Not All Factors Crowd Equally: Modeling, Measuring, and Trading on Alpha Decay

ArXiv ID: 2512.11913 “View on arXiv”

Authors: Chorok Lee

Abstract

We derive a specific functional form for factor alpha decay – hyperbolic decay alpha(t) = K/(1+lambda*t) – from a game-theoretic equilibrium model, and test it against linear and exponential alternatives. Using eight Fama-French factors (1963–2024), we find: (1) Hyperbolic decay fits mechanical factors. Momentum exhibits clear hyperbolic decay (R^2 = 0.65), outperforming linear (0.51) and exponential (0.61) baselines – validating the equilibrium foundation. (2) Not all factors crowd equally. Mechanical factors (momentum, reversal) fit the model; judgment-based factors (value, quality) do not – consistent with a signal-ambiguity taxonomy paralleling Hua and Sun’s “barriers to entry.” (3) Crowding accelerated post-2015. Out-of-sample, the model over-predicts remaining alpha (0.30 vs. 0.15), correlating with factor ETF growth (rho = -0.63). (4) Average returns are efficiently priced. Crowding-based factor selection fails to generate alpha (Sharpe: 0.22 vs. 0.39 factor momentum benchmark). (5) Crowding predicts tail risk. Out-of-sample (2001–2024), crowded reversal factors show 1.7–1.8x higher crash probability (bottom decile returns), while crowded momentum shows lower crash risk (0.38x, p = 0.006). Our findings extend equilibrium crowding models (DeMiguel et al.) to temporal dynamics and show that crowding predicts crashes, not means – useful for risk management, not alpha generation.

Keywords: Alpha Decay, Factor Investing, Game-Theoretic Equilibrium, Crowding Analysis, Fama-French Factors, Equities

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper derives a specific functional form for alpha decay from a game-theoretic equilibrium model, indicating advanced mathematical formulation, and rigorously tests it against multiple alternatives using extensive historical Fama-French data with statistical metrics like R-squared and out-of-sample forecasts.

  flowchart TD
    A["Research Goal<br>Model & Validate Factor Alpha Decay"] --> B["Data Input<br>Fama-French Factors 1963-2024"]

    B --> C["Methodology<br>Game-Theoretic Equilibrium Model"]
    
    C --> D["Computational Process<br>Fit Hyperbolic vs Linear/Exponential Models"]
    
    D --> E{"Key Findings"}
    
    E --> F["<b>(1) Model Validation</b><br>Hyperbolic Decay fits Mechanical Factors<br>(Momentum R² = 0.65)"]
    E --> G["<b>(2) Crowding Divergence</b><br>Mechanical vs Judgment-based Factors"]
    E --> H["<b>(3) Acceleration</b><br>Crowding increased post-2015<br>(ETF growth ρ = -0.63)"]
    E --> I["<b>(4) Return Efficiency</b><br>Crowding selects failed strategies<br>(Sharpe 0.22 vs 0.39)"]
    E --> J["<b>(5) Tail Risk Prediction</b><br>Crowding predicts crashes<br>(Reversal 1.7-1.8x crash risk)"]