Half-life of mean reversion, explained

When the gap between two cointegrated stocks stretches, it tends to drift back toward normal. The half-life measures how quickly that has happened in the past: the typical number of trading days for a stretched gap to shrink by half.

Reading it

• A half-life of 3 days means a stretch has typically shrunk by half within about three trading days — a fast-reverting pair.
• A half-life of 10 days means the same process has usually taken around two weeks.
• Most of the gap is usually gone after about two half-lives, which is why PairsCopilot describes a pair's typical time to close as roughly twice its half-life.

Why it matters

The half-life sets the clock. A pair that has historically taken a week to close is held about a week; one that takes a month ties up capital — and pays the cost of borrowing the short stock — for a month. It also defines when a setup has simply taken too long: a gap that is still open well past its usual time is a sign the relationship may not be behaving as before.

PairsCopilot closes a modeled trade that has neither closed its gap nor reached its safety stop within about twice its half-life, and reports it as "Closed: max hold reached".

What it is not

The half-life is an average of past behaviour. It does not promise that the next gap will close on schedule, or at all. It is one input among several, recomputed as new prices arrive.