Bayesian Alternatives to the Black-Litterman Model

TL;DR

This paper introduces Bayesian modifications to the Black-Litterman model by incorporating priors on returns and covariance matrices, and evaluates their performance through sensitivity analysis and empirical testing on January 2018 data.

Contribution

It presents novel Bayesian variants of the Black-Litterman model, integrating priors on returns and covariance matrices for improved portfolio optimization.

Findings

Bayesian models outperform traditional Black-Litterman in certain scenarios

Sensitivity analysis reveals the impact of investor confidence levels

Models show promising results on real market data

Abstract

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.