This project is to apply Copula Function to pair trading strategy in American stock market by Python and R.
I used the package rpy2.robjects in Python to help me run the R code in Python environment because I can combine the benefit of Pyhton and R together. Python does better on big data and R is good for applying copula approach.
In statistics, a copula function is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform. Copulas are used to describe the dependence between random variables.
The objective of pairs trading is to identify the relative overvalued and undervalued positions between two stocks that are closely related, with a long-run relationship.
Such relative mispricing occurs if the spread between the two stocks deviates from its equilibrium, and excess returns will be generated if the pair is mean-reverting (that is, any deviations are temporary, and will return to its equilibrium after a period of adjustment). In this situation, the strategy will simultaneously short the relatively overvalued stock and long the relatively undervalued.
Therefore, the most important part is the identify the relative overvalued stock and the undervalued stock. That’s what copula can help us.
I downloaded the all the 505 stocks' daily close price in S&P 500 index from Bloomberg form 2008 to 2018. And after calculating the log-retrun, I tested the correlation for all the stocks pairs and selected the pairs whose absolute correlation is greater than 0.85.
For each selected stock pairs, Calculate the marginal distributions by the R function fit.gpd and fit the copula function with “BiCopSelect” function in the packages “VineCopula”, which can help to select the best-fitted copula from a set of copula family.
Stocks are relatively undervalued if the conditional probability is less than 0.5 and relatively overvalued if the conditional probability is greater than 0.5. Therefore, Our strategy selects the upper bound of 0.95 and lower bound of 0.05 for the threshold of conditional probabilities as trading triggers.
And When the both conditional probability cross the 0.5 boundary, we close the position. Which means when the 0.95 probability come below 0.5 and the 0.05 probability go above 0.5, that’s the exit signal.
[Nonlinear dependence modeling with bivariate copulas: Statistical arbitrage pairs trading on the S&P 100] by Christopher Krauss and Johannes Stübinger