Cointegration and Pairs Trading

Two non-stationary series $X_t$ and $Y_t$ are cointegrated if some linear combination $X_t - \beta Y_t$ is stationary. Each series wanders, but they wander together.

Cointegrated pairs are the foundation of statistical arbitrage. If $\log P_A$ and $\log P_B$ are cointegrated with hedge ratio $\beta$, the spread $\log P_A - \beta \log P_B$ is stationary and mean-reverting. When the spread widens, sell the rich asset and buy the cheap one; when it reverts, close the position.

Practical pipeline: pre-screen pairs, test for cointegration (Engle-Granger or Johansen test), estimate the hedge ratio, model spread dynamics (often AR(1) or Ornstein-Uhlenbeck), and trade when the spread crosses entry/exit thresholds expressed in standard deviations.

Limits: cointegration relationships break. Companies merge, regulations change, structural breaks appear. Successful pairs traders monitor for changes in the cointegration relationship and exit when it deteriorates.