Selecting the best of Portfolio in cross efficiency evaluation with negative data

摘要

The present study is an attempt toward evaluating the performance of portfolios andasset selection using cross-efficiency evaluation. Cross-efficiency evaluation is aneffective way of ranking decision making units (DMUs) in data envelopmentanalysis (DEA). Mean – variance model (MV model) and mean-variance-skewness(MVS model) are proposed based on Data Envelopment Analysis, which thevariance of the assets is used as an input to the DEA and expected return andskewness are the output. Conventional DEA models assume non-negative values forinputs and outputs. However, we know that unlike return and skewness, variance isthe only variable in the model that takes non-negative values. This paper focuses onthe evaluation process of the efficiencies in the cross-efficiency matrix withnegative data. The problem consists of choosing an optimal set of assets in order tominimize the risk and maximize return. This method is illustrated by application inIranian stock companies and extremely efficiencies are obtained via cross-efficiencyfor making the best portfolio. The finding could be used for constructing the bestportfolio in stock companies, in various finance organization and public and privatesector companies.