A Comparison of the Black-Litterman Model and the Mean-variance Approach: Generating Investor Views through Premium Prediction Models

Kristina Steinstø & Michelle Nguyen

Student thesis: Master thesis


The scope of this thesis is to examine asset allocation using Markowitz's Modern Portfolio Theory and the Black-Litterman model. Further, it compares the performance of the allocation models over an out-of-sample period running from 01-01-2000 to 31-12-2018, reflecting a real investment scenario. The analysis applies a simple multi-asset portfolio consisting of equities (SPX Index) and bonds (LUATTRUU Index).
Generating portfolio allocations using historical measures has often shown to be imprecise, which can be seen in the mean-variance optimization process. The implication is finely solved by Black and Litterman (1990), who used equilibrium returns derived from the Capital Asset Pricing Model as a benchmark for the expected excess returns of the portfolio. Further, the model gives the investor the possibility of combining their subjective views of the return movements with quantitative benchmark data, using Bayesian statistics. Equity and bond prediction models are applied to determine the individual beliefs of the investor, and the respective uncertainty regarding the established views.
The thesis investigates the out-of-sample performance of mean-variance, CAPM and Black-Litterman portfolios using rolling window estimates of the expected return vectors and covariance matrices. The models are evaluated by performance measures such as the Sharpe ratio, the certainty equivalent, M-squared and t-statistics, in addition to presenting the cumulative realized portfolio returns. The overall conclusion of this study provides evidence that the Black-Litterman portfolio performs more inferior than the traditional mean-variance portfolio, especially during recessions and crisis, when evaluating the performance measures stated above. All portfolios show significant t-statistics; however, their performance appears to differ substantially over the total out-of-sample period.

EducationsMSc in Finance and Investments, (Graduate Programme) Final Thesis
Publication date2020
Number of pages138