The Robustness of Portfolio Optimization Models

Abstract

The optimization of investment portfolios is a topic of major importance in financial decision making, and many relevant models can be found in the literature. These models extend the traditional mean-variance framework using a variety of other risk-return measures. Existing comparative studies have adopted a rather restrictive approach, focusing solely on the minimum risk portfolio without considering the whole set of efficient portfolios, which are also relevant for investors. This chapter focuses on the performance of the whole efficient set. To this end, the authors examine the out-of-sample robustness of efficient portfolios derived by popular optimization models, namely the traditional mean-variance model, mean-absolute deviation, conditional value at risk, and a multi-objective model. Tests are conducted using data for S&P 500 stocks over the period 2005-2016. The results are analyzed through novel performance indicators representing the deviations between historical (estimated) efficient frontiers, actual out-of-sample efficient frontiers, and realized out-of-sample portfolio results.