On the Bayesian Interpretation of Black-Litterman

Abstract

We present the most general model of the type considered by Black and Litterman (1991) after fully clarifying the duality between Black-Litterman optimization and Bayesian regression. Our generalization is itself a special case of a Bayesian network or graphical model. As an example, we work out in full detail the treatment of views on factor risk premia in the context of APT. We also consider a more speculative example in which the portfolio manager specifies a view on realized volatility by trading a variance swap.

Keywords: Black-Litterman, Portfolio Optimization, APT, Bayesian statistics

JEL Classification: G11