Mean reversion and momentum are the two dominant, statistically documented families of quantitative return anomalies. They are near opposites: mean reversion bets that extreme deviations correct, momentum bets that trends persist. Most systematic portfolios blend both because they tend to perform in different market regimes.
Mean Reversion: The Statistical Basis
A mean-reverting series can be modeled with an Ornstein-Uhlenbeck process, whose key parameter is the speed of reversion. The half-life tells you how many periods it takes to close half the gap back to equilibrium.
half-life = −ln(2) / λ, where Δx(t) = λ(μ − x(t−1)) + ε(t)If λ = 0.05 per day, half-life = −ln(2)/−0.05 ≈ 13.9 days. This tells you the natural holding period for a mean-reversion trade on that series — entering earlier is premature, holding much longer than 2-3 half-lives adds risk without added expected payoff.
Momentum: The Statistical Basis
Momentum strategies typically rank assets by trailing 3-12 month returns and go long the winners, short the losers (or simply long winners in a long-only context). The classic finding, robust across decades and asset classes, is that recent winners continue outperforming for several months before reversing.
| Dimension | Mean Reversion | Momentum |
|---|---|---|
| Typical horizon | Minutes to weeks | Weeks to months |
| Works best in | Range-bound, high-liquidity markets | Trending markets with sustained flows |
| Fails in | Strong trends (keeps fading a real move) | Choppy/range markets (whipsaws) |
| Risk profile | Small frequent wins, occasional large loss | Larger, less frequent wins, frequent small losses |
Diagnosing the Regime: The Hurst Exponent
Rather than guessing which model fits, quants estimate a Hurst exponent on a rolling window. Values below 0.5 suggest mean-reverting behavior, values above 0.5 suggest trending/persistent behavior, and values near 0.5 suggest the series is close to a random walk where neither approach has a durable edge.
Mean-reversion traders who don't check regime will 'buy the dip' repeatedly into a genuine downtrend, averaging down into a structural decline. This is the single most common way systematic mean-reversion accounts blow up.
Combining Both
- ▸Use momentum as a regime filter for mean reversion: only fade extremes when longer-term trend is flat or opposing the extreme.
- ▸Diversify across both simultaneously with independent capital allocations to smooth the equity curve across regimes.
- ▸Recompute the Hurst exponent or ADF test periodically — regimes shift, sometimes for years at a time.
The Bottom Line
Neither mean reversion nor momentum is universally superior — each is a bet on a specific statistical regime. The traders who blow up are usually the ones who never tested which regime their strategy actually needs to survive.