Linear-Betas in the Cross-Section of Returns

Abstract

This paper evaluates the in-sample, out-of-sample, and subperiod characteristics of cross-sectional conditional beta models following Fama and French (2020) and Fama and MacBeth (1973). This class of model generally assumes that risk-premiums are linear in the characteristics used to generate them, but I explore the performance of risk-premiums generated using characteristics as inputs to a simple function. In-sample, I reject the linear Fama and French model that assumes characteristics are conditional betas in favor of a linear conditional beta model following Shanken (1990) which provides a significantly lower zero-beta rate. Out-of-sample, I find the linear-beta model has a lower bias and Clark and West (2007)-adjusted MSPE, but comes at the cost of a larger variance than the Fama and French model.

Keywords: Fama-MacBeth, Cross-Section, Time-Varying Beta, Linear-Beta Model

JEL Classification: G10, G12, G19