A Particle Swarm Optimization Heuristic for the Index Tacking Problem

Considering the market is efficient, an obvious portfolio management strategy is passive where the challenge is to track a certain benchmark like a stock index such that equal returns and risks are achieved. An index tracking problem is to minimize the tracking error between a portfolio and a certain benchmark. In this paper, we present a heuristic approach based on particle swarm optimization (PSO) techniques to optimize the solution of the index tracking problem. Our objective is to replicate the performance of a given portfolio under the condition that the number of stocks allowed in the portfolio is smaller than the number of stocks in the benchmark index. In order to evaluate the performance of PSO, the results in this study has been used to compare with those obtained by the genetic algorithms (GAs). The computational results show that particle swarm optimization approach is efficient and effective for solving index tracking optimization problems and the performance of PSO is better than GAs.