A Bayesian Multi-Factor Model of Instability in Prices and Quantities of Risk in U.S. Financial Markets

This paper analyzes the empirical performance of two alternative ways in which multi-factor models with time-varying risk exposures and premia may be estimated. The first method echoes the seminal twopass approach advocated by Fama and MacBeth (1973). The second approach extends previous work by Ouysse and Kohn (2010) and is based on a Bayesian approach to modelling the latent process followed by risk exposures and idiosynchratic volatility. Our application to monthly, 1979-2008 U.S. data for stock, bond, and publicly traded real estate returns shows that the classical, two-stage approach that relies on a nonparametric, rolling window modelling of time-varying betas yields results that are unreasonable. There is evidence that all the portfolios of stocks, bonds, and REITs have been grossly over-priced. On the contrary, the Bayesian approach yields sensible results as most portfolios do not appear to have been misspriced and a few risk premia are precisely estimated with a plausibile sign. Real consumption growth risk turns out to be the only factor that is persistently priced throughout the sample.