Particle swarm optimization algorithm for mean-variance portfolio optimization: A case study of Istanbul Stock Exchange

Abstract

While investors used to create their portfolios according to traditional portfolio theory in the past, today modern portfolio approach is widely preferred. The basis of the modern portfolio theory was suggested by Harry Markowitz with the mean variance model. A greater number of securities in a portfolio is difficult to manage and has an increased transaction cost. Therefore, the number of securities in the portfolio should be restricted. The problem of portfolio optimization with cardinality constraints is NP-Hard. Meta-heuristic methods are generally preferred to solve since problems in this class are difficult to be solved with exact solution algorithms within acceptable times. In this study, a particle swarm optimization algorithm has been adapted to solve the portfolio optimization problem and applied to Istanbul Stock Exchange. The experiments show that while in low risk levels it is required to invest into more number of assets in order to converge unconstrained efficient frontier, as risk level increases the number of assets to be held is decreased.