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:

  1. Quick exits: Don't fight sustained trends
  2. Position sizing: Small positions
  3. Diversification: Multiple uncorrelated signals
  4. 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.

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:

  1. Stop losses: Don't let trends destroy you
  2. Position sizing: Small (1/4 of trend strategy)
  3. Diversification: Many uncorrelated bets
  4. 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