The Black-Litterman Approach and Views from Predictive Regressions: Theory and Implementation

A major attraction of the Black-Litterman approach for portfolio optimization is the potential for integrating subjective views on expected returns. Usually, these views are based on some kind of subjective market expertise. We provide a new framework where the views and their uncertainty are derived from predictive regressions estimated in a Bayesian framework. First, we provide a theoretical foundation for this approach showing that the Bayesian estimation of predictive regressions fits perfectly to the basic idea of Black-Litterman. The subjective views about expected returns and the associated uncertainty can be directly obtained from the results of predictive regressions. The subjective element of the approach is introduced in terms of the investor's beliefs about the degree of predictability of the regression. Second, we apply the approach to a global portfolio using the dividend yield and price-earnings ratio as predictors. We show how different prior beliefs on predictability imply different subjective views on the global portfolio. We discuss the implications of modeling beliefs in this way and provide guidelines for implementing the approach.