Summary Portfolio optimization is a selection of the best combination of financial assets that maximizes the return and minimizes the risk. As the stock return distributions exhibit skewness, kurtosis, and heavy‐tailedness, for asset performance evaluation through the data envelopment analysis (DEA), we assume that the asset returns follow a pure jump Lévy process. For this purpose, two risk measures are provided as value‐at‐risk (VaR) and conditional VaR (CVaR). To deal with negative values, the range directional measure (RDM) model is utilized in the appropriate Lévy process, and inefficiency measurements are compared. Moreover, the asset price jumps have significant effects on the input and output of DEA models, risk measures, mean returns, and efficiency scores. In this regard, there are two optimization problems integrating DEA based on the variance gamma (VG) Lévy process, in which the input and output are stochastic. One of these two problems is a multi‐objective optimization model that evaluates more reliable efficiency scores than the other models. For this purpose, the VG parameters are estimated through the moments estimation method in order to analyze seven companies listed in the Tehran stock exchange (TSE). Finally, the Kolmogorov–Smirnov goodness‐of‐fit test is conducted. The results indicate that the VG model fits properly and is well suited to assets returns.

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.

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