Multi-asset portfolio optimization and out-of-sample performance : an evaluation of Black-Littermann, mean variance and nai͏̈ve diversification approaches

The Black-Litterman (BL) model aims to enhance asset allocation decisions by overcoming the weaknesses of standard mean-variance (MV) portfolio optimization. In this study we implement the BL model in a multi-asset portfolio context. Using an investment universe of global stock indices, bonds, and commodities, we empirically test the out-of-sample portfolio performance of BL optimized portfolios and compare the results to mean-variance (MV), minimum-variance, and na ve diversified portfolios (1/N-rule) for the period from January 1993 to December 2011. We find that BL optimized portfolios perform better than MV and na ve diversified portfolios in terms of out-of-sample Sharpe ratios even after controlling for different levels of risk aversion, realistic investment constraints, and transaction costs. Interestingly, the BL approach is well suited to alleviate most of the shortcomings of MV optimization. The resulting portfolios are less risky, are more diversified across asset classes, and have less extreme asset allocations. Sensitivity analyses indicate that the outperformance of the BL model is due to the consideration of the reliability of return estimates and a lower portfolio turnover. -- Portfolio Optimization ; Black-Litterman Model