Application of Quadratic Programming on Portfolio Optimization Using Wolfe’s Method and Particle Swarm Optimization Algorithm

Abstract

Stock portfolios can be modeled into quadratic programming problems using the Markowitz mean-variance model. Quadratic programming problems can be solved using two methods, namely classical and heuristic methods. In this research, the classical method uses Wolfe’s method, while the heuristic method uses the particle swarm optimization (PSO) algorithm. This research aims to determine optimal results in portfolio problems using two methods, namely Wolfe’s method and the PSO algorithm. The data used in this research is data from 10 stock companies that distribute the highest dividends in the IDX High Dividend 20 category for the 2022 period. The research results discuss the portfolios of PT Astra International Tbk and PT. Indo Tambangraya Megah Tbk. Based on the result, using Wolfe’s method, the ASII and ITMG stock portfolios are obtained, namely the optimal proportion of ASII shares = 0.76401 or 76.401% and ITMG shares = 0.23598 or 23.598%, while the PSO algorithm obtains a portfolio of ASII and ITMG shares, namely ASII shares = 75.02% and ITMG shares = 24.98%. Compared to Wolfe’s method, the PSO algorithm has a smaller Z value 5.7.