExpander') + @staticmethod def _chebyshev(series: pd.Series, degree: int): """ diff --git a/arbitragelab/ml_approach/filters.py b/arbitragelab/ml_approach/filters.py index af0c8319..0c826da2 100644 --- a/arbitragelab/ml_approach/filters.py +++ b/arbitragelab/ml_approach/filters.py @@ -12,6 +12,8 @@ from sklearn.preprocessing import MinMaxScaler from arch.univariate import ZeroMean, EWMAVariance +from arbitragelab.util import devadarsh + class CorrelationFilter: """ Correlation Filter implementation. @@ -34,6 +36,8 @@ def __init__(self, buy_threshold: float = 0.4, sell_threshold: float = 0.8, look self.frame = None self.transformed = None + devadarsh.track('CorrelationFilter') + def fit(self, frame: pd.DataFrame): """ Sets the correlation benchmark inside of the class object. @@ -180,6 +184,8 @@ def __init__(self, buy_threshold: float, sell_threshold: float): self.frame = None self.transformed = None + devadarsh.track('ThresholdFilter') + def plot(self) -> list: """ Function to plot buy and sell events. @@ -271,6 +277,8 @@ def __init__(self, lookback: int = 80): self.rolling_mean_vol = None self.vol_forcast_series = None + devadarsh.track('VolatilityFilter') + def plot(self) -> list: """ Function to plot spread series, regime states, and forecasted volatility. diff --git a/arbitragelab/ml_approach/neural_networks.py b/arbitragelab/ml_approach/neural_networks.py index 2b2fe6e2..b60ce8fa 100644 --- a/arbitragelab/ml_approach/neural_networks.py +++ b/arbitragelab/ml_approach/neural_networks.py @@ -15,6 +15,8 @@ import matplotlib.pyplot as plt +from arbitragelab.util import devadarsh + class BaseNeuralNetwork: """ Skeleton Class to be inherited by child neural network implementations. @@ -98,6 +100,8 @@ def __init__(self, frame_size: int, hidden_size: int = 2, num_outputs: int = 1, self.hidden_layer_activation_function = hidden_layer_activation_function self.output_layer_activation_function = output_layer_act_func + devadarsh.track('MultiLayerPerceptron') + def build(self): """ Builds and compiles model architecture. @@ -162,6 +166,8 @@ def __init__(self, input_shape: tuple, hidden_size: int = 10, num_outputs: int = self.hidden_layer_activation_function = hidden_layer_activation_function self.output_layer_activation_function = output_layer_act_func + devadarsh.track('RecurrentNeuralNetwork') + def build(self): """ Builds and compiles model architecture. @@ -225,6 +231,8 @@ def __init__(self, frame_size: int, hidden_size: int = 2, num_outputs: int = 1, self.hidden_layer_activation_function = hidden_layer_activation_function self.output_layer_activation_function = output_layer_act_func + devadarsh.track('PiSigmaNeuralNetwork') + def build(self): """ Builds and compiles model architecture. diff --git a/arbitragelab/ml_approach/regressor_committee.py b/arbitragelab/ml_approach/regressor_committee.py index b21d9aca..88fccf13 100644 --- a/arbitragelab/ml_approach/regressor_committee.py +++ b/arbitragelab/ml_approach/regressor_committee.py @@ -11,6 +11,7 @@ from matplotlib.axes._axes import Axes from arbitragelab.ml_approach import neural_networks +from arbitragelab.util import devadarsh # This silencer is related to the protected access # pylint: disable=W0212, import-outside-toplevel, unused-import @@ -46,6 +47,8 @@ def __init__(self, regressor_params: dict, regressor_class: str = 'MultiLayerPer self.verbose = verbose self.rvoter = None + devadarsh.track('RegressorCommittee') + def fit(self, xtrain: pd.DataFrame, ytrain: pd.DataFrame, xtest: pd.DataFrame, ytest: pd.DataFrame): """ Fits the member models, then the voting object. diff --git a/arbitragelab/ml_approach/tar.py b/arbitragelab/ml_approach/tar.py index 896fb733..999d274a 100644 --- a/arbitragelab/ml_approach/tar.py +++ b/arbitragelab/ml_approach/tar.py @@ -9,6 +9,8 @@ import statsmodels.api as sm from statsmodels.regression.linear_model import RegressionResults +from arbitragelab.util import devadarsh + class TAR(): """ The Threshold AutoRegressive Model is an extension provided by Enders and @@ -27,6 +29,8 @@ def __init__(self, price_data: pd.DataFrame): self.spread = price_data self.results = None + devadarsh.track('TAR') + @staticmethod def _tag_regime(series: pd.Series) -> pd.DataFrame: """ diff --git a/arbitragelab/optimal_mean_reversion/cir_model.py b/arbitragelab/optimal_mean_reversion/cir_model.py index f9cd2aa5..94ac3af5 100644 --- a/arbitragelab/optimal_mean_reversion/cir_model.py +++ b/arbitragelab/optimal_mean_reversion/cir_model.py @@ -46,6 +46,7 @@ def __init__(self): super().__init__() self.B_value = None + devadarsh.track('CoxIngersollRoss') def fit(self, data: pd.DataFrame, data_frequency: str, discount_rate: tuple, transaction_cost: tuple, diff --git a/arbitragelab/optimal_mean_reversion/xou_model.py b/arbitragelab/optimal_mean_reversion/xou_model.py index b41721b2..ff72bcd7 100644 --- a/arbitragelab/optimal_mean_reversion/xou_model.py +++ b/arbitragelab/optimal_mean_reversion/xou_model.py @@ -31,6 +31,7 @@ def __init__(self): super().