Time-Varying Beta and the Value Premium: A Single-Index Varying-Coefficient Model Approach

Abstract

We revisit conditional CAPM by modeling alpha and beta as flexible functions of state variables identified via formal variable selection. In post-1963 sample, beta of the value premium comoves strongly with unemployment, inflation, and price-earnings ratio in a countercyclical manner. We also uncover a novel nonlinear dependence of alpha on business conditions: It falls sharply and becomes even negative during severe economic downturns but is positive and flat otherwise. Conditional CAPM performs better than unconditional CAPM but does not fully explain the value premium. Our findings are consistent with a conditional CAPM with rare disasters or a multi-factor model.