Pairs Trading: A Statistical Arbitrage Introduction

Pairs trading is market-neutral: you go long one instrument and short a correlated peer, betting the spread between them reverts to its historical mean. The edge comes from a temporary divergence, not from market direction.

The foundation: cointegration, not correlation

Correlation measures whether two assets move together; cointegration measures whether the spread between them is stationary — it returns to a stable mean. You need cointegration. Two assets can be highly correlated yet drift apart forever (e.g. two growth stocks where one outgrows the other). Test with the Engle-Granger or Johansen test; aim for a p-value below 0.05 on a 1–2 year window.

Building the spread

• Run an OLS regression of price A on price B to get the hedge ratio β.
• Spread = Price A − β × Price B.
• Compute the rolling z-score of the spread: z = (spread − mean) / std, over a 60-day window.

Entry rules

• Short the spread (short A, long B) when z > +2.0.
• Long the spread (long A, short B) when z < −2.0.
• Size the legs so dollar exposure matches: shares of B = β × shares of A. This is what makes it market-neutral.

Stop and target

• Target: exit at z = 0 (the mean). That is the full fill.
• Stop: exit if |z| exceeds 3.5–4.0. A spread that keeps diverging past 4 sigma is breaking down — the cointegration relationship has shifted (a merger, a fundamental change). Hold on and it can run to 8 sigma and beyond.
• R/R: typically 1.5–2R because the target is 2 sigma and the stop is around 4 sigma.

What breaks pairs

• Fundamental regime change: a buyout, bankruptcy, or business-model shift severs the link. Always check news on a diverging pair.
• Beta drift: β changes over time. Re-estimate monthly and re-hedge.
• Transaction costs: two legs, two spreads, two commissions. The spread move must exceed ~0.3–0.5% round-trip to be profitable. Trade liquid pairs (large-cap equities, major ETFs).

Sizing and review

Risk 0.5–1% per pair. Track each pair's hit rate and average R; retire pairs whose cointegration p-value rises above 0.10 or whose fill rate drops below 60% over 20 trades. Pairs trading is a portfolio strategy — running 5–10 uncorrelated pairs smooths the returns and reduces reliance on any single relationship holding.