Fama-French Three-Factor Model Fama-French 三因子模型

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theory theory

Apply the Fama-French three-factor model to decompose asset returns into market, size, and value factors. Use this skill when the user needs to explain cross-sectional return differences, evaluate fund performance beyond CAPM alpha, assess small-cap or value tilts in a portfolio, or when they ask 'why do small caps earn more', 'is value premium real', or 'what factors drive returns'.

學術研究技能：Fama-French Three-Factor Model 分析與應用。

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Overview概述

Fama and French (1993) extended CAPM by adding two factors — size (SMB) and value (HML) — to explain cross-sectional variation in stock returns that CAPM alone cannot capture. The model shows that small-cap and high book-to-market stocks earn systematic premiums.

When to Use使用時機

Explaining why CAPM alpha is nonzero for certain portfolios
Evaluating fund manager skill after controlling for factor exposures
Constructing factor-tilted portfolios
Academic research on asset pricing anomalies

When NOT to Use不適用時機

For fixed income or derivatives pricing (equity-focused factors)
When factor data is unavailable for the market in question
As a complete model — profitability and investment factors may also matter (five-factor)

Assumptions前提假設

IRON LAW: Single-factor models (CAPM) underestimate expected returns
for small-cap and value stocks. Size and value represent systematic
risk factors that command their own premia.

Key assumptions:

SMB and HML capture systematic risk, not mispricing
Factor premia are persistent across time periods and markets
Factors are constructed from observable, rebalanced portfolios

Framework 框架

Step 1 — Obtain Factor Data

Rm-Rf: market excess return
SMB (Small Minus Big): return of small-cap portfolio minus large-cap portfolio
HML (High Minus Low): return of high B/M portfolio minus low B/M portfolio

Step 2 — Run Time-Series Regression

Ri - Rf = ai + bi(Rm-Rf) + si(SMB) + hi(HML) + ei. See references/ for construction details.

Step 3 — Interpret Factor Loadings

bi: market sensitivity (same as CAPM beta)
si: size exposure (positive = small-cap tilt)
hi: value exposure (positive = value tilt, negative = growth tilt)

Step 4 — Evaluate Alpha

If alpha (ai) is statistically insignificant, returns are explained by factor exposures — no manager skill.

Output Format輸出格式

Gotchas注意事項

Factor premia vary across countries and time periods — not guaranteed to persist
HML has weakened post-publication; some attribute this to arbitrage
Five-factor model (2015) adds profitability (RMW) and investment (CMA) — three-factor may be insufficient
Factor construction methodology matters; different breakpoints yield different results
High R-squared does not mean the model is "correct" — it means factors explain variance
Debate persists whether factors represent risk or mispricing

References參考資料

Fama, E. & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
Fama, E. & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.
Fama, E. & French, K. (1992). The cross-section of expected stock returns. Journal of Finance, 47(2), 427-465.

Tags標籤

Fama-Frenchthree-factorSMBHML