Half-Life: How Fast a Spread Returns to Its Mean
The <strong>half-life</strong> of a cointegrated pair is the expected number of days for its spread to return halfway from its current level to its long-run equilibrium. It is derived from the mean-reversion speed parameter (λ) of an Ornstein-Uhlenbeck process fit to the spread: <code>half_life = ln(2) / |λ|</code>. Short half-lives signal fast-reverting relationships. Long half-lives signal relationships that drift before correcting.
What it measures
Imagine the spread between two cointegrated instruments as a rubber band tethered to a central value. Half-life tells you how taut the band is. A 5-day half-life means the pair pulls strongly toward its equilibrium — if the spread is stretched today, expect half the stretch to be gone within a week. A 60-day half-life means the band is slack — the pair may drift in one direction for months before correcting.
How to read it
Closelook classifies half-lives in four bands:
- < 5 days — fast reversion. The pair is tightly anchored. Deviations correct quickly. Good setups for short-horizon mean-reversion trades.
- 5-20 days — medium reversion. Workable mean-reversion, but watch for half-life drift (see below).
- 20-60 days — slow reversion. The pair is cointegrated in principle but hasn't been asked to correct much. Positions need patience.
- > 60 days — questionable. The statistical test still passes, but the relationship is too loose to trade. Treat the pair as a research signal, not a tradeable spread.
The Lab's cointegration page shows each pair's current half-life alongside its 26-week trajectory. A half-life trending down means the relationship is tightening — either the mechanism driving cointegration is strengthening, or a shock pushed the pair into a regime where correction is more urgent.
Why it matters
Half-life is where cointegration stops being abstract and becomes tradeable. A pair with a 2-sigma spread stretch and an 8-day half-life is a very different trade from one with a 2-sigma stretch and a 60-day half-life. The first is a straightforward mean-reversion setup; the second is a bet that the historical relationship will reassert itself in a time horizon longer than most portfolios are willing to hold.
Half-life also decays. A relationship that used to have a 10-day half-life might drift to 30 days as the structural linkage weakens. Tracking the trajectory week-over-week is how you notice a cointegrated pair going structurally stale before it breaks statistically.
In the Lab
Each of the 28 tracked pairs in the Cointegration Matrix exposes its current half-life in the tooltip and pair-detail view. The half-life trend chart (52-week) shows whether the pair's mean-reversion speed is stable, shortening, or lengthening.