A Constrained Portfolio Selection Model Solved by Particle Swarm Optimization Under Different Risk Measures

Abstract

Portfolio selection has been one of the crucial problems in financial engineering. Investors’ interest is to construct a portfolio having a balance between the investor’s risk-taking and his/her expectations about the portfolio returns. The Markowitz model is a nonlinear constrained multi-objective optimization model that is usually impossible to solve at a good time. In this chapter, the purpose is to examine portfolio optimization models and applications of the particle swarm optimization (PSO) technique in solving these models. A constrained portfolio selection model has been developed, which is solved by the PSO technique as a metaheuristic approach using data from the Tehran Stock Exchange (TSE) to assess the developed model. In this case, the effects of three different risk measures have been analyzed on the constructed portfolios. The numerical results show that conditional value at risk (CVaR) performs better than the other two risk measures, including semivariance and variance. However, from the diversification perspective, the model with the variance risk measure produces a more diversified portfolio compared to the other two risk measures, although the differences are trivial.