Mean Reversion
The tendency of prices or returns to revert to a long-run average after deviations.
Definition
Mean reversion is the idea that after a large move (up or down), price or return tends to move back toward its historical mean. Often modeled with z-scores or half-life of reversion.
Why it matters
- Strategies that “fade” extremes (e.g. buy after -2σ move) rely on mean reversion.
- Works in range-bound regimes; fails in strong trends.
Common mistakes
- Assuming mean reversion without testing (e.g. unit root vs stationary).
- Using a single lookback; half-life can vary.
- Ignoring regime (reversion in calm markets, momentum in crisis).
Notation
Ornstein–Uhlenbeck: ( dX_t = \theta(\mu - X_t)dt + \sigma dW_t ). Half-life ( \approx \ln(2)/\theta ).