Affiliations: [a] Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
| [b] Department of Mathematics, Allameh Tabataba’i University, Tehran, Iran
Correspondence:
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Corresponding author. M. Sanei, Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. E-mail: [email protected].
Abstract: According to modern finance theory and increasing need for efficient investments, we evaluate the portfolio performance based on the data envelopment analysis method. By the fact that stock market’s return distributions usually exhibit skewness, kurtosis and heavy-tails, we consider some appropriate underlying distributions that affect the input and output of the model. In this regard, the multivariate skewed t and the multivariate generalized hyperbolic as the heavy-tailed distributions of Normal mean-variance mixture are applied. The models are inspired by the Range Directional Measure (RDM) model to deal with negative values. The value-at-risk (VaR) and conditional VaR (CVaR) as risk measures are used in these optimization problems. We estimate the parameters of such distributions by Expectation Maximization algorithm. Then we present an empirical investigation to measure the relative efficiency of two sets of seven groups of companies from different industries of Iran stock exchange market. By comparing the results of introduced models with previous RDM approach, we show that how well the distribution of assets affect the performance evaluation.
Keywords: Data envelopment analysis, normal mean-variance mixture distributions, portfolio optimization, VaR, CVaR
