The Not-So-Well-Known Three-and-One-Half Factor Model

Abstract

Equity analysts conceptualize the Fama-French framework as a tool for studying the size and value characteristics of equity portfolios along with the market return. But the market return is not the return to market beta. In fact, commercial providers of equity risk models typically include both a market factor and a beta factor, along with variations of the size and value factors. In other words, in equity risk modeling practice, the basic Fama-French framework includes four factors not just three. Unlike the other three factors, the intercept term (i.e., market factor) does not have a coefficient that varies across securities so can be described as just half a factor. We clarify the nature and role of the “first” factor in equity return models and explain that the distinction between the market portfolio return and the return to the cross-sectional variation in security beta also applies to portfolio performance measurement. Specifically, the realized alphas of low (high) beta portfolios are reduced (increased) when a beta factor is included. The problem of ignoring the beta factor in performance measurement pertains to fully invested portfolios that have a low or high beta based on security selection, not to changes in portfolio beta induced by cash or leverage.

Keywords: Portfolio Theory, Linear Factor Model, CAPM Beta, Portfolio Performance Attribution, Three Factor Model, Four Factor Model

JEL Classification: G11