Particle Swarm Algorithm: An Application on Portfolio Optimization

Introduction

This chapter focuses on the heuristic optimization technique that proceeds from the inspiration of Swarm Intelligence: Particle Swarm Optimization (PSO). The PSO is mostly used in multicriteria optimization problems. In recent years artificial intelligence techniques are mostly used in portfolio optimization. Optimization is the process of obtaining the best solution when performing certain operations for a given purpose. Before, optimization problems used to be defined by the mathematical functions. Due to the lack of flexibility and disadvantages of such methods, new methods have been developed and inspired by events in nature. Optimization algorithms based on natural events are called Heuristic algorithms. Heuristic algorithms are the algorithms that are inspired by natural phenomena to accomplish any purpose or goal. There is a convergence to the optimum solution in the solution space, but no definite solution can be guaranteed in these algorithms. With the rise of the use of heuristics based methods in problem solving in science, heuristics based methods are widely used in quantitative decision making. PSO, one of a heuristic method, was first introduced by Russel Eberhart and James Kennedy in 1995. It is inspired by simulating the behaviours of the bird and fish swarms. Collection of something such as birds and fish flocks that move somewhere in large numbers is called Swarm Behaviour (Mishra et al. 2013). PSO is a technique that is developed by taking advantage of the collective action of particles in the swarm. Each of the particles represents a solution candidate and forms the ideal solution space of an optimization problem (Cura, 2009).

As the Portfolio Optimization Problems are considered in this book, in this chapter it is aimed to give an explanation about the theorical structure of Particle Swarm Optimization and application of PSO for the portfolio optimization problem is set.

Portfolio optimization is a crucially important problem in modern finance. Portfolio selection is the decision of forming the optimum portfolio from a number of assets under certain expectations and constraints. Solving this kind of problem is quite difficult because of the large amount of complex data and other constraints. The general purpose of portfolio optimization is to discover an efficient frontier that yields the highest expected return on each level of portfolio risk. If a portfolio consists of funds in various kind of assets, then we can say that the portfolio is well diversified. Such portfolios may support a higher return at the lower possible risk. H. Markowitz’s Portfolio Theory for portfolio selection indicates that as you add new assets to an investment portfolio the total risk of that portfolio decreases continuously depending on the correlations of asset returns, but the expected return of the portfolio is a weighted average of the expected returns of each asset (Markowitz, 1952). Put it another way, inverstors may decrease their risk by investing in portfolios rather than in individual assets. In time, some additions are made to the Markowitz model and it was attempted to improve the solution process by different algorithms. The literature indicates that there are so many papers on portfolio optimization problem that studied the Markowitz optimum portfolio using heuristic techniques. These techniques could be more suitable for solving problems in portfolio management than others. However, the studies that deal with this problem by using particle swarm optimization (PSO) approach are quite rare. In this chapter, a heuristics model of PSO has been explained in detail and presented how to implement Markowitz portfolio optimization using PSO technique.