Evolutionary Multiobjective Optimization for Portfolios in Emerging Markets: Contrasting Higher Moments and Median Models

Abstract

Multi-objective Evolutionary algorithms are well suited to Portfolio Optimization and hence have been applied in complex situations were traditional mathematical programming falls short. Often they were used in portfolios scenario of classical Mean-Variance which are not applicable to the Emerging Markets. Emerging Markets are characterized by return distributions that have shown to exhibit significance departure from normality and are characterized by skewness and fat tails. Therefore higher moments models and median models have been suggested in the literature for asset allocation in this case. Three higher moment models namely the Mean-Variance-Skewness, Mean-Variance-Skewness-Kurtosis, Mean-Variance-Skewness-Kurtosis for return and liquidity and three median models namely the Median-Value at Risk, Median-Conditional Value at Risk and Median-Mean Absolute Deviation are formulated as a multi-objective problem and solved using a multi-objective evolutionary algorithm namely the non-dominated sorting genetic algorithm II. The six models are compared and tested on real financial data of the Egyptian Index EGX. The median models were found in general to outperform the higher moments models. The performance of the median models was found to be better as the out-sample time increases.