Some new performance measures may be regarded as alternatives to the most popular criterion for portfolio optimization, the Sharpe ratio. Analysis of some allocation problems here takes into consideration portfolio selection models based on different risk perceptions and sample paths of the final wealth process for each allocation problem. One new performance ratio seems to be suitable for some optimization problems, but we need a thorough classification of the set of performance measures that would be ideal for large classes of financial optimization problems.

This paper uses data envelopment analysis (DEA) approach as a nonparametric efficiency analysis tool to preselect efficient assets in large-scale portfolio problems. Thus, we reduce the dimensionality of portfolio problems, considering multiple asset performance criteria in a linear DEA model. We first introduce several reward/risk criteria that are typically used in portfolio literature to identify features of financial returns. Secondly, we suggest some DEA input/output sets for preselecting efficient assets in a large-scale portfolio framework. Then, we evaluate the impact of the preselected assets in different portfolio optimization strategies. In particular, we propose an ex-post empirical analysis based on two alternative datasets: the components of S &P500 and the Fama and French 100 portfolio formed on size and book to market. According to this empirical analysis we observe better performances of the DEA preselection than the classic PCA factor models for large scale portfolio selection problems. Moreover, the proposed model outperform the S &P500 index and the strategy based on the fully diversified portfolio.