__init__() self.a_tilde = None + devadarsh.track('ExponentialOrnsteinUhlenbeck') diff --git a/arbitragelab/other_approaches/kalman_filter.py b/arbitragelab/other_approaches/kalman_filter.py index 1291ed2e..0b45abf3 100644 --- a/arbitragelab/other_approaches/kalman_filter.py +++ b/arbitragelab/other_approaches/kalman_filter.py @@ -67,6 +67,7 @@ def __init__(self, observation_covariance: float = 0.001, transition_covariance: # Helper variables from Kalman filter self.R = None # Prediction variance-covariance self.beta = np.array([0, 0]) # Starting state prediction + devadarsh.track('KalmanFilterStrategy') def update(self, x: float, y: float): diff --git a/arbitragelab/other_approaches/pca_approach.py b/arbitragelab/other_approaches/pca_approach.py index 7bbfeb1b..71f7a4c6 100644 --- a/arbitragelab/other_approaches/pca_approach.py +++ b/arbitragelab/other_approaches/pca_approach.py @@ -44,6 +44,7 @@ def __init__(self, n_components: int = 15): self.n_components = n_components # Number of PCA components self.pca_model = PCA(n_components) # Model for PCA calculation + devadarsh.track('PCAStrategy') @staticmethod diff --git a/arbitragelab/stochastic_control_approach/ou_model_jurek.py b/arbitragelab/stochastic_control_approach/ou_model_jurek.py index e2786b6c..373faa28 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_jurek.py +++ b/arbitragelab/stochastic_control_approach/ou_model_jurek.py @@ -18,6 +18,7 @@ import matplotlib.pyplot as plt from arbitragelab.cointegration_approach.engle_granger import EngleGrangerPortfolio +from arbitragelab.util import devadarsh class OUModelJurek: @@ -57,6 +58,8 @@ def __init__(self): self.gamma = None # Coefficient of relative risk aversion self.beta = None # Rate of time preference + devadarsh.track('OUModelJurek') + @staticmethod def _calc_total_return_indices(prices: pd.DataFrame) -> pd.DataFrame: diff --git a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py index 61cd23c3..039b6290 100644 --- a/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py +++ b/arbitragelab/stochastic_control_approach/ou_model_mudchanatongsuk.py @@ -16,6 +16,8 @@ import pandas as pd import scipy.optimize as so +from arbitragelab.util import devadarsh + class OUModelMudchanatongsuk: """ @@ -53,6 +55,8 @@ def __init__(self): # Params inputted by user self.gamma = None # Parameter of utility function (self.gamma < 1) + devadarsh.track('OUModelMudchanatongsuk') + @staticmethod def _data_preprocessing(prices: pd.DataFrame) -> pd.DataFrame: diff --git a/arbitragelab/util/data_importer.py b/arbitragelab/util/data_importer.py index b759ea78..95f87835 100644 --- a/arbitragelab/util/data_importer.py +++ b/arbitragelab/util/data_importer.py @@ -9,6 +9,8 @@ import yfinance as yf import yahoo_fin.stock_info as ys +from arbitragelab.util import devadarsh + class DataImporter: """ Wrapper class that imports data from yfinance and yahoo_fin. @@ -29,6 +31,8 @@ def get_sp500_tickers() -> list: tickers_sp500 = ys.tickers_sp500() + devadarsh.track('get_sp500_tickers') + return tickers_sp500 @staticmethod @@ -41,6 +45,8 @@ def get_dow_tickers() -> list: tickers_dow = ys.tickers_dow() + devadarsh.track('get_dow_tickers') + return tickers_dow @staticmethod @@ -77,6 +83,8 @@ def get_price_data(tickers: list, start_date: str, end_date: str, price_data = yf.download(tickers, start=start_date, end=end_date, interval=interval, group_by='column')['Close'] + devadarsh.track('get_price_data') + return price_data @staticmethod diff --git a/arbitragelab/util/indexed_highlight.py b/arbitragelab/util/indexed_highlight.py index b6d52599..03fb6443 100644 --- a/arbitragelab/util/indexed_highlight.py +++ b/arbitragelab/util/indexed_highlight.py @@ -9,6 +9,8 @@ import matplotlib.pyplot as plt from mpldatacursor import DataCursor, HighlightingDataCursor +from arbitragelab.util import devadarsh + class IndexedHighlight(HighlightingDataCursor): """ This class extends HighlightingDataCursor to add support for @@ -26,6 +28,8 @@ def __init__(self, axes, **kwargs): self.highlights = [self.create_highlight(artist) for artist in artists] plt.setp(self.highlights, visible=False) + devadarsh.track('IndexedHighlight') + def update(self, event, annotation): """ On each update event, this method will loop through all SubPlot objects diff --git a/arbitragelab/util/rollers.py b/arbitragelab/util/rollers.py index 79c9f48d..d51502c1 100644 --- a/arbitragelab/util/rollers.py +++ b/arbitragelab/util/rollers.py @@ -10,6 +10,7 @@ from matplotlib.axes._axes import Axes from arbitragelab.util.base_futures_roller import BaseFuturesRoller +from arbitragelab.util import devadarsh class CrudeOilFutureRoller(BaseFuturesRoller): """ @@ -67,6 +68,8 @@ def _get_rolldates(self, dataset: pd.DataFrame) -> pd.Series: all_roll_overs = pd.concat([pd.Series(roll_over_dates_for_holidays), pd.Series(dataset.iloc[roll_over_dates_for_business_days].index.values)]) + devadarsh.track('CrudeOilFutureRoller') + return all_roll_overs.sort_values().values @@ -91,6 +94,8 @@ def _get_rolldates(self, dataset: pd.DataFrame) -> pd.Series: nbp_roll_dates = final_df['expiry'].drop_duplicates().dropna().values[:-1] + devadarsh.track('NBPFutureRoller') + return nbp_roll_dates @@ -137,6 +142,8 @@ def _get_rolldates(self, dataset: pd.DataFrame) -> pd.Series: rb_roll_dates = target_dates['target_date'].drop_duplicates() + devadarsh.track('RBFutureRoller') + return rb_roll_dates.dropna().values[1:] @@ -192,6 +199,8 @@ def _get_rolldates(self, dataset: pd.DataFrame) -> pd.Series: all_roll_overs = pd.concat([pd.Series(roll_over_dates_for_holidays), pd.Series(dataset.iloc[roll_over_dates_for_business_days].index.values)]) + devadarsh.track('GrainFutureRoller') + return all_roll_overs.sort_values().values @@ -241,6 +250,8 @@ def _get_rolldates(self, dataset: pd.DataFrame) -> pd.Series: all_roll_overs = pd.concat([pd.Series(roll_over_dates_for_holidays), pd.Series(dataset.iloc[roll_over_dates_for_business_days].index.values)]) + devadarsh.track('EthanolFutureRoller') + return all_roll_overs.sort_values().values def plot_historical_future_slope_state(m1_last: pd.Series, m2_open: pd.Series) -> Axes: @@ -261,4 +272,6 @@ def