Fama-French Three-Factor Model vs. CAPM Risk Factors

Posted on Oct 16, 2025 in Finance

Important Risk Factors in Asset Pricing

Industry Factor

F_Industry = R_Industry – R_Stocks: Stocks in the same industry are all exposed to industry-specific shocks (demand, prices, technology).
This implies stocks in the same industry tend to have higher correlations with each other.
Stocks in an industry will have a large beta with respect to that industry’s factor (B_Industry). Stocks in nearby industries will have moderate B_Industry, and stocks in unrelated industries will have zero B_Industry.

Size Factor

F_Size = R_Small – R_Big: Stocks for big companies are exposed to different risks than small stocks (e.g., small companies often require external capital more frequently).
This implies small stocks have higher correlation with each other, and big stocks have higher correlation with each other.
Small stocks have positive B_Size; big stocks have negative B_Size.

Value Factor

F_Value = R_Value – R_Growth: This factor reflects the difference in returns from two styles of investing: Value versus Growth.
Value Investing: Choosing stocks with cheap prices relative to measures of fundamental or accounting value.
Growth Investing: Choosing stocks projected to have fast growth in sales and/or profits.
Value stocks are exposed to different risks than growth stocks (e.g., technological innovation).
This implies value stocks have higher correlation with each other, and growth stocks have higher correlation with each other.
Value stocks have positive B_Value; Growth stocks have negative B_Value.

The Fama-French Three-Factor Model (FF3F)

Fama and French propose the following model as an alternative to the Capital Asset Pricing Model (CAPM):

E(R_j) = R_f + β_m E(R_m – R_f) + β_s E(R_SMB) + β_h E(R_HML)

R_m: Market rate of return
R_SMB: Return on Small Minus Big firms (Small-minus-Big factor)
R_HML: Return on firms with High book-to-market ratios minus firms with low book-to-market ratios (High-Minus-Low factor)
β_m: Market beta
β_s: Beta on Small-Minus-Big factor
β_h: Beta on High-Minus-Low factor

Interpreting Multifactor Models

The Fama-French three-factor model captures size and value effects. However, it does not fully explain why investors care about the common risks associated with small and value stocks.

Some argue that Value is related to expected returns not because it is related to risk, but because it is driven by mispricing.

Regardless of the underlying cause, both sides agree that pricing models are useful to characterize where returns come from, especially when benchmarking portfolio managers.

Multifactor models generally describe realized returns better than expected returns.

Applications of Pricing Models

Cost of Capital Estimation

CAPM vs. FF 3-Factor Model for Cost of Capital

CAPM:

Does not adequately explain expected returns, which is the primary purpose of determining the cost of capital.

Fama-French 3-Factor Model:

Does explain expected returns on average.
However, for individual stocks, beta estimates are noisy and can change over time—even more so than the CAPM (three estimates instead of one).
For cost of equity capital estimates, one might be better off attenuating beta toward 1.0. This approach:
- In practice, fits better with E(r).
- Avoids strategic gaming of the cost of capital.
- Downside: Ignores differences in risk across firms.

Portfolio Performance Evaluation

CAPM vs. FF 3-Factor Model for Performance Evaluation