Statistical Arbitrage: Pairs Trading and Cointegration

Module: Fintech AI | Difficulty: Advanced

Cointegration

Engle-Granger Test

1. Regress on
2. Test residuals for unit root
3. If stationary, pair is cointegrated

Half-Life of Mean Reversion

where is the AR(1) coefficient.

import numpy as np
from statsmodels.tsa.stattools import coint

class PairsTrading:
    def __init__(self, lookback=60, z_entry=2, z_exit=0.5):
        self.lookback = lookback; self.z_entry = z_entry; self.z_exit = z_exit
    def find_pairs(self, prices_df, significance=0.05):
        pairs = []
        symbols = prices_df.columns
        for i in range(len(symbols)):
            for j in range(i+1, len(symbols)):
                score, pvalue, _ = coint(prices_df[symbols[i]], prices_df[symbols[j]])
                if pvalue < significance:
                    pairs.append((symbols[i], symbols[j], pvalue))
        return pairs
    def generate_signal(self, prices1, prices2):
        spread = prices1 - np.polyfit(prices2, prices1, 1)[0] * prices2
        z = (spread[-1] - spread.mean()) / spread.std()
        if z < -self.z_entry: return 'long_spread'
        elif z > self.z_entry: return 'short_spread'
        elif abs(z) < self.z_exit: return 'close'
        return 'hold'

Research Insight: Pairs trading profitability has declined as more participants exploit the same opportunities. However, the strategy remains profitable when combined with machine learning for pair selection and signal generation. The key is finding pairs with fast mean reversion and high Sharpe ratios.