plot_historical_future_slope_state(m1_last: pd.Series, m2_open: pd.Series) - ax_object.fill_between(premium.index, perc_chg, where=perc_chg < 0, facecolor='red') ax_object.legend(["", "Contango", "Backwardation"]) + devadarsh.track('plot_historical_future_slope_state') + return ax_object From 7a5a73572adb4aa5a2f76b101ed6fc1ad1c7ca64 Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 16:22:08 +0200 Subject: [PATCH 098/103] Minor code adjustments to CVine Module --- .../copula_approach/vinecop_generate.py | 34 ++++++++++++------- .../copula_approach/vinecop_strategy.py | 4 +++ 2 files changed, 26 insertions(+), 12 deletions(-) diff --git a/arbitragelab/copula_approach/vinecop_generate.py b/arbitragelab/copula_approach/vinecop_generate.py index cf75828a..94000b53 100644 --- a/arbitragelab/copula_approach/vinecop_generate.py +++ b/arbitragelab/copula_approach/vinecop_generate.py @@ -15,6 +15,8 @@ import pyvinecopulib as pv import scipy.integrate as integrate +from arbitragelab.util import devadarsh + class RVineCop: """ @@ -22,6 +24,10 @@ class RVineCop: """ def __init__(self): + """ + Initialize. + """ + pass @@ -49,6 +55,8 @@ def __init__(self, cvine_cop: pv.Vinecop = None): # The pv.Vinecop being wrapped self.cvine_cop = cvine_cop + devadarsh.track('CVineCop') + def fit_auto(self, data: pd.DataFrame, pv_target_idx: int = 1, if_renew: bool = True, alt_cvine_structure=False): """ Auto fit data to the C-vine copula by selecting the center stock. @@ -121,7 +129,7 @@ def _get_possible_cvine_structs_alt(data_dim: int, pv_target_idx: int) -> List[t in [Stubinger et al. 2016]. :param data_dim: (int) The number of stocks. - :param pv_target_idx: (int). The stock to be targeted for trading. This is indexed from 1, hence 1 corresponds + :param pv_target_idx: (int) The stock to be targeted for trading. This is indexed from 1, hence 1 corresponds to the 0th column data in a pandas data frame. :return: (List[tuple]) The list of all possible C-vine structures stored as tuples. """ @@ -150,7 +158,7 @@ def _get_possible_cvine_structs(data_dim: int, pv_target_idx: int) -> List[tuple tuple, as claimed in [Stubinger et al. 2016]. For a tuple (4, 2, 1, 3), it says stock 4 is the targeted stock. :param data_dim: (int) The number of stocks. - :param pv_target_idx: (int). The stock to be targeted for trading. This is indexed from 1, hence 1 corresponds + :param pv_target_idx: (int) The stock to be targeted for trading. This is indexed from 1, hence 1 corresponds to the 0th column data in a pandas data frame. :return: (List[tuple]) The list of all possible C-vine structures stored as tuples. """ @@ -197,6 +205,7 @@ def get_condi_probs(self, u: Union[pd.DataFrame, np.array], pv_target_idx: int = # When the input is a pd.Dataframe condi_probs = u.apply(lambda row: self._get_condi_prob(row, pv_target_idx, eps), axis=1) + # The result is a pd.Series with matching indices return condi_probs @@ -268,6 +277,7 @@ def get_cop_densities(self, u: Union[pd.DataFrame, np.array], num_threads: int = u_np = np.array(u) pdfs = self.cvine_cop.pdf(u_np, num_threads) pdfs_series = pd.Series(pdfs, index=u.index) + # The result is a pd.Series with matching indices return pdfs_series @@ -281,7 +291,6 @@ def get_cop_evals(self, u: pd.DataFrame) -> pd.Series: :param u: (Union[pd.DataFrame, np.array]) The quantiles data to be used. The input can be a pandas dataframe, or a numpy array vector. The formal case yields the result with in pandas series in matching indices, and the latter yields a single float number. - :return: (Union[pd.Series, float]) The calculated cdf. If the input is a dataframe then the result is a series with matching indices. If the input is a 1D np.array then the result is a float. """ @@ -297,10 +306,11 @@ def get_cop_evals(self, u: pd.DataFrame) -> pd.Series: u_np = np.array(u) cdfs = self.cvine_cop.cdf(u_np) cdfs_series = pd.Series(cdfs, index=u.index) + # The result is a pd.Series with matching indices return cdfs_series - def simulate(self, n: int, qrn: bool = False, num_threads: int = 1, seeds: List[int] = None) -> np.ndarray: + def simulate(self, n: int, qrn: bool = False, num_threads: int = 1, seeds: List[int] = None) -> np.array: """ Simulate from a vine copula model. @@ -308,8 +318,8 @@ def simulate(self, n: int, qrn: bool = False, num_threads: int = 1, seeds: List[ :param qrn: (bool) Optional. Set to True for quasi-random numbers. Defaults to False. :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. :param seeds: (List[int]) Optional. Seeds of the random number generator. If empty then the random generator - will be seeded randomly. Defaults to []. - :return: (pd.ndarray) The generated random samples from the vine copula. + will be seeded randomly. Defaults to None. + :return: (pd.array) The generated random samples from the vine copula. """ if seeds is None: @@ -325,10 +335,10 @@ def aic(self, u: pd.DataFrame, num_threads: int = 1) -> float: :param u: (pd.DataFrame) The quantile data used for evaluation. :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. - :return: (float) calculated AIC value. + :return: (float) Calculated AIC value. """ - u_np = u.to_numpy() # Transit to numpy ndarrays + u_np = u.to_numpy() # Transit to numpy arrays aic_value = self.cvine_cop.aic(u_np, num_threads) return aic_value @@ -339,10 +349,10 @@ def bic(self, u: pd.DataFrame, num_threads: int = 1) -> float: :param u: (pd.DataFrame) The quantile data used for evaluation. :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. - :return: (float) calculated BIC value. + :return: (float) Calculated BIC value. """ - u_np = u.to_numpy() # Transit to numpy ndarrays + u_np = u.to_numpy() # Transit to numpy arrays bic_value = self.cvine_cop.bic(u_np, num_threads) return bic_value @@ -353,10 +363,10 @@ def loglik(self, u: pd.DataFrame, num_threads: int = 1) -> float: :param u: (pd.DataFrame) The quantile data used for evaluation. :param num_threads: (int) Optional. The number of threads to use for calculation. Defaults to 1. - :return: (float) calculated sum of log-likelihood. + :return: (float) Calculated sum of log-likelihood. """ - u_np = u.to_numpy() # Transit to numpy ndarrays + u_np = u.to_numpy() # Transit to numpy arrays loglik_value = self.cvine_cop.loglik(u_np, num_threads) return loglik_value diff --git a/arbitragelab/copula_approach/vinecop_strategy.py b/arbitragelab/copula_approach/vinecop_strategy.py index dda58fb1..9a544934 100644 --- a/arbitragelab/copula_approach/vinecop_strategy.py +++ b/arbitragelab/copula_approach/vinecop_strategy.py @@ -11,7 +11,9 @@ from typing import List, Union, Callable, Tuple import pandas as pd import numpy as np + from arbitragelab.copula_approach.vinecop_generate import CVineCop +from arbitragelab.util import devadarsh class CVineCopStrat: @@ -41,6 +43,8 @@ def __init__(self, cvinecop: CVineCop = None, signal_to_position_table: pd.DataF else: self.signal_to_position_table = signal_to_position_table + devadarsh.track('CVineCopStrat') + def calc_mpi(self, returns: pd.DataFrame, cdfs: List[Callable], pv_target_idx: int = 1, subtract_mean: bool = False) -> pd.Series: """ From 0a6f969d6da41712a3bc51c55a91be4fc2dcc7c2 Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 16:23:30 +0200 Subject: [PATCH 099/103] Renamed unit test for CVine Module --- tests/test_copula_strategy_mpi.py | 3 ++ ...e.py => test_vinecop_generate_strategy.py} | 29 +++++++++++-------- 2 files changed, 20 insertions(+), 12 deletions(-) rename tests/{test_vinecop_generate.py => test_vinecop_generate_strategy.py} (98%) diff --git a/tests/test_copula_strategy_mpi.py b/tests/test_copula_strategy_mpi.py index 819d6faf..6aeb56fc 100644 --- a/tests/test_copula_strategy_mpi.py +++ b/tests/test_copula_strategy_mpi.py @@ -18,6 +18,9 @@ class TestCopulaStrategyMPI(unittest.TestCase): """ def setUp(self): + """ + Set up the data and parameters. + """ project_path = os.path.dirname(__file__) self.data_path = project_path + r'/test_data' diff --git a/tests/test_vinecop_generate.py b/tests/test_vinecop_generate_strategy.py similarity index 98% rename from tests/test_vinecop_generate.py rename to tests/test_vinecop_generate_strategy.py index 54a6a678..89a03520 100644 --- a/tests/test_vinecop_generate.py +++ b/tests/test_vinecop_generate_strategy.py @@ -2,7 +2,7 @@ # All rights reserved # Read more: https://hudson-and-thames-arbitragelab.readthedocs-hosted.com/en/latest/additional_information/license.html """ -Unit tests for vinecop_generate, vinecop_strategy +Unit tests for vinecop_generate, vinecop_strategy. """ # pylint: disable = invalid-name, protected-access, consider-using-enumerate @@ -12,6 +12,7 @@ import pandas as pd import numpy as np import pyvinecopulib as pv + import arbitragelab.copula_approach.vinecop_generate as vg import arbitragelab.copula_approach.vinecop_strategy as vs import arbitragelab.copula_approach.copula_calculation as ccalc @@ -23,6 +24,10 @@ class TestVineCop(unittest.TestCase): """ def setUp(self) -> None: + """ + Set up the data and parameters. + """ + project_path = os.path.dirname(__file__) data_path = project_path + "/test_data/prices_10y_SP500.csv" sp500_prices = pd.read_csv(data_path, index_col=0, parse_dates=True).fillna(method='ffill') @@ -127,7 +132,7 @@ def test_get_condi_probs_priv(self) -> None: Test the _get_condi_probs function from CVineCop. """ - # Ignore possible integration warnings. + # Ignore possible integration warnings warnings.filterwarnings(action='ignore', message='The integral is probably divergent') cvinecop = vg.CVineCop(self.pv_cvine_cop) @@ -146,7 +151,7 @@ def test_get_condi_probs(self) -> None: Test the get_condi_probs function from CVineCop. """ - # Ignore possible integration warnings. + # Ignore possible integration warnings warnings.filterwarnings(action='ignore', message='The integral is probably divergent') cvinecop = vg.CVineCop(self.pv_cvine_cop) @@ -275,9 +280,9 @@ def test_fit_auto(self) -> None: expected_aic_1 = -382.98496652926514 self.assertAlmostEqual(aic_1, expected_aic_1, places=3) - # 2. Without renewal, fit the cvine copula using the test set. + # 2. Without renewal, fit the cvine copula using the test set cvinecop.fit_auto(data=self.quantiles_data_test, pv_target_idx=1, if_renew=False) - # Check its aic value on the training data. Should still get the same result. + # Check its aic value on the training data. Should still get the same result aic_2 = cvinecop.aic(u=self.quantiles_data_train, num_threads=1) expected_aic_2 = -382.98496652926514 self.assertAlmostEqual(aic_2, expected_aic_2, places=3) @@ -296,9 +301,9 @@ def test_fit_auto_alt(self) -> None: expected_aic_1 = -379.8244061045313 self.assertAlmostEqual(aic_1, expected_aic_1, places=3) - # 2. Without renewal, fit the cvine copula using the test set. + # 2. Without renewal, fit the cvine copula using the test set cvinecop.fit_auto(data=self.quantiles_data_test, pv_target_idx=1, if_renew=False) - # Check its aic value on the training data. Should still get the same result. + # Check its aic value on the training data. Should still get the same result aic_2 = cvinecop.aic(u=self.quantiles_data_train, num_threads=1) expected_aic_2 = -379.8244061045313 