Fama-French Factors

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. ...

An empirical study of market risk factors for Bitcoin ArXiv ID: 2406.19401 “View on arXiv” Authors: Unknown Abstract The study examines whether fama-french equity factors can effectively explain the idiosyncratic risk and return characteristics of Bitcoin. By incorporating Fama-french factors, the explanatory power of these factors on Bitcoin’s excess returns over various moving average periods is tested through applications of several statistical methods. The analysis aims to determine if equity market factors are significant in explaining and modeling systemic risk in Bitcoin. ...

Data-generating process and time-series asset pricing ArXiv ID: 2405.10920 “View on arXiv” Authors: Unknown Abstract We study the data-generating processes for factors expressed in return differences, which the literature on time-series asset pricing seems to have overlooked. For the factors’ data-generating processes or long-short zero-cost portfolios, a meaningful definition of returns is impossible; further, the compounded market factor (MF) significantly underestimates the return difference between the market and the risk-free rate compounded separately. Surprisingly, if MF were treated coercively as periodic-rebalancing long-short (i.e., the same as size and value), Fama-French three-factor (FF3) would be economically unattractive for lacking compounding and irrelevant for suffering from the small “size of an effect.” Otherwise, FF3 might be misspecified if MF were buy-and-hold long-short. Finally, we show that OLS with net returns for single-index models leads to inflated alphas, exaggerated t-values, and overestimated Sharpe ratios (SR); worse, net returns may lead to pathological alphas and SRs. We propose defining factors (and SRs) with non-difference compound returns. ...

A Literature Review of the Size Effect ArXiv ID: ssrn-1710076 “View on arXiv” Authors: Unknown Abstract The size effect in finance literature refers to the observation that smaller firms have higher returns than larger firms, on average over long horizons. It also Keywords: Size effect, Small-cap premium, Asset pricing, Equity returns, Fama-French factors, Equities Complexity vs Empirical Score Math Complexity: 2.0/10 Empirical Rigor: 3.0/10 Quadrant: Philosophers Why: The paper is a literature review summarizing existing findings with minimal original mathematical derivations or models, and while it discusses empirical results, it does not present new backtests, datasets, or implementation-heavy analysis. flowchart TD A["Research Goal<br>How does firm size impact equity returns?"] --> B["Methodology<br>Literature Review & Empirical Analysis"] B --> C["Data Sources<br>CRSP, Compustat, Fama-French Datasets"] C --> D["Computational Processes<br>Portfolio Sorts, Regression Analysis, Factor Models"] D --> E["Key Findings<br>Size Effect Exists but Varies by Market & Period"] E --> F["Outcomes<br>Small-Cap Premium Often Captured by HML Factor or Disappears in Large Caps"]