Mean Reversion
Quick Reference
Tendenza dei prezzi a ritornare verso la media storica dopo deviazioni. Opposto di trend following.
Definizione
Mean Reversion: Fenomeno per cui prezzi/valori estremi tendono a tornare verso media nel tempo.
Trading implication: - Prezzi alti → aspettati scendano - Prezzi bassi → aspettati salgano
Teoria di Base
Assumption: Mercati hanno valore "fair": - Price > fair value → overpriced → sell - Price < fair value → underpriced → buy
Converge verso fair value over time.
Esempi Naturali
Volatilità
Volatility clustering ma mean reverts: - σ spike a 40% (crisis) - Gradualmente torna a 15-20% (normal) - Long-term mean reversion
Yield Spreads
Credit spreads: - Crisis: Widen a 500 bps - Recovery: Tighten back to 100-150 bps - Mean revert verso historical average
Relative Value
Stock pairs: - Coca-Cola vs Pepsi - Historically trade similar - Se spread diventa troppo largo → mean revert
Mean Reversion Strategies
Basic Approach
If (Price - Moving Average) / Std Dev > +2:
Sell (overbought)
If (Price - Moving Average) / Std Dev < -2:
Buy (oversold)
Z-score based trading.
Pairs Trading
Trade relative value: 1. Find correlated pair (A, B) 2. Calculate spread: Spread = Price_A - β×Price_B 3. Trade when spread deviates from mean 4. Close when spread reverts
Market neutral strategy.
Time Horizons
High Frequency (Seconds-Minutes)
Microstructure mean reversion: - Bid-ask bounce - Order flow imbalances - Very fast mean reversion
But: High costs, need speed, retail can't compete.
Medium Term (Days-Weeks)
Tactical mean reversion: - Oversold/overbought on oscillators - RSI, Stochastics - Moderate speed
Risky: Can trend against you.
Long Term (Months-Years)
Valuation mean reversion: - P/E ratios - Yield curves - Economic cycles
Slow but more reliable.
Mean Reversion vs Trend
Trend Following
- Momentum continues
- Buy high, sell higher
- Positive skew
- Works in trending markets
Mean Reversion
- Extremes reverse
- Buy low, sell high
- Negative skew
- Works in ranging markets
Complementary strategies!
Negative Skew Problem
Mean reversion typical returns: - Many small wins (successfully fade extremes) - Few large losses (when trend develops) - "Picking up pennies in front of steamroller"
Example: - 9 trades: +1%, +1%, +1%, +1%, +1%, +1%, +1%, +1%, +1% = +9% - 1 trade: -15% (trend you fought) - Net: -6%
When Mean Reversion Fails
Regime changes: - New normal established - Old mean no longer relevant
Examples: - Interest rates 1980s: Mean 15% → New mean 2% - Volatility 2020: Old normal 15% → stuck at 25%+ for months
Danger: Fade "extreme" that becomes new normal.
Measuring Mean Reversion
Half-Life
Time for 50% reversion to mean:
Fast mean reversion: Hours-days Slow mean reversion: Months-years
Formula (AR(1) process):
Half-life = -log(2) / log(ρ)
Dove ρ = autocorrelation coefficient.
Hurst Exponent
H < 0.5: Mean reverting H = 0.5: Random walk H > 0.5: Trending
Test per identificare regime.
Safe Mean Reversion
Reduce negative skew risk:
- Quick exits: Don't fight sustained trends
- Position sizing: Small positions
- Diversification: Multiple uncorrelated signals
- Combine with trend: Only fade when no strong trend
Volatility Mean Reversion
Different from price:
Price: Può trend indefinitamente Volatility: Always mean reverts eventually
Application: Blend estimates
σ_blend = 0.7×σ_current + 0.3×σ_long_term
Short-term forecast + long-term mean reversion.
Market Regimes
Ranging Market
Characteristics: - No clear trend - Oscillates around level - Mean reversion thrives
Example: Sideways equity market 2015-2016.
Trending Market
Characteristics: - Sustained directional move - New highs/lows - Mean reversion bleeds
Example: Bull market 2009-2020 (fading rallies = losses).
Combining Strategies
Optimal approach:
Trend filter + Mean reversion: - Only mean revert if no strong trend - Use trend strength indicator - Reduces negative skew
Example:
If Trend_Strength < 0.5:
Use mean reversion signals
Else:
Use trend following signals
Asset Classes
Equities
Individual stocks: Weak mean reversion (trends common) Indices: Moderate mean reversion Relative value: Strong mean reversion (pairs)
FX
Short-term: Mean reverting (intraday) Medium-term: Mixed Long-term: Trends dominate
Commodities
Agricultural: Strong seasonal mean reversion Energy: Moderate mean reversion Metals: Trends can persist
Fixed Income
Yields: Strong mean reversion (economic cycles) Credit spreads: Very strong mean reversion
Statistical Arbitrage
Professional mean reversion:
Characteristics: - 100s-1000s of positions - Diversified across many pairs - Fast execution - Negative skew managed through diversification
Retail difficult: Need scale, speed, costs prohibitive.
Indicators
RSI (Relative Strength Index)
Oscillator 0-100: - RSI > 70: Overbought → sell - RSI < 30: Oversold → buy
Bollinger Bands
Price vs bands: - Above upper band → overbought - Below lower band → oversold
Z-Score
Z = (Price - MA) / StdDev
- |Z| > 2: Extreme, expect reversion
- |Z| < 1: Normal, no signal
Risk Management Critical
Due to negative skew:
- Stop losses: Don't let trends destroy you
- Position sizing: Small (1/4 of trend strategy)
- Diversification: Many uncorrelated bets
- Volatility scaling: Reduce size in high vol
Turnover
Mean reversion = high turnover: - Typical: 15-30× per year - Much higher than trend (5-6×) - Costs can kill profitability
Critical: Low-cost execution, tight spreads.
Performance Characteristics
Typical Mean Reversion Strategy
- SR: 0.30-0.50 (lower than trend)
- Skew: -1.0 to -2.0 (negative!)
- Max DD: Large occasional
- Win rate: 60-70% (higher than trend)
- Turnover: 15-30× (very high)
Errori Comuni
- Fighting strong trends: "It HAS to reverse!"
- No stop losses: Hoping for reversion indefinitely
- Full Kelly sizing: Negative skew + high leverage = ruin
- Ignoring costs: High turnover eats profits
- Wrong time horizon: Intraday strategy on daily data
- No diversification: Single pair = unhedged tail risk
- Assuming linear reversion: Can overshoot before reversing
Concetti Correlati
- [[Skew]] - mean reversion has negative skew
- [[Volatility Clustering]] - short-term, but mean reverts long-term
- [[Correlation]] - pairs trading uses correlation
- [[Turnover]] - mean reversion has very high turnover