self.assertAlmostEqual(aic_2, expected_aic_2, places=3) @@ -335,7 +340,7 @@ def test_calc_mpi(self) -> None: cvinecop = vg.CVineCop(self.pv_cvine_cop) cvstrat = vs.CVineCopStrat(cvinecop) - dataset = self.returns_test.iloc[:10] # Use only 10 data points to speed up calculation. + dataset = self.returns_test.iloc[:10] # Use only 10 data points to speed up calculation # 1. MPIs with no mean subtraction mpis_1 = cvstrat.calc_mpi(returns=dataset, cdfs=self.cdfs, pv_target_idx=1, subtract_mean=False) @@ -363,7 +368,7 @@ def test_signal_to_position_priv(self) -> None: past_positions = [0, 1, -1] signals = [0, 1, -1, 2] - # 1. Default table. + # 1. Default table cvinecop = vg.CVineCop(self.pv_cvine_cop) cvstrat = vs.CVineCopStrat(cvinecop) new_positions = [] @@ -376,7 +381,7 @@ def test_signal_to_position_priv(self) -> None: np.testing.assert_array_equal(new_positions, expected_new_positions) - # 2. Custom table. + # 2. Custom table signal_to_position_table = pd.DataFrame({1: {0: 1, 1: 1, -1: 1}, -1: {0: -1, 1: 0, -1: -1}, 0: {0: 0, 1: 0, -1: 0}, @@ -401,11 +406,11 @@ def test_get_cur_signal_bollinger(self) -> None: cvinecop = vg.CVineCop(self.pv_cvine_cop) cvstrat = vs.CVineCopStrat(cvinecop) - # All possible past CMPI and current CMPI value. + # All possible past CMPI and current CMPI value past_cmpis = [1.2, 1.2, 1.2, 1.2, 0.6, 0.6, 0.6, 0.6, -1.2, -1.2, -1.2, -1.2, -0.6, -0.6, -0.6, -0.6] cur_cmpis = [1.3, 0.8, -0.8, -1.2, 0.8, 1.2, -0.6, -1.2, -1.3, -0.8, 0.8, 1.2, -0.8, -1.2, 0.6, 1.2] - # Set the Bollinger band be: lower bound=-1, running mean=0, upper_bound=1, for eaiser comparison. + # Set the Bollinger band be: lower bound=-1, running mean=0, upper_bound=1, for eaiser comparison signals = [] for p in range(len(past_cmpis)): signals.append(cvstrat.get_cur_signal_bollinger(past_cmpis[p], cur_cmpis[p], running_mean=0, From 7edc13bfed8676f80939bf97902f9787a3639401 Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 16:23:53 +0200 Subject: [PATCH 100/103] Added pyvinecopulib to requirements --- requirements.txt | 2 +- setup.cfg | 1 + 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/requirements.txt b/requirements.txt index 82a6a706..39a11289 100644 --- a/requirements.txt +++ b/requirements.txt @@ -20,7 +20,7 @@ keras==2.3.1 tensorflow==2.2.1 arch==4.16.1 analytics-python==1.2.9 -pyvinecopulib==0.5.4 +pyvinecopulib==0.5.5 # Develop bump2version==1.0.1 diff --git a/setup.cfg b/setup.cfg index 5e259e82..fdea3abb 100644 --- a/setup.cfg +++ b/setup.cfg @@ -63,6 +63,7 @@ install_requires = networkx==2.5 arch==4.16.1 analytics-python==1.2.9 + pyvinecopulib==0.5.5 [options.packages.find] package_dir = From 6a061f8ca07dff54e654998dc35409b57a9d5fcd Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 16:35:34 +0200 Subject: [PATCH 101/103] Adjusted sphinx docs for CVine Copula Module --- .../copula_approach/cvine_copula_strategy.rst | 128 +++++++++--------- .../copula_approach/partner_selection.rst | 6 +- .../copula_approach/vine_copula_intro.rst | 85 ++++++------ docs/source/index.rst | 2 +- 4 files changed, 114 insertions(+), 107 deletions(-) diff --git a/docs/source/copula_approach/cvine_copula_strategy.rst b/docs/source/copula_approach/cvine_copula_strategy.rst index ad578808..cce3995a 100644 --- a/docs/source/copula_approach/cvine_copula_strategy.rst +++ b/docs/source/copula_approach/cvine_copula_strategy.rst @@ -1,8 +1,8 @@ -.. _cvine_copula_strategy: +.. _copula_approach-cvine_copula_strategy: .. note:: - This document is an implementation of: + This document is an implementation of: Stübinger, J., Mangold, B. and Krauss, C. `Statistical arbitrage with vine copulas. `__ Quantitative Finance, 2018. @@ -69,12 +69,17 @@ We work with stocks' **daily returns data** exclusively. .. Note:: Selecting trading candidates is a serious topic, and can largely determine if a strategy is profitable or - not. There are 4 methods proposed in [Stübinger et al. 2018]: - pairwise Spearman's rho, multi-dimensional Spearman's rho, - sum of distance in quantile plots to hyper-diagonal, and a copula-chi-square test for dependence. + not. + There are 4 methods proposed in [Stübinger et al. 2018]: + + * pairwise Spearman's rho, + * multi-dimensional Spearman's rho, + * sum of distance in quantile plots to hyper-diagonal + * copula-chi-square test for dependence. + Loosely speaking, the goal is to find stocks cohorts that are heavily dependent, such that a mean-reversion bet on relative mispricings is profitable. - For more details in implementation, please refer to [Vijay's document]. + For more details in implementation, please refer to :ref:`Vine Copula Partner Selection`. Suppose we have chosen a few cohorts and in each cohort it has a key stock element. We then need to turn the translate @@ -85,7 +90,7 @@ We denote the pseudo-observations as :math:`u_i`'s, and they are all uniform in :scale: 40 % :align: center - (Fig 1: Generate pseudo-observations or quantiles and marginal ECDFs from returns data.) + Fig 1: Generate pseudo-observations or quantiles and marginal ECDFs from returns data. Step 2: Figure out the C-vine Structure @@ -144,7 +149,7 @@ value that fits best the data. :scale: 60 % :align: center - (Fig 2: Determine the C-vine structure by AIC or maximum likelihood. Picture from [Stübinger et al. 2018].) + Fig 2: Determine the C-vine structure by AIC or maximum likelihood. Picture from [Stübinger et al. 2018]. Step 3: Probability Density *************************** @@ -160,8 +165,8 @@ top of the tree). And the final probability density is their product. :scale: 50 % :align: center - (Fig 3: Determine the