A Hybrid Evolutionary Algorithm for Mean-absolute Deviation Portfolio Optimization Problem

Traditionally, classical Markowitz’s model has been usually employed to approach with the portfolio optimization. However, this model, contrary to its theoretical reputation, is scarcely used to construct a large-scale portfolio, due to its unrealistic assumption and tremendous computational complexity associated with solving a large-scale quadratic programming problem. In this paper, a mean-absolute deviation (L1 risk) portfolio optimization model with real feature is introduced. This model, a special case of the piecewise linear risk model, can remove most of the difficulties of Markowitz’s model while maintaining its advantages. Furthermore, motivated by the compensatory property of EA and PSO, where the latter can enhance solutions generated from the evolutionary operations by exploiting their individual memory and social knowledge of the swarm, a hybrid evolutionary algorithm is proposed to solve the model. The experimental results demonstrate the positive effect of this model, and reveal general design guidelines for future practice.