Portfolio Optimization using the Entropic Value-at-Risk: An Investor Preference Approach
Abstract: It is very important for an investor to choose an accurate and effective risk measure when optimizing a portfolio of different assets. Recently, in addition to the standard risk measures such as variance or Value-at-Risk (VaR), more developed risk measures have emerged and one of them is the entropic Value-at-Risk (EVaR). This paper is testing the hypothesis stated by Ahmadi-Javid and Fallah-Tafti (2019) that entropic Value-at-Risk (EVaR) is the better risk measure to use in the portfolio optimization. To achieve this goal, the EVaR-optimized portfolio is compared to the mean-variance optimized portfolio (MV) for investors with different preferences. These preferences are exhibited through utility functions starting from the traditional utility functions such as the power and the exponential utility function and finishing with more complex functions such as the bilinear and S-shaped utility function. The conducted tests have shown that under different utility functions investors had different preferences for these two portfolios. EVaR optimized portfolio was mostly preferred by investors with the bilinear utility function when the kink has a negative value, which means that more risk averse investors were preferring this portfolio.
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