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.

中文翻译：

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资产收益的基本分布对DEA模型中效率的影响

根据现代金融理论和对有效投资的日益增长的需求，我们基于数据包络分析方法评估投资组合的绩效。由于股票市场的收益分布通常表现出偏度，峰度和重尾现象，我们考虑了一些影响模型输入和输出的适当基础分布。在这方面，应用多元偏斜t和多元广义双曲线作为正态均方差混合的重尾分布。这些模型的灵感来自范围方向测量（RDM）模型，以处理负值。在这些优化问题中使用了风险价值（VaR）和有条件VaR（CVaR）作为风险度量。我们通过期望最大化算法估计这种分布的参数。然后，我们提出了一项实证研究，以衡量来自伊朗证券交易所市场不同行业的两组七组公司的相对效率。通过将引入的模型的结果与以前的RDM方法进行比较，我们表明资产分配对绩效评估的影响程度。