A naïve approach to speed up portfolio optimization problem using a multiobjective genetic algorithm

Genetic algorithms (GAs) are appropriate when investors have the objective of obtaining mean-variance (VaR) efficient frontier as minimising VaR leads to non-convex and non-differential risk-return optimisation problems. However GAs are a time-consuming optimisation technique. In this paper, we propose to use a naïve approach consisting of using samples split by quartile of risk to obtain complete efficient frontiers in a reasonable computation time. Our results show that using reduced problems which only consider a quartile of the assets allow us to explore the efficient frontier for a large range of risk values. In particular, the third quartile allows us to obtain efficient frontiers from the 1.8% to 2.5% level of VaR quickly, while that of the first quartile of assets is from 1% to 1.3% level of VaR.