Portfolio optimization with optimal expected utility risk measures

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.

Multiobjective portfolio optimization: Forecasting and evaluation under investment horizon heterogeneity

“…The objectives of a portfolio maker is to maximize the “return” objectives and minimize the “risk” measures to reach a trade‐off (Gabrielli et al, 2022; Geissel et al, 2022; Nasini et al, 2022), which forms a multiobjective “return‐risk” optimization problem. Here are some classic single return objectives ( ) and risk measures ( ).…”