Applied Mathematics & Information Sciences

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The purpose of this study is to evaluate various tools used for improving performance of portfolios and assets selection using mean-value at risk models. The study is mainly based on a non-parametric efficiency analysis tool, namely Data Envelopment Analysis (DEA). Conventional DEA models assume non-negative values for inputs and outputs, but variance is the only variable in models that takes non-negative values. At the beginning variance was considered as a risk measure. However, both theories and practices indicate that variance is not a good measure of risk and has some disadvantages. This paper focuses on the evaluation process of the portfolios and replaces variance by value at risk (VaR) and tries to decrease it in a mean-value at risk framework with negative data by using mean-value at risk efficiency (MVE) model and multi objective mean-value at risk (MOMV) model. Finally, a numerical example with historical and Monte Carlo simulations is conducted to calculate value at risk and determine extreme efficiencies that can be obtained by mean-value at risk framework.

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