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The Black-Litterman Asset Allocation Model: An Empirical Comparison to the Classical Mean-Variance Framework
Linköping University, Department of Management and Engineering, Economics. Linköping University, Faculty of Arts and Sciences.
Linköping University, Department of Management and Engineering, Economics. Linköping University, Faculty of Arts and Sciences.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Within the scope of this thesis, the Black-Litterman Asset Allocation Model (as presented in He & Litterman, 1999) is compared to the classical mean-variance framework by simulating past performance of portfolios constructed by both models using identical input data. A quantitative investment strategy which favours stocks with high dividend yield rates is used to generate private views about the expected excess returns for a fraction of the stocks included in the sample. By comparing the ex-post risk-return characteristics of the portfolios and performing ample sensitivity analysis with respect to the numerical values assigned to the input variables, we evaluate the two models’ suitability for different categories of portfolio managers. As a neutral benchmark towards which both portfolios can be measured, a third market-capitalization-weighted portfolio is constructed from the same investment universe. The empirical data used for the purpose of our simulations consists of total return indices for 23 of the 30 stocks included in the OMXS30 index as of the 21st of February 2014 and stretches between January of 2003 and December of 2013.


The results of our simulations show that the Black-Litterman portfolio has delivered risk-adjusted return which is superior not only to that of its market-capitalization-weighted counterpart but also to that of the classical mean-variance portfolio. This result holds true for four out of five simulated strengths of the investment strategy under the assumption of zero transaction costs, a rebalancing frequency of 20 trading days, an estimated risk aversion parameter of 2.5 and a five per cent uncertainty associated with the CAPM prior. Sensitivity analysis performed by examining how the results are affected by variations in these input variables has also shown notable differences in the sensitivity of the results obtained from the two models. While the performance of the Black-Litterman portfolio does undergo material changes as the inputs are varied, these changes are nowhere near as profound as those exhibited by the classical mean-variance portfolio.


In the light of our empirical results, we also conclude that there are mainly two aspects which the portfolio manager ought to consider before committing to one model rather than the other. Firstly, the nature behind the views generated by the investment strategy needs to be taken into account. For the implementation of views which are of an α-driven character, the dynamics of the Black-Litterman model may not be as appropriate as for views which are believed to also influence the expected return on other securities. Secondly, the soundness of using market-capitalization weights as a benchmark towards which the final solution will gravitate needs to be assessed. Managers who strive to achieve performance which is fundamentally uncorrelated to that of the market index may want to either reconsider the benchmark weights or opt for an alternative model.

Place, publisher, year, edition, pages
2014. , 57 p.
Keyword [en]
Black-Litterman mean-variance portfolio optimization efficient frontier sensitivity analysis high-yield strategy canonical reverse optimization equilibrium portfolio CAPM
National Category
URN: urn:nbn:se:liu:diva-111570ISRN: LIU-IEI-FIL-A--14/01735--SEOAI: diva2:758241
Subject / course
Master Thesis in Business and Economics Programme (Economics)
Available from: 2014-10-27 Created: 2014-10-25 Last updated: 2014-10-27Bibliographically approved

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Hirani & Wallström (2014)(913 kB)609 downloads
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Hirani, ShyamWallström, Jonas
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