Abstract
The purpose of this article is to evaluate optimal expected utility risk measures (OEU) in a risk-constrained portfolio optimization context where the expected portfolio return is maximized. We compare the portfolio optimization with OEU constraint to a portfolio selection model using value at risk as constraint. The former is a coherent risk measure for utility functions with constant relative risk aversion and allows individual specifications to the investor’s risk attitude and time preference. In a case study with three indices, we investigate how these theoretical differences influence the performance of the portfolio selection strategies. A copula approach with univariate ARMA-GARCH models is used in a rolling forecast to simulate monthly future returns and calculate the derived measures for the optimization. The results of this study illustrate that both optimization strategies perform considerably better than an equally weighted portfolio and a buy and hold portfolio. Moreover, our results illustrate that portfolio optimization with OEU constraint experiences individualized effects, e.g., less risk-averse investors lose more portfolio value in the financial crises but outperform their more risk-averse counterparts in bull markets.
Highlights
In this article, we consider portfolio selection problems that maximize the expected portfolio return while constraining the associated risk
A portfolio optimization problem with optimal expected utility risk measures (OEU) constraint is compared with one using value at risk (V@R) as risk restriction
In this article we investigate portfolio optimization subject to a risk constraint specified in terms of the following utility-based risk measure
Summary
We consider portfolio selection problems that maximize the expected portfolio return while constraining the associated risk. In contrast to Chabaane et al (2006), they found downside risk measures to be superior to the standard deviation. Another notable paper on portfolio optimization under risk constraints is Adam et al (2008) where moment-based, distortion and spectral risk measures are used as risk constraints. With a bootstrapping analysis of 14 asset classes, Xiong and Idzorek (2011) showed that the mean-conditional value at risk optimization problem outperforms the variance-constrained optimization during the financial crisis of 2008/2009. An application of Allen et al (2016) on European market indices did not find downside risk optimization strategies to be superior to the mean-variance problem for periods of crisis
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