Abstract
As we know, there is a belief in the finance literature that Value at Risk (VaR) and Conditional Value at Risk (CVaR) are new approaches to manage and control the risk. Regard to, value at risk is not a coherent risk measure and it is not sub-additive and convex, so, we have considered conditional value at risk as a risk measure by different confidence level in the Mean-CVaR and multi objective proportional change Mean-CVaR models and compared these models with our previous mean-VaR models. This paper focuses on the performance evaluation process and portfolios selection by using Data Envelopment Analysis (DEA). Conventional DEA models assume non-negative values for inputs and outputs, but many of data take the negative value. Therefore, we have used our models based on Range Directional Measure (RDM) that can take positive and negative values. Here value at risk is obtained by non-parametric methods such as historical simulation and Monte Carlo simulation. Finally, a numerical example in Iran's market is presented.
Highlights
Portfolio selection and portfolio management are the most important problems from the past that have attracted the attention of investors
Regard to Value at Risk (VaR) is a very popular risk measure but it is not a coherent risk measure and it has undesirable mathematical characteristic such as a lack of sub-additivity and convexity, we proposed Mean-Conditional Value at Risk (CVaR) model and multi objective proportional change Mean-CVaR by mean of return as output and risk measure CVaR as input. we used Multi Objective Decision Making (MODM) to maximize the mean of return and minimize the risk measure of CVaR
Based on the Range Directional Measure (RDM) model provided by Portela et al [19], we propose the Mean-CVaR model and the multi objective proportional change Mean-CVaR model
Summary
Portfolio selection and portfolio management are the most important problems from the past that have attracted the attention of investors. Markowitz [14] proposed his model that was named Markowitz or mean-variance (MV) model He believed that all investors want maximum return and minimum risk in their investment. This number, is the result of shortage function which tries to summarize value of efficiency by a number In those papers, variance was considered as a risk measure. Regard to VaR is a very popular risk measure but it is not a coherent risk measure and it has undesirable mathematical characteristic such as a lack of sub-additivity and convexity, we proposed Mean-CVaR model and multi objective proportional change Mean-CVaR by mean of return as output and risk measure CVaR as input.
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