Particle Swarm Optimization Algorithm for Determining Global Optima of Investment Portfolio Weight Using Mean-Value-at-Risk Model in Banking Sector Stocks

Moh. Alfi Amal (), Herlina Napitupulu and Sukono
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Moh. Alfi Amal: Magister Program in Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor, Sumedang 45363, Indonesia
Herlina Napitupulu: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor, Sumedang 45363, Indonesia
Sukono: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor, Sumedang 45363, Indonesia

Mathematics, 2024, vol. 12, issue 24, 1-34

Abstract: Computational algorithms are systematically written instructions or steps used to solve logical and mathematical problems with computers. These algorithms are crucial to rapidly and efficiently analyzing complex data, especially in global optimization problems like portfolio investment optimization. Investment portfolios are created because investors seek high average returns from stocks and must also consider the risk of loss, which is measured using the value at risk (VaR). This study aims to develop a computational algorithm based on the metaheuristic particle swarm optimization (PSO) model, which can be used to solve global optimization problems in portfolio investment. The data used in the simulation of the developed computational algorithm consist of daily stock returns from the banking sector traded in the Indonesian capital market. The quantitative research methodology involves formulating an algorithm to solve the global optimization problem in portfolio investment with mathematical calculations and quantitative data analysis. The objective function is to maximize the mean-value-at-risk model for portfolio investment, with constraints on the capital allocation weights in each stock within the portfolio. The results of this study indicate that the adapted PSO algorithm successfully determines the optimal portfolio weight composition, calculates the expected return and VaR in the optimal portfolio, creates an efficient frontier surface graph, and establishes portfolio performance measures. Across 50 trials, the algorithm records an average expected return of 0.000737, a return standard deviation of 0.00934, a value at risk of 0.01463, and a Sharpe ratio of 0.0504. Further evaluation of the PSO algorithm’s performance shows high consistency in generating optimal portfolios with appropriate parameter selection. The novelty of this research lies in developing an accurate computational algorithm for determining the global optima of mean-value-at-risk portfolio investments, yielding precise, consistent results with relatively fast computation times. The contribution to users is an easy-to-use tool for computational analysis that can assist in decision-making for portfolio investment formation.

Keywords: systematic; local and global optimum; investment portfolio; value at risk (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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