factor-investing
Factor Investing
Core Concepts
From CAPM to Multifactor Models
CAPM prices a single source of risk: E(R_i) - R_f = beta * (E(R_m) - R_f). Persistent anomalies — small caps, cheap (high book-to-market) stocks, and recent winners earning more than beta predicts — motivated adding factors. Fama-French (1993) added size and value to the market factor (3-factor model); Carhart (1997) added momentum; Fama-French (2015) added profitability and investment (5-factor model):
R_i - R_f = alpha + b_MKT*MKT + b_SMB*SMB + b_HML*HML [+ b_RMW*RMW + b_CMA*CMA] [+ b_UMD*UMD] + epsilon
The key reinterpretation: a manager's CAPM alpha may be nothing more than static factor exposure. Alpha only means skill after controlling for the factors an investor could buy cheaply. Single-factor OLS mechanics, t-statistics, and the CAPM regression itself live in the statistics-fundamentals skill; this skill generalizes to K regressors and interprets the output.