Alternative econometric implementations of multi-factor models of the 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 two-pass approach introduced by Fama and MacBeth (1973). The second approach is based on a Bayesian latent mixture model with breaks in risk exposures and idiosyncratic volatility. Our application to monthly, 1980–2010 U.S. data on stock, bond, and publicly traded real estate returns shows that the classical, two-stage approach that relies on a nonparametric, rolling window estimation of time-varying betas yields results that are unreasonable. There is evidence that most portfolios of stocks, bonds, and REITs have been grossly over-priced. On the contrary, the Bayesian approach yields sensible results and a few factor risk premia are precisely estimated with a plausible sign. Predictive log-likelihood scores indicate that discrete breaks in both risk exposures and variances are required to fit the data.