A NAÏVE APPROACH TO SPEED UP PORTFOLIO OPTIMIZATION PROBLEM USING A MULTIOBJECTIVE GENETIC ALGORITHM

Abstract

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.

Keywords

• Efficient portfolio
• Genetic algorithm
• Value‑at‑Risk