Bayesian Alternatives to the Black-Litterman Model

The Black-Litterman model combines investors' personal views with historical data and gives optimal portfolio weights. In this paper we will introduce the original Black-Litterman model (section 1), we will modify the model such that it fits in a Bayesian framework by considering the investors' personal views to be a direct prior on the means of the returns and by adding a typical Inverse Wishart prior on the covariance matrix of the returns (section 2). Lastly, we will use Leonard and Hsu's (1992) idea of adding a prior on the logarithm of the covariance matrix (section 3). Sensitivity simulations for the level of confidence that the investor has in their own personal views were performed and performance of the models was assessed on a test data set consisting of returns over the month of January 2018.