CAPM and Factor Models

Decomposing returns into systematic exposures.

The Capital Asset Pricing Model (CAPM) is the simplest factor model: each asset's expected excess return is proportional to its beta to the market:

E[R_i - R_f] = \beta_i\, E[R_m - R_f]

The intuition: investors only get paid for systematic risk that can't be diversified away.

Multi-factor extensions have largely supplanted single-factor CAPM. Fama-French three-factor adds size and value:

E[R_i - R_f] = \beta_i^{MKT} \text{MKT} + \beta_i^{SMB} \text{SMB} + \beta_i^{HML} \text{HML}

Five-factor adds profitability and investment. Carhart's momentum factor and Asness-Frazzini quality factor are also widely used. Modern factor models often have $20$ + factors covering style, sector, country, and macro exposures.

Factor models serve two purposes: explaining returns (decomposing past performance) and forecasting risk (covariance matrices implied by factor exposures are far more stable than raw sample covariances).