Cointegration

What is Cointegration?

Cointegration is a long-run statistical tether between price series. Two or more series that each wander without a fixed mean are cointegrated when some linear combination of them is stationary: the weighted spread oscillates around a stable level even though the individual legs drift freely. The idea was formalized by Engle and Granger (1987). The Engle-Granger procedure tests it by regressing one leg on the other and checking the residual for stationarity; the Johansen test generalizes to several series at once and counts how many independent cointegrating relationships exist. It is distinct from correlation, which measures whether returns move together bar to bar, not whether levels stay anchored over months.

The concept matters because it is the statistical justification for spread and pairs trading: if the spread is stationary, deviations from its mean are expected, though never guaranteed, to be corrected, so the spread can be normalized (commonly z-scored) and faded at extremes with a hedge ratio taken from the cointegrating regression. The standing caveat is fragility: a relationship estimated in one window can weaken or break when fundamentals change, and a spread can keep widening far longer than a backtest suggests.

How traders use it

• Pairs selection and sizing: screen related instruments for cointegration, take the hedge ratio from the regression, and trade z-score extremes of the spread back toward its mean, the core of a pairs trading stack.
• Relationship monitoring: re-test the spread on rolling windows so positions are only taken while the equilibrium still appears intact, and stand down when the residual stops testing stationary.
• Hedging: constructing offsetting positions whose combined value tracks the stationary combination, reducing exposure to the common drift the legs share.

Cointegration vs related concepts