joint density :math:`f(u_1, u_2, u_3, u_4)` from the vine copula. Here the notation - :math:`f(x_1, x_2, x_3, x_4)` is okay since we start from the beginning only using quantiles data, so :math:`u_i = x_i`.) + Fig 3: Determine the joint density :math:`f(u_1, u_2, u_3, u_4)` from the vine copula. Here the notation + :math:`f(x_1, x_2, x_3, x_4)` is okay since we start from the beginning only using quantiles data, so :math:`u_i = x_i`. Step 4: Conditional Probability ******************************* @@ -227,7 +232,7 @@ Bollinger band's width. :scale: 25 % :align: center - (Fig 4: Positions of the target stock and the associated Bollinger Band.) + Fig 4: Positions of the target stock and the associated Bollinger Band. Now we total net positions for each key stock in each cohort. Then we formulate our dollar-neutral strategy by trading against a cheap broad-based market index such as SPY, similar to the method used in [Avellaneda and Lee, 2010]. @@ -244,7 +249,7 @@ used as a sanity check on whether our vine copula model is off. :scale: 40 % :align: center - (Fig 5: CMPI and cumulative log returns of the target stock. Their shape looks very similar.) + Fig 5: CMPI and cumulative log returns of the target stock. Their shape looks very similar. Comments ######## @@ -279,66 +284,67 @@ Implementation .. automodule:: arbitragelab.copula_approach.vinecop_strategy .. autoclass:: CVineCopStrat - :members: __init__, calc_mpi, get_positions_bollinger, get_cur_signal_bollinger, get_cur_pos_bollinger, positions_to_units_against_index + :members: __init__, calc_mpi, get_positions_bollinger, get_cur_signal_bollinger, get_cur_pos_bollinger, positions_to_units_against_index Example -******* +####### .. code-block:: - # Importing the module and other libraries - from arbitragelab.copula_approach.vinecop_generate import CVineCop - from arbitragelab.copula_approach.vinecop_strategy import CVineCopStrat - from arbitragelab.copula_approach.copula_calculation import to_quantile - import pandas as pd - import numpy as np - - # Loading stocks data. Use 1 cohort for example: suppose stocks 'AAPL', 'MSFT', 'AMZN', 'FB' - # form the cohort, and 'AAPL' is the target stock. - sp500_returns = pd.read_csv('all_sp500_returns.csv', index_col='Dates', parse_dates=True) - returns_train = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']][:800] - returns_test = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']][800:1100] - - prices_aapl_spy = pd.read_csv('all_sp500_prices.csv', - index_col='Dates', parse_dates=True)[['AAPL', 'SPY']][800:1100] - - rts_train_quantiles, cdfs = to_quantile(returns_train) - rts_test_quantiles, _ = to_quantile(returns_train) - - # Instantiate a CVineCop (C-vine copula) class to fit - cvinecop = CVineCop - - # Fit C-vine automatically, 'AAPL' is the target stock - # Note that pv_target_idx is indexed from 1 - vinecop_structure = cvinecop.fit_auto(data=rts_train_quantiles, pv_target_idx=1, if_renew=True) - # Print the vine copula structure as a sanity check. You can directly fit internally by just using - # cvinecop.fit_auto(data=rts_train_quantiles, pv_target_idx=1, if_renew=True) if you do not want to - # print structures. - print(vinecop_structure) - - # Instantiate a CVineCopStrat (trading) class from the fitted C-vine copula - cvstrat = CVineCopStrat(cvinecop) - - # Generate positions over the test data, return the Bollinger band for sanity check - # Note that the cdfs should be from the training set. - positions, bband = cvstrat.get_positions_bollinger(returns=returns_test, cdfs=cdfs, - if_return_bollinger_band=True) - positions = positions.shift(1) # Avoid look-back bias - - # Formulate units from the positions against the SPY index, with 100,000 dollar investment - units = cvstrat.positions_to_units_against_index(target_stock_prices=prices_aapl_spy['AAPL'], - index_prices=prices_aapl_spy['SPY'], - positions=positions, - multiplier=100000) + # Importing the module and other libraries + import pandas as pd + import numpy as np + + from arbitragelab.copula_approach.vinecop_generate import CVineCop + from arbitragelab.copula_approach.vinecop_strategy import CVineCopStrat + from arbitragelab.copula_approach.copula_calculation import to_quantile + + # Loading stocks data. Use 1 cohort for example: suppose stocks 'AAPL', 'MSFT', 'AMZN', 'FB' + # form the cohort, and 'AAPL' is the target stock. + sp500_returns = pd.read_csv('all_sp500_returns.csv', index_col='Dates', parse_dates=True) + returns_train = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']][:800] + returns_test = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']][800:1100] + + prices_aapl_spy = pd.read_csv('all_sp500_prices.csv', + index_col='Dates', parse_dates=True)[['AAPL', 'SPY']][800:1100] + + rts_train_quantiles, cdfs = to_quantile(returns_train) + rts_test_quantiles, _ = to_quantile(returns_train) + + # Instantiate a CVineCop (C-vine copula) class to fit + cvinecop = CVineCop() + + # Fit C-vine automatically, 'AAPL' is the target stock + # Note that pv_target_idx is indexed from 1 + vinecop_structure = cvinecop.fit_auto(data=rts_train_quantiles, pv_target_idx=1, if_renew=True) + # Print the vine copula structure as a sanity check. You can directly fit internally by just + # using cvinecop.fit_auto(data=rts_train_quantiles, pv_target_idx=1, if_renew=True) if you + # do not want to print structures. + print(vinecop_structure) + + # Instantiate a CVineCopStrat (trading) class from the fitted C-vine copula + cvstrat = CVineCopStrat(cvinecop) + + # Generate positions over the test data, return the Bollinger