What is Mean Reversion? The Physics of Price Equilibrium

Mean reversion is the theory that prices eventually return to their long-term average. Explore the Ornstein-Uhlenbeck process and the math of equilibrium.

Five years of pair returns between PEP and KO revealed why Mean Reversion is the most reliable source of alpha in market-neutral trading. Mean reversion is the mathematical assumption that an asset's price or volatility will tend to move back toward its historical average over time.

In stochastic calculus, we model a mean-reverting price $x_t$ using the Ornstein-Uhlenbeck (OU) process: $dx_t = \theta (\mu - x_t)dt + \sigma dW_t$. In this equation, $\mu$ is the long-term mean, $\sigma$ is the volatility, and $\theta$ is the speed of mean reversion. The larger the $\theta$, the faster the price returns to its average after a shock.

Not all assets revert to a mean. Growth stocks often exhibit trending behavior (momentum), which is the opposite of mean reversion. Quants use the Hurst Exponent ($H$) to classify time series. If $H < 0.5$, the series is mean-reverting. If $H > 0.5$, it is trending. If $H = 0.5$, it is a random walk (Brownian Motion).

1. Overextended Moves: When an asset is $2$ or $3$ standard deviations away from its moving average. 2. Cointegration: Two stocks that move together, where the difference (spread) between them is stationary. 3. Volatility: Market volatility is almost always mean-reverting, even if the underlying prices are not. This connects to concepts like the volatility smile and SABR model.

To trade a mean reversion strategy, you must first prove the asset is not in a momentum phase.