The Decision Support of the Securities Portfolio Composition Based on the Particle Swarm Optimization

Stochastic behavioral methods are becoming increasingly widespread for optimization tasks solving. One of these methods is the particle swarm optimization (PSO). The particle swarm is an algorithm for finding optimal regions of complex search spaces through the interaction of individuals in a population of particles. Its effectiveness and efficiency has rendered it a valuable metaheuristic approach in various scientific fields where complex optimization problems appear. Investment activity in the stock market is an area where the use of optimization techniques is required. The volatility and unpredictability of future stock prices create a situation of uncertainty for decision making in the financial market. Investors are forced to solve a multi-criteria optimization problem when forming an effective securities portfolio. This article proposes to use PSO to compile an optimal securities portfolio based on combined entropy risk index indicators. The portfolio consisted of 8 shares of Russian companies, the shares of each stock in the portfolio were found using particle swarm optimization. The efficiency of the modified algorithm is investigated, coefficients are proposed, and the results of a computational experiment are obtained. Keywords—swarm intelligence, particle swarm optimization, multi-objective optimization task, securities portfolio, indexentropic risk measures. I. SECURITY PORTFOLIO The problem of securities portfolio formation is the actual issue in the modern economy. Depositors are investing assets in securities at the world's stock markets every day. The securities portfolio structure optimization is one of the main decision-making tasks in investment activity in the stock market. It is necessary to form such a portfolio of securities, which will bring the best result within a certain period. It is very difficult to generate an optimal portfolio in the face of uncertainty. In this paper a methodology for forming a securities portfolio based on combined index-entropy risk measures using the particle swarm optimization algorithm is outlined. A securities portfolio is a set of individual types of securities selected by an investor to achieve certain goals. The variety of securities in the market allow to form many securities portfolios different in composition. Investment portfolios may be different in terms of a return and a risk, depending on the current and strategic goals of investors. Let the portfolio structure be represented as the vector X=(x1,x2,...,xn), where xi is the share of the i – th stock in the portfolio (i = 1, n ̅̅ ̅̅ ), i.e. xi ≥ 0, ∑ xi = 1, n i=1 where n is the quantity of stocks. The value of the portfolio Pj(X) at the time moment j is equal to the sum of the product of the price of the i – th stock and its share in the portfolio: Pj(X) = ∑ cijxi, n i=1 () where cij is the price of the i-th stock on the j-th day (j = 1, T ̅̅ ̅̅ ), T is the considered time horizon. The yield of the securities portfolio Vj(X) is calculated by using following formula: Vj(X) = ∑ cijxi n i=1 ∑ ci1xi n i=1 = Pj(X) P1(X) () All financial transactions, including the formation of a securities portfolio, are associated with risk. The volatility and unpredictability of future stock prices (and therefore the portfolio) creates certain risks for portfolio investor, who needs to manage risks reasonably. The investor have to form a portfolio of financial instruments in such a way as to protect against various types of risk. Risk refers to the possibility of non-receipt of the expected income or loss (full or partial) of the funds invested in this security. Risk is a reflection of the uncertainty in the receipt of income by the investor, so each investor has a subjective attitude to the investment process – a measure of risk aversion. The use of optimization techniques in the investment theory began with the solution of the problem of constructing an optimal portfolio based on two criteria – profitability and risk. As a rule, securities with a low risk have a small expected return, and securities that can generate high returns have significant risk indicators. Since a portfolio is a set of various securities, the investor will always face the problem of choosing the currently effective investment portfolio. The choose of investors determined by the presence of a certain 7th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2019) Copyright © 2019, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Intelligent Systems Research, volume 166