CAPM and Factor Models — Section 22: Portfolio Theory

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).

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}