A hybrid algorithm for portfolio selection: An application on the Dow Jones Index (DJI)

Abstract

With the developing technology, investors have started to direct their investments by using computer software. The fact that these software do not take investor’s views into account causes all investors to achieve the same expected return at the same risk level. In this study, in order to find a solution to this problem, a two-stage portfolio selection model, which takes investment data and expert opinions into consideration, is proposed. In the first stage, the weight of the criteria in the portfolio selection problem was determined by the Constrained Fuzzy Analytic Hierarchy Process method. In the second stage, the fuzzy linear programming (FLP) problem created using the weights of the specified criteria is solved by fuzzy logic approach. These two methods in the literature use triangular fuzzy numbers (TFNs) in the solution process of the problem. In this study, methods are developed by creating mathematical models that makes the triangular fuzzy number-oriented theoretical infrastructures of the two methods used suitable for the use of trapezoidal fuzzy numbers (TrFNs). As a result, a new hybrid portfolio selection algorithm is proposed in which the methods developed for TrFNs in the first and second stage are used together. In the application section, portfolio distribution was made with the proposed hybrid model based on TrFNs by using the return rates of 30 stocks included in the Dow Jones Index, financial ratios of the stocks and decision makers’ opinions between January 1, 2018 and December 31, 2020. In the conclusion section of the study, as a result of the portfolio distributions obtained from each method, the total return amounts obtained when the investment was made in January 2021 according to the rate of return of the stocks were compared.