Portfolio Optimization: An Evaluation of the Black-Litterman Approach

Erik Nordin

Student thesis: Master thesis

Abstract

This thesis evaluates the Black-Litterman model on the basis of portfolio performance, asset allocation process statistics and portfolio sensitivity with respect to changes in model parameters. The Black-Litterman model, which is derived from Bayesian statistical methods, produces posterior estimates of the mean of the distribution of excess asset returns over the risk free rate and the covariance of that estimate. These estimates are then used to optimize portfolios in a in a monthly portfolio optimization process over ten years. The model features an attractive possibility to blend subjective views about asset returns, called the conditional probability distribution, and the implied market returns, called the prior probability distribution, which is derived using an equilibrium approach. The keyword being possibility since the investor is in no way required to provide a view for each of the assets. This follows intuition, because if subjective views are absent it is not plausible that any other estimate is better than the market. Furthermore, this possibility separates it from the classical mean-variance approach which requires that the investor provides mean estimates for all assets regardless of expectations. Two Black-Litterman portfolios are compared with two mean-variance portfolios and a benchmark portfolio, MSCI ACWI IMI. All portfolios use the same, simple covariance matrix estimate. The first Black-Litterman portfolio and the mean-variance portfolios use five diversified indices as assets. Two of these assets are highly correlated which opens up for analysis of how the models handle this issue. The second portfolio uses four assets after the two highly correlated assts are removed. The Black-Litterman model is fed some subjective, static, views on asset returns which are based on academic research results. The first part of the thesis analysis investigates the performance of these portfolios using Sharpe- and Information ratios. Then, the allocation process is analyzed in depth. Moreover, causes of asset portfolio weight divergence are investigated. The second part of the analysis investigates portfolio sensitivity. Several of the model parameters are used in a variety of combinations. Given these combinations, the effects on portfolio construction and performance are investigated. The general conclusion of this research is that the Black-Litterman approach to asset allocation carries significant power. It is a vast improvement over the mean-variance approach.

EducationsMSc in Applied Economics and Finance, (Graduate Programme) Final Thesis
LanguageEnglish
Publication date2012
Number of pages137