Mean Reversion¶
OVERVIEW¶
Mean reversion is the tendency of a measurable quantity — price, volatility, spread, or valuation ratio — to return to its long-run average after deviating significantly from it. Tapeboard surfaces mean-reversion signals across equities, spreads, and implied volatility in real time.
Note
Mean reversion is the mathematical opposite of momentum. Most quantitative strategies combine both: momentum in trending regimes, mean reversion in ranging ones.
Extremes are treated as temporary, not self-reinforcing. A mean-reversion position bets on a quantity returning toward its historical norm after breaching a defined threshold.
HOW MEAN REVERSION IS QUANTIFIED¶
Tapeboard uses four core measures to detect and rank mean-reversion setups:
| Measure | Formula / Definition | Interpretation |
|---|---|---|
| Ornstein-Uhlenbeck Process | dX_t = θ(μ − X_t)dt + σdW_t |
Continuous-time model; θ = speed, μ = long-run mean |
| Z-Score | (Current Value − Rolling Mean) / Rolling Std Dev |
Practical signal threshold; ±2 or ±3 triggers entry |
| Half-Life | −ln(2) / ln(β₁) where β₁ = lag-1 autocorrelation |
Time for a deviation to revert 50% toward the mean |
| Hurst Exponent | H < 0.5 = mean-reverting; H = 0.5 = random walk; H > 0.5 = trending | Regime classification for a given instrument |
Tip
Use the Hurst Exponent column in the scanner to pre-filter instruments before applying z-score thresholds. Applying mean-reversion logic to a trending instrument (H > 0.5) produces false signals.
WORKED EXAMPLE¶
SPY has a 20-day rolling mean of $520 and a 20-day standard deviation of $8. During a sharp intraday selloff, SPY drops to $496.
A z-score of −3.0 places SPY three standard deviations below its rolling mean. Historically, SPY closes at or below −3 sigma fewer than 0.3% of trading days.
| Parameter | Value |
|---|---|
| Entry | $496 (−3.0σ) |
| Target | $512 (−1.0σ) |
| Stop | $492 (−3.5σ) |
A pairs trader observing QQQ at −1.1 sigma would go long SPY / short QQQ, targeting normalization of the spread between them.
FEATURES¶
Signal Types¶
| Signal | Timeframe | Trigger |
|---|---|---|
| Gap Fade | Intraday | Gap-open beyond ±2σ from prior close or VWAP |
| Bollinger Band Extreme | Swing | Price touches outer band with elevated RSI reading |
| Pairs Spread | Statistical arb | Cointegrated pair spread reaches z-score threshold |
| IV Mean Reversion | Options | IV Rank or IV Percentile at historical extremes |
Scanner Columns¶
| Column | Description |
|---|---|
| Z-Score (20D) | Distance from 20-day rolling mean in standard deviations |
| Half-Life (days) | Estimated days to 50% reversion based on AR(1) regression |
| Hurst Exponent | Regime indicator; values below 0.5 confirm mean-reverting behavior |
| IV Rank | How far current implied volatility sits relative to its 52-week range |
HOW TO USE¶
- Open the Scanner and apply the Mean Reversion preset filter.
- Sort by Z-Score (20D) descending to surface the most extreme deviations.
- Confirm H < 0.5 in the Hurst Exponent column before acting on a signal.
- Check Half-Life to size holding period — longer half-lives require wider stops and more capital patience.
- Set entry at the current z-score level, target at −1σ or the rolling mean, and stop beyond the next sigma band.
- For pairs trades, navigate to Pairs → select two cointegrated instruments → monitor the live spread z-score chart.
Note
Always define maximum acceptable loss before entering a mean-reversion position. The strategy carries asymmetric loss exposure — price can move substantially further against you before reversing.
LIMITATIONS AND MISCONCEPTIONS¶
| Risk | Detail |
|---|---|
| Mean definition matters | A 20-day mean and a 200-day mean produce opposing signals in a trending market |
| Permanent mean shifts | Fundamentally impaired companies or regime changes can render any static mean misleading |
| Lookback sensitivity | Hurst Exponent and Half-Life values change materially with the lookback period selected |
| Path risk | Positions can extend well beyond entry before reverting — size accordingly |
| Drifting mean | A stock in secular decline makes a static rolling mean an unreliable anchor |
Tip
Not all deviations revert. Screen for structural breaks and recent fundamental catalysts before treating a large z-score as a signal rather than a warning.