Multi-Asset Portfolio Optimization and Out-of-Sample Performance: An Evaluation of Black-Litterman, Mean Variance and Naïve Diversification Approaches

European Journal of Finance, Forthcoming.

48 Pages Posted: 12 Jun 2012 Last revised: 6 Dec 2014

See all articles by Wolfgang Bessler

Wolfgang Bessler

University of Hamburg

Heiko Opfer

Deka Investment GmbH

Dominik Wolff

Deka Investment GmbH; Technical University of Darmstadt; Frankfurt University of Applied Sciences

Date Written: December 2014

Abstract

The Black-Litterman model aims to enhance asset allocation decisions by overcoming the problems of mean-variance portfolio optimization. We propose a sample based version of the Black-Litterman model and implement it on a multi-asset portfolio consisting of global stocks, bonds, and commodity indices, covering the period from January 1993 to December 2011. We test its out-of-sample performance relative to other asset allocation models and find that Black-Litterman optimized portfolios significantly outperform naïve-diversified portfolios (1/N-rule and strategic weights), and consistently perform better than mean-variance, Bayes-Stein, and minimum-variance strategies in terms of out-of-sample Sharpe ratios, even after controlling for different levels of risk aversion, investment constraints, and transaction costs. The BL model generates portfolios with lower risk, less extreme asset allocations, and higher diversification across asset classes. Sensitivity analyses indicate that these advantages are due to more stable mixed return estimates that incorporate the reliability of return predictions, smaller estimation errors, and lower turnover.

Keywords: Portfolio Optimization, Black-Litterman, Mean-Variance, Minimum Variance, Bayes-Stein, Naïve diversification, 1/N, Markowitz

JEL Classification: C61, G11

Suggested Citation

Bessler, Wolfgang and Opfer, Heiko and Wolff, Dominik and Wolff, Dominik, Multi-Asset Portfolio Optimization and Out-of-Sample Performance: An Evaluation of Black-Litterman, Mean Variance and Naïve Diversification Approaches (December 2014). European Journal of Finance, Forthcoming., Available at SSRN: https://ssrn.com/abstract=2081636 or http://dx.doi.org/10.2139/ssrn.2081636

Wolfgang Bessler (Contact Author)

University of Hamburg ( email )

Allende-Platz 1
Hamburg, 20146
Germany

Heiko Opfer

Deka Investment GmbH ( email )

Mainzer Landstrasse 16
Frankfurt am Main, 60325
Germany

Dominik Wolff

Deka Investment GmbH ( email )

Mainzer Landstrasse 16
Frankfurt am Main, 60325
Germany

Technical University of Darmstadt

Hochschulstraße 1
S1|02 40
Darmstadt, Hessen D-64289
Germany

Frankfurt University of Applied Sciences ( email )

Nibelungenplatz 1
Frankfurt / Main, 60318
Germany

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