A model simulation shows how pairs trading could be used for two S&P500 traded stocks. It proofs that the strategy is successful on real data, which is downloaded via the pandas-datareader. In the report and poster section a profound analysis of the pairs trading underlying Ornstein-Uhlenbeck process is done. Rigorous mathematical formulations can be found in this section also.
Keywords: Stochastic differential equations, Ornstein-Ulenbeck Process, Pairs Trading, S&P500
- Load stock data from slib.py with stockvals().
- Determine two stocks suitable for the pairs trading strategy with find_cointegrated_pairs() in CointHurst.py. Note tha the output 'pairs' already suggest pairs of stocks with a significance level below 0.05 using a cointegration test. A full map of pvalues for pairwise cointegration can be displayed with covplot().
- Use pairstrade() in PairsTrade.py to execute the pairs trading strategy on the two stocks (id0, id1) under consideration. The parameters that determine the success of the strategy are defined in the pairstrade() input param: f8[d,buy_signal,sell_signal] - threshold parameters for the time window, buying and selling signal. A graph that shows the buying and selling signal and how much money the strategy would have made can be displayed by setting plot = True.
import pandas_datareader.data as web
from statsmodels.tsa.stattools import coint
import numpy as np
import matplotlib.pyplot as plt
import slib as slb #Custom library
#%% Load data
names[indices.astype(int)],symbols[indices.astype(int)],variation,close_val,open_val = stockvals(df,start_date,end_date)
data = pd.DataFrame.from_records(close_val)
#%% Find suitable stocks for pairs trading
scores, pvalues, pairs = slb.find_cointegrated_pairs(close_val)
slb.covplot(pvalues,symbols,'Cointegration')
#%% Perform trading strategy
start_year = 2010; end_year = 2020;
d, buy_signal, sell_signal = 252 0.05, 0.01
param = [d,buy_signal,sell_signal]
money,buy,sell,k,Y_tilde,t,S0,S1 = slb.pairstrade(param,data_train,id0,id1,names,start_year,end_year,plot=True)| Cointegration |
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Map of p-values for pairwise cointegration. The statistical test for cointegration checks how likely the closing values of two stocks are mean reversive. The null hypothesis is no cointegration. Hence low p-values suggest that the stochastic processes under consideration show the property of being mean reversiv and can be described as an Ornstein-Uhlenbeck processes. They are thus suitable to perform the pairs trading strategy.
| Buying-Selling Signal | Trade Performance |
|---|---|
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Buying and selling signals for two suitable S&P500 stocks (Adobe Inc.-Cintas Corporation) over a time period of 10 years (2010-2020). The strategy started with 0 EUR, ended with 3000 EUR of hypothetical profit.
Fork from the Developer- branch and pull request to merge back into the original Developer- branch.
Working updates and improvements will then be merged into the Master branch, which will always contain the latest working version.
With:
Numpy,
Matplotlib,
Pandas, pandas-datareader, Statsmodels,
slib (custom)