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Pairs trading questions
Denis Khripushin
posted Oct 29, 2019
Pairs Trading Mean Reversion

Hi all,

Could someone please help me with solving the following questions ?

I formed a stock universe where the program seeks cointegrated pairs using python (stocks from SP500). Also there are functions to plot the spread.
So I defined z-score, linear regression and price ratio functions.
Here are GILD/WFC pair, for instance. The slope for our combination is 0.74
1. What exactly positions should I open using the z-score plot at the current moment (when z-score below 0 , around -2)? Should it be opened short WFC vs long 0.74*GILD or long WFC vs short 0.74*GILD ?
2. about fitting the spread to OU process. Here are the formula to compute the speed of mean-reversion .
B - slope = 0.74
So in our example : the speed = -lnB/t = -ln0.74/1/252 = 0.3/0.00396 = 75.75 days for reverting to the equilibrium level , are these arguments correct ?

Thank's in advance.

1 response
Karl Mun
Oct 29, 2019

Hi Denis, there is a good example: Quantopian Lecture 46 based on an implementation by Ernest Chan in algorithmic trading.

You may find these functions in the example algorithm useful for your purpose:

def hedge_ratio(Y, X, add_const=True):  
def computeHoldingsPct(yShares, xShares, yPrice, xPrice):

For simplicity, the notional weights for y_target_shares = ±1 and X_target_shares = ∓hedge are for purpose of the lecture, and may not be applicable to the specifics of your actual pairs.

Hope this helps.

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