Markowitz-Based Portfolio Selection with Cardinality Constraints Using Improved Particle Swarm Optimization

Abstract

This work presents particle swarm optimization (PSO), a collaborative population-based meta-heuristic algorithm for solving the Cardinality Constraints Markowitz Portfolio Optimization problem (CCMPO problem). To our knowledge, an efficient algorithmic solution for this nonlinear mixed quadratic programming problem has not been proposed until now. Using heuristic algorithms in this case is imperative. To solve the CCMPO problem, the proposed improved PSO increases exploration in the initial search steps and improves convergence speed in the final search steps. Numerical solutions are obtained for five analyses of weekly price data for the following indices for the period March, 1992 to September, 1997: Hang Seng 31 in Hong Kong, DAX 100 in Germany, FTSE 100 in UK, S&P 100 in USA and Nikkei 225 in Japan. The test results indicate that the proposed PSO is much more robust and effective than existing PSO algorithms, especially for low-risk investment portfolios. In most cases, the PSO outperformed genetic algorithm (GA), simulated annealing (SA), and tabu search (TS).