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

Abstract

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 advocated by Fama and MacBeth (1973). The second approach 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 plausible sign. Real consumption growth risk turns out to be the only factor that is persistently priced throughout the sample.

Keywords: Bayesian estimation, Latent jumps, Stochastic volatility, Linear factor models

JEL Classification: G11, C53