Particle Swarm Algorithm: An Application on Portfolio Optimization

Particle Swarm Algorithm: An Application on Portfolio Optimization

Burcu Adiguzel Mercangoz (Istanbul University, Turkey)
Copyright: © 2019 |Pages: 33
DOI: 10.4018/978-1-5225-8103-1.ch002

Abstract

Optimization is discovering an alternative with the most cost-effective or highest-achievable performance under the given constraints, by maximizing desired factors and minimizing undesired ones. Portfolio optimization in finance depends on selecting assets from an opportunity set which yields highest expected return on each level of portfolio risk. Optimization algorithms based on natural events are called heuristic algorithms. The particle swarm optimization (PSO) is a population-based heuristic optimization technique. The technique is inspired by the ability of animals such as birds and fish to adapt to their environment by applying a “sharing of knowledge” approach, to find rich food sources and to avoid hunting. This chapter focuses on portfolio selection problems and shows how to manage financial portfolios using a particle swarm optimization (PSO) technique which is a heuristic algorithm. In order to better understand the subject, the technique has been evaluated in Istanbul Stock Exchange for three transportation sector stocks.
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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.

Key Terms in this Chapter

Particle: It is a combination of individuals in the swarm. It is the potential solution in the PSO algorithm.

Global Best: Whole particles are neighbours of each other. Therefore, the neighbour with the best possible value in the swarm is taken in to consideration in order to calculate the best.

Swarm Intelligence: That is interested in designing of intelligent systems inspired from the simultaneously behaviour of social animal swarms.

Personal Best: The neighbours of a particle are defined as a certain number of particles. Thereby, personal best is the best of the particle within a local area.

Swarm: For a community of animals such as fish flock or bee colonies that behaeive simultaneously is called “swarm”.

Portfolio Optimization Problem: A problem that arises from the desire to minimize risk while maximizing the investor's returns.

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