Portfolio Performance Evaluation in a Modified Mean-Variance-Skewness Framework with Negative Data

Document Type : Research Paper


1 Department of Mathematics‎ and Computer Science‎, ‎Faculty of Econimics Allameh Tabataba’i University.

2 Department of Applied Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.


   The present study is an attempt toward evaluating the performance of portfolios using mean-variance-skewness model with negative data. Mean-variance non-linear framework and mean-variance-skewness non- linear framework had been proposed based on Data Envelopment Analysis, which the variance of the assets had been used as an input to the DEA and expected return and skewness were the output. Conventional DEA models assume non-negative values for inputs and outputs. However, we know that unlike return and skewness, variance is the only variable in the model that takes non-negative values. This paper focuses on the evaluation process of the portfolios in a mean-variance-skewness model with negative data. The problem consists of choosing an optimal set of assets in order to minimize the risk and maximize return and positive skewness. This method is illustrated by application in Iranian stock companies and extremely efficiencies are obtained via mean-variance-skewness non-linear framework with negative data for making the best portfolio. The finding could be used for constructing the best portfolio in stock companies, in various finance organization and public and private sector companies.