Macroeconomic Factors Strike Back: A Bayesian Change-Point Model of Time-Varying Risk Exposures and Premia in the U.S. Cross-Section

Abstract

This paper proposes a Bayesian estimation framework for a typical multi-factor model with time-varying risk exposures to macroeconomic risk factors and corresponding premia to price U.S. stocks and bonds. The model assumes that risk exposures and idiosynchratic volatility follow a break-point latent process, allowing for changes at any point in time but not restricting them to change at all points. An empirical application to 40 years of U.S. data and 23 portfolios shows that the approach yields sensible results compared to previous two-step methods based on naive recursive estimation schemes, as well as a set of alternative model restrictions. A variance decomposition test shows that although most of the predictable variation comes from the market risk premium, a number of additional macroeconomic risks, including real output and inflation shocks, are significantly priced in the cross-section. A Bayes factor analysis decisively favors the proposed change-point model.