APT and Fama-French
Does CAPM Hold in the Real World?
Other factors seem to matter empirically, including:
- book-to-market effects,
- liquidity effects,
- trading-volume effects.
CAPM nevertheless remains useful in practice for cost of capital estimation and performance attribution.
- Many firms still use CAPM to estimate the cost of capital.
- Asset managers use CAPM for performance attribution.
- Pension sponsors use CAPM for risk budgeting and asset allocation.
Arbitrage Pricing Theory
Under a multi-factor model,
\[ R_i - r_f = \beta_{i1}F_1 + \beta_{i2}F_2 + \cdots + \beta_{iK}F_K + \varepsilon_i \]
Then expected excess returns satisfy
\[ \mathbb{E}[R_i] - r_f = \beta_{i1}\pi_1 + \beta_{i2}\pi_2 + \cdots + \beta_{iK}\pi_K \]
APT says many sources of systematic risk may price assets, and expected returns must be a linear combination of those risk exposures.
A weakness of APT is that it does not itself identify which factors matter, and its linear factor structure is itself a restrictive assumption.
Fama-French Three-Factor Model
The Fama-French model augments the market factor with two empirically motivated factors:
- SMB: small minus big
- HML: high book-to-market minus low book-to-market
Empirically, small firms tend to outperform large firms, and high book-to-market value firms tend to outperform low book-to-market growth firms.
High book-to-market firms are often more financially constrained, less profitable, and more sensitive to downturns, which is one reason they may earn a risk premium.
The standard regression is
\[ R_i - r_f = \alpha_i + \beta_i(R_M-r_f) + s_i\,SMB + h_i\,HML + \varepsilon_i \]
In practice, we estimate factor risk premia, measure each stock's sensitivity to those factors, and then use those exposures to evaluate expected returns and performance.