Strategy
Pairs Trading: Cointegration, Half-Life, Exit Triggers
Pairs trading bets that two cointegrated instruments will revert to their long-run relationship. The math is elegant; the operational discipline is where most pairs strategies fail.
Pairs trading bets that two instruments with a stable long-run statistical relationship will revert to that relationship after temporary divergence. It is the canonical statistical arbitrage strategy — and the canonical example of how a clean math model meets messy live execution.
Core mechanic
- Find a cointegrated pair. Run an Engle-Granger or Johansen test on price series. Pairs that pass cointegration tests have a stationary spread; pairs that pass only correlation tests do not.
- Compute the spread:
spread_t = log(P_A,t) − β × log(P_B,t), where β is the cointegration coefficient. - Trade z-scores of the spread. Enter when |z| > entry threshold; exit at z = 0 (or opposite-sign threshold).
Half-life and exit timing
The half-life of a stationary AR(1) spread tells you how long mean reversion typically takes:
half_life = ln(2) / |ln(ρ)|
where ρ is the AR(1) coefficient. A half-life of 5 days means a typical divergence takes 5 days to halve. A half-life of 60 days means the spread mean-reverts on the order of a quarter — sometimes too slow to be tradeable.
Practical rule: if half-life > 30 days, the carrying cost of the position usually exceeds the edge.
Failure modes
- Cointegration breaks. Two stocks were cointegrated for 5 years. Then one company changes business model. The spread doesn't mean-revert; it walks away.
- Crowded trades. When other quant desks identify the same pair, the spread compresses too fast for entry and stays at zero. Edge gone.
- Borrow / financing changes. Short-leg borrow cost spikes during stress. Pair trade economics fall apart.
Implementation discipline
- Re-test cointegration monthly. A pair that tested 1% significant a year ago may have drifted to 10%. Stop trading pairs that fail re-tests.
- Stop-loss on z-score, not P&L. If z keeps widening past your entry threshold, the pair is breaking — exit, don't add.
- Beta-hedge the basis risk. Even cointegrated pairs have residual market sensitivity in stress.