Intelligent portfolio optimization using water cycle and gray wolf algorithms

Abstract

Objective: This study evaluates and compares the performance of two groups of optimization approaches for portfolio optimization in the Iranian stock market, which exhibits high volatility and inefficiencies, against the classical Markowitz mean-variance model. The primary aim is to identify the optimal asset allocation among 64 listed companies on the Tehran Stock Exchange over a five-year period (2019–2024) and to critically assess the trade-offs offered by each method in terms of risk, return, and computational efficiency. This point suggests that innovative metaheuristic solutions can deliver better performance than the classical Markowitz model in certain practical aspects of investment, while the final choice should align with the investor’s priorities. The study provides an efficient framework for portfolio managers to combine optimization tools according to risk–return goals and decision deadlines.



Method: This study employs a comparative analytical framework, placing the classical Markowitz mean–variance optimization model against two metaheuristic algorithms: the Water Cycle Algorithm (WCA) and Grey Wolf Optimizer (GWO). Using five-year historical data from 64 Tehran Stock Exchange companies (1), optimal portfolios are constructed for each method. A comprehensive risk evaluation framework is then applied to assess portfolio performance not only through traditional metrics such as the Sharpe ratio and standard deviation but also through advanced risk measures, including Value at Risk (VaR), Conditional Value at Risk (CVaR), and Maximum Drawdown (MDD), to provide a multi-faceted examination. In this context, the computational efficiency of each algorithm is also measured precisely.

Findings: The results yield nuanced and noteworthy insights. The Water Cycle Algorithm demonstrates a substantial advantage in computational efficiency, being approximately 6.7 times faster than the Grey Wolf Optimizer. Additionally, it achieves excellent performance in minimizing Maximum Drawdown, a critical risk metric for capital preservation in the long term. However, contrary to the initial hypothesis, the Markowitz model excels in controlling daily volatility (standard deviation) and reducing tail risk from extreme events better than WCA. GWO consistently performs weaker across all key performance metrics. These findings emphasize that the superiority of an algorithm depends heavily on the particular risk criterion prioritized by the investor, rather than presenting a universal winner.

Conclusion: The results indicate that modern metaheuristic methods like WCA are not complete substitutes but rather powerful complements to classical models. WCA emerges as a leading tool for investors prioritizing computational speed and resilience to prolonged market downturns. By contrast, the Markowitz model remains a strong choice for managing short-term volatility. The study underscores the necessity of aligning the optimization tool with specific investment objectives and risk definitions, providing a practical framework for investors and portfolio managers in emerging markets like Iran. The research, by offering a cohesive comparative framework, demonstrates that experimental implementation and continuous evaluation—taking into account various risk dimensions (VaR, CVaR, MDD) and computational efficiency metrics—can contribute to improved decision-making quality in markets characterized by imperfect information.