Clustering Stock Exchange data by Using Evolutionary Algorithms for Portfolio Management

Abstract

1. Introduction Nowadays, choosing a suitable portfolio is one of the most important issues that investors of financial markets face with it. Markowitz [1] was the first person who outlined diversification in portfolio. He believed that investors pay attention simultaneously into risk and revenue. Investors are looking for increasing the expected revenue and reducing the risk. In Markowitz Model, the mean is a standard for the revenue; standard deviation and variance are standards for measuring risk. After Markowitz model, people such as Sharpe [2], Elton et. al [3] and Konno [4] offered new solutions to solve problems of Markowitz model and portfolio selection. Among methods used recently in choosing portfolio are single- and multi-objective evolutionary algorithms. One of advantages of these algorithms is their nonlinearity. These algorithms are very efficient for choosing portfolio when there are a number of assets. In methods used for solving optimization problems, experiences of nature and their Imitation has been applied. In order to solve problems in evolutionary algorithms, developmental process of animals, plants and organisms generally has been inspired from the nature. Since organisms have developed their own solutions for solving problems during thousands of years, they have obtained a relatively optimal solution for their lives. As one of methods for solving problems inspired from natural development, evolutionary algorithms are able to find an optimal response and solve complex and time-consuming calculations. Traditional methods cannot deal with it. Inheritance and reproduction, random change and natural selection are operators that make possible transition from one generation of organism to another. In fact, chance and natural selection are considered as two important factors in the evolution. [5] The present research is aimed to use clustering to improve performance of NSGA-II algorithm in choosing portfolio. Clustering analysis is a method for grouping data or observations regarding their similarity or proximity. By clustering analysis, data or observations are divided into homogenous and heterogeneous groups. By clustering, we are going to find similar data in order to identify behaviours well and get a better result. In present research, stock exchange has been clustered using imperialist competitive algorithm, ant colony algorithm, particle swarm optimization algorithm and k-means, Fcm, Som methods. Then, due to similarity of stocks in each cluster, few stocks have been chosen from each cluster. Therefore, among chosen stocks, the portfolio has been selected using NSGA-II algorithm. Results indicate that in practice, clustering reduces the time required for choosing portfolio. Therefore the risk will be reduced due to diversification of portfolio. 2. Literature Review In this section, studies done on portfolio management and clustering methods will be dealt with in brief. 2.1. Portfolio Management By a quantitative definition of investment risk for investors and selection of assets and portfolio management, Markowitz offered a mathematical approach. According to him, investors can obtain an efficient portfolio per certain revenue by minimizing portfolio risk or per a certain risk by maximizing portfolio revenue [1]. Many studies have been done on portfolio management using evolutionary algorithms. Chiam .et.al [6] have offered a new method for portfolio management using NSGA-II algorithm. In this method, the number of stocks present in each portfolio can be chosen. Duran .et.al [7] and Chang .et.al [8] indicated efficiency of evolutionary algorithms for portfolio management when many stocks are under study. Sadeghi and Zandieh [9] offered a game theory model in order to manage portfolio in product market. Ostermark [10] have used fuzzy model to manage portfolio 2.2. Clustering Techniques K-means method is one of the famous methods of clustering. …