An Enhanced Particle Swarm Optimization with Mutation for Mean-Value-at-Risk Portfolio Optimization in the Indonesian Banking Sector - Anam, Syaiful; Bukhori, Hilmi Aziz; Maulana, Avin; Maulana, M. Idam; Rasikhun, Hady (Informatika, Universitas Jenderal Soedirman, 2025)
Portfolio optimization in emerging markets is challenging because high volatility and non-normal return distributions reduce the effectiveness of traditional mean–variance models, which tend to underestimate downside risk. This study aims to develop and evaluate an Enhanced Particle Swarm Optimization with Mutation (PSO with Mutation) for portfolio optimization under the Mean-Value-at-Risk (Mean-VaR) framework in the Indonesian banking sector. The novelty of this approach lies in integrating a mutation operator into standard PSO to maintain population diversity, prevent premature convergence, and improve exploration of the solution space. To evaluate the method, daily adjusted closing prices of 31 Indonesian bank stocks from January 2020 to July 2025 were collected. Preprocessing included removing tickers with incomplete data and computing daily returns. The optimization problem was formulated using Mean-VaR as the risk measure, with portfolio weight constraints. The proposed PSO with Mutation was benchmarked against standard PSO, Genetic Algorithm (GA), Bat Algorithm (BA), BA with Mutation, and classical models (Markowitz and Monte Carlo–based VaR). Performance was assessed using expected return, Mean-VaR, risk-adjusted return, Sharpe ratio, execution time, and stability across 25 independent runs. The results show that PSO with Mutation achieved a competitive expected return (0.0020), the lowest Mean-VaR (0.0311), the highest risk-adjusted return (0.0650), and the lowest variability across runs, while maintaining acceptable execution time. These findings confirm that mutation-enhanced PSO provides a robust, balanced, and efficient solution for portfolio optimization, making it highly relevant for investors in volatile emerging markets and advancing research on hybrid metaheuristics in financial optimization.