Half-life of mean reversion
A z-score says how far out a spread is. Half-life says how long it has historically taken to come halfway back — the difference between a trade and a wait.
The missing dimension
A spread two standard deviations from its mean is interesting. A spread two standard deviations from its mean that historically takes eleven days to come halfway back is a different proposition from one that takes four months.
Both show the same z-score. Only one of them fits inside a holding period you would tolerate, and only one of them has a funding cost you can estimate.
Half-life is the number that separates them.
How it is estimated
The estimate comes from an Ornstein–Uhlenbeck model — the standard continuous-time description of a quantity pulled back toward an average. Its discrete form is a regression of the change in the spread on the level of the spread:
Δspread(t) = λ · spread(t−1) + ε
The idea is direct. If λ is negative, then a spread sitting above its mean tends to fall, and one sitting below tends to rise: the further out it is, the harder it is pulled back. λ measures the strength of that pull.
From λ, the half-life follows:
half-life = −ln(2) / λ
That is the number of bars over which half of a deviation has historically been eliminated. It is the same arithmetic as radioactive decay, applied to distance from a mean.
A worked value: λ = −0.063 gives −0.693 / −0.063 ≈ 11 bars. On daily candles, eleven days to close half the gap — so roughly 22 to close three quarters of it, and so on. The decay is geometric, not linear, which means the last part of the journey takes as long as the first part did.
When the estimate is meaningless
This is where most of the practical value sits, because the formula returns a number in cases where it should not.
λ positive or zero. The spread was not being pulled back at all over the window — it was drifting, or wandering without an anchor. The formula yields a negative or infinite half-life. There is no reversion to measure. This site reports nothing rather than a number.
Half-life longer than the sample. A 90-bar window that produces a 260-bar half-life has not observed a single full reversion. The estimate is an extrapolation from a fragment of one, and the confidence interval around it is wide enough to be useless. This site discards these estimates rather than reporting them — a blank cell on a pair page means the estimate failed a check, not that the data was missing.
Half-life of one or two bars. Technically strong reversion; practically, usually microstructure. Bid-ask bounce and stale quotes produce exactly this signature. Worth treating as a data-quality flag.
Reading the value
The units are bars on the timeframe you are looking at, not days. On a 1-hour chart, a half-life of 11 means eleven hours. The site labels the unit alongside the value for this reason.
Rough bands, for daily bars:
Under 10 — fast. The spread has historically snapped back quickly. Also the range where microstructure noise is easiest to mistake for reversion.
10 to 30 — the range where a deviation and a plausible holding period line up.
30 to 90 — slow. The position has to survive a long time, and the funding cost of holding both legs starts to compete with the size of the move.
Above 90, or absent — either no measurable reversion, or reversion too slow to distinguish from drift.
The assumption underneath
Half-life describes what happened inside the fitted window and carries one assumption that deserves to be stated: that the relationship producing the reversion continues to exist.
Nothing in the estimate can verify that. A pair can have a clean, fast, well-measured half-life over the last quarter and no relationship at all going forward, because one of the legs changed — a new listing venue, a protocol migration, an unlock schedule, a change in what the asset is understood to be. The statistic will keep reporting the historical figure until the window rolls past the break.
Treat a good half-life as a reason the pair is worth understanding, not as evidence it will behave. And read it together with the hedge ratio and correlation: a fast half-life on a pair whose β is unstable is a precise measurement of an unstable thing.
Every pair page on this site shows the half-life with its unit and its window, and the screener can be sorted by it.
These pages describe how the site computes its metrics. They are not trading advice and not a recommendation to enter any position.