MEAN-EXPECTED SHORTFALL PORTFOLIO OPTIMIZATION USING A GENETIC ALGORITHM

Vladislav Radak¹, Aleksandar Damjanović¹, Vladimir Ranković² and Mikica Drenovak²

¹University Union, School of Computing, the Republic of Serbia

²University of Kragujevac, Faculty of Economics, the Republic of Serbia

Capital requirements for the market risk exposure of banks is a nonlinear function of the expected shortfall (ES), which is calculated based on a bank’s actual portfolio, i.e. the portfolio represented by the bank’s current holdings. To tackle portfolio optimization with respect to the ES, a genetic algorithm (GA) is used in this paper. The paper examines the effectiveness of a specific GA technique, namely the Strength Pareto Evolutionary Algorithm 2 (SPEA2) for portfolio optimization when the expected return (the mean) and percentage ES are set as the optimization goals. In addition, the differences between the mean-ES optimal portfolios and the mean-VaR optimal portfolios obtained by using the same optimization algorithm is analyzed in the study. The results document that the SPEA2 method provides well-distributed portfolios along the efficient frontier covering different risk levels. Compared to the mean-VaR optimal portfolios, the mean-ES optimal portfolios document superiority over the entire efficient frontier in the mean-ES plane. Concurrently, the converted mean-ES portfolios seem to converge towards the mean-VaR portfolios in the mean-VaR plane and nearly coincide for the high levels of the expected return.

Keywords: portfolio optimizacija, očekivani gubitak, VaR, SPEA2

JEL Classification: C61, C63, G11, G17, G21