The statistics of reversion

A mean-reversion strategy is an applied statistics problem wearing a trading costume. Three ideas carry almost all of it: the mean, the spread, and stationarity. Understand those three in plain language and you can see through most of the marketing that surrounds the strategy.

The mean is a choice, not a fact

There is no single “true” mean for a price. A 20-day moving average, a 200-day one, a valuation model and a pairs relationship are all defensible means, and they disagree constantly. Choosing the window is the first real decision in any reversion strategy, because it defines what counts as normal. A short window calls a price stretched after a quick move; a long window waits for a deep one. Neither is right in the abstract — the right window is the one whose stretches actually tend to close on the clock you intend to trade.

The spread tells you when a gap is unusual

A gap from the mean is only informative relative to how much the price normally moves. The standard deviation — the typical size of a wiggle around the mean — is the yardstick. A price two standard deviations below its mean has stretched into territory it reaches only occasionally; a price half a deviation away is barely off its perch. Most systematic reversion rules are, underneath, a statement like “act when the gap exceeds this many deviations, and close as it shrinks back toward zero.” The conviction grade on a measured model is a refinement of exactly this: how unusual was the stretch, scored against the model's own history.

Stationarity: the property that makes reversion possible

Here is the idea the marketing leaves out. Reversion only makes sense if the price has a stable level to revert to. A statistician calls a series with a stable mean and spread “stationary.” A pure random walk is not stationary — it has no home to return to, so betting it reverts is betting on nothing. Real prices sit somewhere in between, and the genuine edge in reversion trading is finding the series, the pair, or the regime where the behaviour is stationary enough that stretches really do tend to close. This is also why a strategy that worked for years can stop working: the series stopped being stationary, and the mean it was reverting to walked away.

The one-line test for any reversion claim: is there a reason this price has a stable level to come back to? If the answer is “it just always has,” treat the strategy as fragile until the record proves otherwise.

From statistics to a graded trade

A model puts these three ideas to work mechanically. It fixes a mean, measures the current stretch in standard deviations, checks that the series has behaved as if it has a stable level, and only then issues a trade — with a conviction grade that encodes how far into the tail the stretch sits. Because the grade is a measured quantity rather than a feeling, it can be calibrated, recorded, and — on the worked example — hashed in place so it cannot be revised after the outcome. That is the bridge from the statistics on this page to a grade that actually means something.