band for sanity check + # Note that the cdfs should be from the training set. + positions, bband = cvstrat.get_positions_bollinger(returns=returns_test, cdfs=cdfs, + if_return_bollinger_band=True) + positions = positions.shift(1) # Avoid look-back bias + + # Formulate units from the positions against the SPY index, with 100,000 dollar investment + units = cvstrat.positions_to_units_against_index(target_stock_prices=prices_aapl_spy['AAPL'], + index_prices=prices_aapl_spy['SPY'], + positions=positions, + multiplier=100000) Research Notebooks ################## -The following research notebook can be used to better understand the basic copula strategy. +The following research notebook can be used to better understand the C-Vine copula strategy. -* `Basic Copula Strategy`_ +* `C-Vine Copula Strategy`_ -.. _`Basic Copula Strategy`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Copula%20Approach/Copula_Strategy_Basic.ipynb +.. _`C-Vine Copula Strategy`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Copula%20Approach/CVine_Copula_Strategy.ipynb References ########## diff --git a/docs/source/copula_approach/partner_selection.rst b/docs/source/copula_approach/partner_selection.rst index 91b094fc..36b70b85 100644 --- a/docs/source/copula_approach/partner_selection.rst +++ b/docs/source/copula_approach/partner_selection.rst @@ -9,9 +9,9 @@ `A multivariate linear rank test of independence based on a multiparametric copula with cubic sections. (2015) `__ by Mangold, B. -======================================== -Vine Copula Partner Selection Approaches -======================================== +============================= +Vine Copula Partner Selection +============================= This module contains implementation of the four partner selection approaches mentioned in Section 3.1.1 of Statistical Arbitrage with Vine Copulas. diff --git a/docs/source/copula_approach/vine_copula_intro.rst b/docs/source/copula_approach/vine_copula_intro.rst index d51c89c3..e0324f16 100644 --- a/docs/source/copula_approach/vine_copula_intro.rst +++ b/docs/source/copula_approach/vine_copula_intro.rst @@ -1,4 +1,4 @@ -.. _vine_copula_intro: +.. _copula_approach-vine_copula_intro: .. Note:: @@ -146,7 +146,7 @@ It turns out that this decomposition can be visualized in a graph structure as f :scale: 28 % :align: center - (Fig 1: A vine copula tree structure for 3 random variables.) + Fig 1: A vine copula tree structure for 3 random variables. Here every node stands for either joint density or marginal density, and bivariate copulas are used to connect the nodes. You can visualize them as trees and the leaves are on the top. All the leaves stand @@ -166,7 +166,7 @@ They can be visualized as follows: :scale: 28 % :align: center - (Fig 2: R-vine, C-vine and D-vine.) + Fig 2: R-vine, C-vine and D-vine. For an R-vine, for each level of the tree, it needs to satisfy the following conditions: @@ -186,7 +186,7 @@ For a D-vine, each tree is a *path*: there is one road that goes through all the :scale: 28 % :align: center - (Fig 3: C-vine and its tuple representation.) + Fig 3: C-vine and its tuple representation. The representation of a generic R-vine is slightly more complicated, and requires a lower triangular matrix (some places uses an upper triangular matrix for representation, and they are indeed identical). @@ -196,9 +196,9 @@ Let's look at the following R-vine with 7 random variables for example: :scale: 50 % :align: center - (Fig 4: An R-vine tree. Picture from Dissmann, J., Brechmann, E.C., Czado, C. and Kurowicka, D., 2013. Selecting and + Fig 4: An R-vine tree. Picture from Dissmann, J., Brechmann, E.C., Czado, C. and Kurowicka, D., 2013. Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59, - pp.52-69.) + pp.52-69. The R-vine tree in Fig 4 can be represented by the following matrix: @@ -255,8 +255,8 @@ impose some structures for model interpretability. :scale: 40 % :align: center - (Fig 4: C_vine and D-vine tree. Picture from Brechmann, E. and Schepsmeier, U., 2013. Cdvine: - Modeling dependence with c-and d-vine copulas in r. Journal of statistical software, 52(3), pp.1-27.) + Fig 5: C_vine and D-vine tree. Picture from Brechmann, E. and Schepsmeier, U., 2013. Cdvine: + Modeling dependence with c-and d-vine copulas in r. Journal of statistical software, 52(3), pp.1-27. C-vine and D-vine are the most commonly used ones in practice for dependence modeling. C-vine due to its star-like structure, is useful when we have a key variable that largely governs the variable interactions @@ -349,58 +349,59 @@ Implementation .. automodule:: arbitragelab.copula_approach.vinecop_generate .. autoclass:: CVineCop - :members: __init__, fit_auto, get_condi_probs, get_cop_densities, get_cop_evals, simulate, aic, bic, loglik + :members: __init__, fit_auto, get_condi_probs, get_cop_densities, get_cop_evals, simulate, aic, bic, loglik Example -******* +####### .. code-block:: - # Importing the module and other libraries - from arbitragelab.copula_approach.vinecop_generate import CVineCop - from arbitragelab.copula_approach.copula_calculation import to_quantile - import pandas as pd - import numpy as np - - # Loading stocks data - sp500_returns = pd.read_csv('all_sp500_returns.csv', index_col='Dates', parse_dates=True) - subsample_returns = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']] - subsample_rts_quantiles, _ = to_quantile(subsample_returns) - quantiles_example = pd.DataFrame([0.1, 0.2, 0.3, 0.8], - [0.5, 0.1, 0.9, 0.2]) + # Importing the module and other libraries + import pandas as pd + import numpy