A Multi-Period Black-Litterman Model

Abstract

The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems and assumes that the horizon of expert forecasts matches that of the investor. We consider a multi-period generalization where the horizon of expert views may differ from that of a dynamically-trading investor. By exploiting an underlying graphical structure relating the asset prices and views, we derive the conditional distribution of asset returns when the price process is geometric Brownian motion. We also show that it can be written in terms of a multi-dimensional Brownian bridge. The new price process is an affine factor model with the conditional log-price process playing the role of a vector of factors. We derive an explicit expression for the optimal dynamic investment policy and analyze the hedging demand associated with the new covariate. More generally, the paper shows that Bayesian graphical models are a natural framework for incorporating complex information structures in the Black-Litterman model.