Dynamically Weighted Continuous Ant Colony Optimization for Bi-Objective Portfolio Selection Using Value-at-Risk

Abstract

An adaptation of Ant Colony for Continuous Domains (ACOR) to bi-objective optimization problems is proposed and used to solve the optimal portfolio selection problem in Markowitz’s risk-return framework. The utilized risk measure is Value-at-Risk (VaR). In adapting ACOR to bi objective optimization, a dynamically weighted aggregation of objective values by a normalized Tchebychev norm is used to obtain a set of non-dominated Pareto optimal solutions to the problem. The proposed method (DW-ACOR) is tested on a set of past return data of 12 assets on Tehran Stock Exchange (TSE). Historical Simulation (HS) is utilized to obtain an estimate of the VaR. In order to compare the performance of DW-ACOR with a successful multi objective evolutionary algorithm (MOEA), NSGA-II is also used to solve the same portfolio selection problem. A comparison of the obtained results, shows that the proposed method offers high quality solutions and a wide range of risk-return trade-offs. While NSGA-II obtains a set of somewhat more widely spread solutions, the quality of the solutions obtained by DW-ACOR is higher as they are closer to the true Pareto front of the problem.