Portfolio optimisation in emerging markets: mean and median models assessment

Portfolio optimisation is instrumental in financial decision making. The basic Markowitz model is considered a milestone in financial theory but many examples including emerging markets were shown not to follow Markowitz's assumption of normality, hence alternative models have been suggested. The traditional mathematical programming that suits well the Markowitz model falls short in other complex situations of alternative portfolio models. Multi-objective evolutionary algorithms are well suited to solve these models with conflicting objectives regardless of their complexity and mathematical nature. Four models that belong to the mean models are compared to three median models and are formulated as multi-objective problems and solved using the non-dominated sorting genetic algorithm-II. The models are tested on real data of the Egyptian index and compared to two other emerging markets. The results show the outperformance of the median models over the mean models and the tail risk measures over the symmetric risk measures.