Comparison and robustification of Bayes and Black-Litterman models

For determining an optimal portfolio allocation, parameters representing the underlying market—characterized by expected asset returns and the covariance matrix—are needed. Traditionally, these point estimates for the parameters are obtained from historical data samples, but as experts often have strong opinions about (some of) these values, approaches to combine sample information and experts’ views are sought for. The focus of this paper is on the two most popular of these frameworks—the Black-Litterman model and the Bayes approach. We will prove that—from the point of traditional portfolio optimization—the Black-Litterman is just a special case of the Bayes approach. In contrast to this, we will show that the extensions of both models to the robust portfolio framework yield two rather different robustified optimization problems.