Dealing with Data: An Empirical Analysis of Bayesian Extensions to the Black-Litterman Model

Portfolio Optimization is a common financial econometric application that draws on various types of statistical methods. The goal of portfolio optimization is to determine the ideal allocation of assets to a given set of possible investments. Many optimization models use classical statistical methods, which do not fully account for estimation risk in historical returns or the stochastic nature of future returns. By using a fully Bayesian analysis, however, this analysis is able to account for these aspects and also incorporate a complete information set as a basis for the investment decision. The information set is made up of the market equilibrium, an investor/expert’s personal views, and the historical data on the assets in question. All of these inputs are quantified and Bayesian methods are used to combine them into a succinct portfolio optimization model. For the empirical analysis, the model is tested using monthly return data on stock indices from Australia, Canada, France, Germany, Japan, the U.K. and the U.S.