Khodier Rahenda, Radi Ahmed, Ayman Basel, Gheith Mohamed
Department of Industrial and Manufacturing Engineering, Egypt-Japan University of Science and Technology, Alexandria, 21934, Egypt.
Production Engineering Department, Alexandria University, Alexandria, 21544, Egypt.
Sci Rep. 2024 Sep 28;14(1):22523. doi: 10.1038/s41598-024-71193-w.
Financial Portfolio Optimization Problem (FPOP) is a cornerstone in quantitative investing and financial engineering, focusing on optimizing assets allocation to balance risk and expected return, a concept evolving since Harry Markowitz's 1952 Mean-Variance model. This paper introduces a novel meta-heuristic approach based on the Black Widow Algorithm for Portfolio Optimization (BWAPO) to solve the FPOP. The new method addresses three versions of the portfolio optimization problems: the unconstrained version, the equality cardinality-constrained version, and the inequality cardinality-constrained version. New features are introduced for the BWAPO to adapt better to the problem, including (1) mating attraction and (2) differential evolution mutation strategy. The proposed BWAPO is evaluated against other metaheuristic approaches used in portfolio optimization from literature, and its performance demonstrates its effectiveness through comparative studies on benchmark datasets using multiple performance metrics, particularly in the unconstrained Mean-Variance portfolio optimization version. Additionally, when encountering cardinality constraint, the proposed approach yields competitive results, especially noticeable with smaller datasets. This leads to a focused examination of the outcomes arising from equality versus inequality cardinality constraints, intending to determine which constraint type is more effective in producing portfolios with higher returns. The paper also presents a comprehensive mathematical model that integrates real-world constraints such as transaction costs, transaction lots, and a dollar-denominated budget, in addition to cardinality and bounding constraints. The model assesses both equality/inequality cardinality constraint versions of the problem, revealing that the inequality constraint tends to offer a wider range of feasible solutions with increased return potential.
金融投资组合优化问题（FPOP）是定量投资和金融工程的基石，专注于优化资产配置以平衡风险和预期回报，这一概念自1952年哈里·马科维茨的均值 - 方差模型以来不断发展。本文介绍了一种基于黑寡妇算法的投资组合优化新元启发式方法（BWAPO）来解决FPOP。该新方法解决了投资组合优化问题的三个版本：无约束版本、等基数约束版本和不等式基数约束版本。为BWAPO引入了新特性以更好地适应该问题，包括（1）交配吸引力和（2）差分进化变异策略。将所提出的BWAPO与文献中用于投资组合优化的其他元启发式方法进行了评估，其性能通过使用多个性能指标在基准数据集上的比较研究证明了其有效性，特别是在无约束均值 - 方差投资组合优化版本中。此外，在遇到基数约束时，所提出的方法产生了有竞争力的结果，在较小数据集上尤其明显。这导致对由等式与不等式基数约束产生的结果进行重点研究，旨在确定哪种约束类型在产生具有更高回报的投资组合方面更有效。本文还提出了一个综合数学模型，该模型除了基数和边界约束外，还整合了诸如交易成本、交易批量和以美元计价的预算等现实世界约束。该模型评估了问题的等式/不等式基数约束版本，结果表明不等式约束往往能提供更广泛的可行解决方案，且具有更高的回报潜力。
