Return Z-Score Reversion

The z-score mean reversion strategy is the most statistically clean version of mean reversion trading: it standardises the recent return relative to its own historical distribution, then trades when that standardised deviation exceeds a threshold. It is agnostic about price levels — it operates entirely in the space of standardised deviations.

The idea originates in statistics. A z-score of +2 means the observation is 2 standard deviations above the recent mean — an event that under normality would occur about 2.5% of the time. If returns are mean-reverting, a z-score of +2 is a bet that the extreme observation will be followed by a correction toward zero. The larger the absolute z-score, the stronger the signal.

This is closely related to the "convergence trade" logic underlying statistical arbitrage: you are not betting on a direction per se, but on the reversion of a statistical anomaly. Unlike price-level strategies (Bollinger Bands), the z-score approach works on returns, which are more naturally stationary than price levels.

Key assumptions: (1) Log returns are approximately i.i.d. within the rolling window — the window mean and variance are meaningful parameters. (2) Autocorrelation in returns is negative at short lags (mean reversion). (3) The threshold is appropriately set for the instrument's volatility regime. If returns are fat-tailed (as they typically are), the 1.5-sigma event is more common than normality predicts.

The strategy fails in trending markets and during regime changes. When a new information event causes a sustained shift in the price level, the z-score keeps rising rather than reverting. Position sizing is critical: because the strategy can be wrong during trending regimes for long stretches, naive full-position sizing leads to deep drawdowns. Many practitioners use Kelly-scaled or volatility-targeted position sizing alongside z-score signals.