A Cross-Sectional Test of Linear Factor Models With Time-Varying Risk Premia

This paper explores the ability of theoretically-based asset pricing models such as the CAPM and the consumption CAPM referred to jointly as the (C)CAPM to explain the cross-section of average stock returns. Unlike many previous empirical tests of the (C)CAPM, we specify the pricing kernel as a conditional linear factor model, as would be expected if risk premia vary over time. Central to our approach is the use of a conditioning variable which proxies for fluctuations in the log consumption-aggregate wealth ratio and is likely to be important for summarizing conditional expectations of excess returns. We demonstrate that such conditional factor models are able to explain a substantial fraction of the cross-sectional variation in portfolio returns. These models perform much better than unconditional (C)CAPM specifications, and about as well as the threefactor Fama-French model on portfolios sorted by size and book-to-market ratios. This specification of the linear conditional consumption CAPM is able to account for the difference in returns between low book-to-market and high book-to-market firms and exhibits no evidence of residual size or book-to-market effects. (JEL G10, E21)