as np + + from arbitragelab.copula_approach.vinecop_generate import CVineCop + from arbitragelab.copula_approach.copula_calculation import to_quantile + + # Loading stocks data + sp500_returns = pd.read_csv('all_sp500_returns.csv', index_col='Dates', parse_dates=True) + subsample_returns = sp500_returns[['AAPL', 'MSFT', 'AMZN', 'FB']] + subsample_rts_quantiles, _ = to_quantile(subsample_returns) + quantiles_example = pd.DataFrame([[0.1, 0.2, 0.3, 0.8], + [0.5, 0.1, 0.9, 0.2]]) - # Instantiate a CVineCop class - cvinecop = CVineCop + # Instantiate a CVineCop class + cvinecop = CVineCop() - # Fit C-vine automatically, assuming AAPL is the target stock - # Note that pv_target_idx is indexed from 1 - cvinecop.fit_auto(data=subsample_rts_quantiles, pv_target_idx=1, if_renew=True) + # Fit C-vine automatically, assuming AAPL is the target stock + # Note that pv_target_idx is indexed from 1 + cvinecop.fit_auto(data=subsample_rts_quantiles, pv_target_idx=1, if_renew=True) - # Calculate probability densities - prob_densities = cvinecop.get_cop_densities(u=quantiles_example) + # Calculate probability densities + prob_densities = cvinecop.get_cop_densities(u=quantiles_example) - # Calculate conditional (cumulative) densities, assuming AAPL is the target stock - condi_probs = cvinecop.get_condi_probs(u=quantiles_example, pv_target_idx=1) + # Calculate conditional (cumulative) densities, assuming AAPL is the target stock + condi_probs = cvinecop.get_condi_probs(u=quantiles_example, pv_target_idx=1) - # Calculate cumulative density (copula evaluation by definition) - cop_evals = cvinecop.get_cop_evals(u=quantiles_example) + # Calculate cumulative density (copula evaluation by definition) + cop_evals = cvinecop.get_cop_evals(u=quantiles_example) - # Simulate n=1000 samples - samples_df = cvinecop.simulate(n=1000) + # Simulate n=1000 samples + samples_df = cvinecop.simulate(n=1000) - # Calculate AIC, BIC and Log-Likelihood - aic = cvinecop.aic(u=subsample_rts_quantiles) - bic = cvinecop.bic(u=subsample_rts_quantiles) - loglik = cvinecop.loglik(u=subsample_rts_quantiles) + # Calculate AIC, BIC and Log-Likelihood + aic = cvinecop.aic(u=subsample_rts_quantiles) + bic = cvinecop.bic(u=subsample_rts_quantiles) + loglik = cvinecop.loglik(u=subsample_rts_quantiles) Research Notebooks ################## The following research notebook can be used to better understand the vine copula approach. -* `Basic Copula Strategy`_ +* `C-Vine Copula Strategy`_ -.. _`Basic Copula Strategy`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Copula%20Approach/Copula_Strategy_Basic.ipynb +.. _`C-Vine Copula Strategy`: https://github.com/Hudson-and-Thames-Clients/arbitrage_research/blob/master/Copula%20Approach/CVine_Copula_Strategy.ipynb References ########## @@ -408,4 +409,4 @@ References * `Stübinger, J., Mangold, B. and Krauss, C., 2018. Statistical arbitrage with vine copulas. Quantitative Finance, 18(11), pp.1831-1849. `__ * `Joe, H. and Kurowicka, D. eds., 2011. Dependence modeling: vine copula handbook. World Scientific. `__ * `Yu, R., Yang, R., Zhang, C., Špoljar, M., Kuczyńska-Kippen, N. and Sang, G., 2020. A Vine Copula-Based Modeling for Identification of Multivariate Water Pollution Risk in an Interconnected River System Network. Water, 12(10), p.2741. `__ -* `Dissmann, J., Brechmann, E.C., Czado, C. and Kurowicka, D., 2013. Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59, pp.52-69. `__ \ No newline at end of file +* `Dissmann, J., Brechmann, E.C., Czado, C. and Kurowicka, D., 2013. Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59, pp.52-69. `__ diff --git a/docs/source/index.rst b/docs/source/index.rst index 4490c527..5dbba4be 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -107,8 +107,8 @@ This project is licensed under an all rights reserved licence. copula_approach/mispricing_index_strategy copula_approach/vine_copula_intro copula_approach/cvine_copula_strategy - copula_approach/utility_functions copula_approach/partner_selection + copula_approach/utility_functions .. toctree:: :maxdepth: 2 From f23f8f7ead7134c36d75d9606ac906c467d5c83a Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 16:38:40 +0200 Subject: [PATCH 102/103] Added CVine Copula Module to the changelog --- docs/source/changelog.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/source/changelog.rst b/docs/source/changelog.rst index 1f1c402e..1989ea60 100644 --- a/docs/source/changelog.rst +++ b/docs/source/changelog.rst @@ -12,6 +12,8 @@ Changelog .. For Help: https://releases.readthedocs.io/en/latest/index.html +* :feature:`44` CVine Copula and CVine Copula Strategy added to the Copula Approach Module. +* :support:`44` CVine Copula and CVine Copula Strategy documentation. * :feature:`40` Vine Copula Partner Selection Approaches added to the Copula Approach Module. * :support:`40` Vine Copula Partner Selection Approaches documentation. * :support:`38` Removed TensorFlow from requirements and adjusted installation guide. From 9fb0dbc0d844a0f822ece8c37df128520006041f Mon Sep 17 00:00:00 2001 From: PanPip Date: Tue, 13 Apr 2021 16:57:21 +0200 Subject: [PATCH 103/103] Minor pylint fix --- arbitragelab/copula_approach/vinecop_generate.py | 2 -- 1 file changed, 2 deletions(-) diff --git a/arbitragelab/copula_approach/vinecop_generate.py b/arbitragelab/copula_approach/vinecop_generate.py index 94000b53..95e280bf 100644 --- a/arbitragelab/copula_approach/vinecop_generate.py +++ b/arbitragelab/copula_approach/vinecop_generate.py @@ -28,8 +28,6 @@ def __init__(self): Initialize. """ - pass - class CVineCop(RVineCop): """