What does the Fama-French three-factor model add beyond CAPM?

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AcadiFi · Accepted Answer

Fama and French (1993) found that two additional factors beyond market beta explain cross-sectional stock returns: SMB (Small Minus Big) captures the small-cap premium, and HML (High Minus Low) captures the value premium based on book-to-market ratio. The regression is: R_i - R_f = α + β_mkt × (R_mkt - R_f) + β_SMB × SMB + β_HML × HML + ε. Example: Brighton Value Fund has 10 years of monthly returns. OLS yields β_mkt = 0.92, β_SMB = 0.35, β_HML = 0.48, α = -0.04% per month. Annualized alpha = -0.48%, meaning after controlling for market, size, and value tilts, the fund underperformed its factor-implied return. Its positive SMB loading (tilted small) and positive HML loading (tilted value) explained the bulk of its raw outperformance. ```mermaid flowchart LR A[Market
Excess] --> E[Expected
Return] B[SMB
Factor] --> E C[HML
Factor] --> E E --> D[Alpha
Residual] ``` Interpretation: a β_HML > 0 means the portfolio behaves like a value portfolio; it earns more when value stocks beat growth stocks. The three-factor model typically raises R² from about 70% (CAPM) to 90%+ for diversified portfolios. Critics note SMB's premium has narrowed post-1990s and HML is correlated with profitability, motivating the five-factor extension.

What does the Fama-French three-factor model add beyond CAPM?

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