نوع مقاله : مقاله علمی پژوهشی
نویسندگان
گروه مهندسی صنایع، دانشگاه یزد، یزد، ایران
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
Objective: The creation of diversification and optimal asset allocation within a portfolio has consistently represented a complex decision-making challenge. In this study, projects are integrated as a novel asset class within the investment domain, alongside conventional risky assets such as securities and Exchange-Traded Funds (ETFs). Subsequently, utilizing a mathematical model rooted in the principles of post-modern portfolio theory, an optimal combination of all assets within the portfolio is derived.
Methodology: The mathematical model employed is based on the Omega ratio. To enhance its alignment with real-world scenarios, various constraints, including boundary, cardinality, and logical constraints, are incorporated. The model is examined within a single-period probabilistic framework, utilizing the Omega ratio as the objective function. Given the nature of this ratio, its maximization is achievable solely through iterative approaches. Consequently, the problem is solved through the integration of Monte Carlo Simulation (MCS) with a metaheuristic algorithm. The solution process begins by feeding probability distribution functions—derived from expert interviews for projects and historical data for exchange-traded assets—into the MCS. This generates 5,000 scenarios, producing expected return rates for each asset. Subsequently, these return rates are combined with asset weights proposed by the metaheuristic algorithm, and the resulting Omega ratio is reported back to the algorithm. Based on the received response and its predefined structure, the algorithm modifies the asset weights to maximize the Omega ratio. This iterative process continues until the algorithm reaches a predetermined number of iterations. In this research, the Marine Predators Algorithm (MPA) is implemented as the metaheuristic algorithm. To optimize its performance, the initial parameters of the algorithm are selected using the Taguchi Design of Experiments (DOE) technique. The MPA, developed in 2020, is founded upon the theory of survival of the fittest, wherein predators with a superior ability to locate prey thrive.
Results: The remarkably small error exhibited by the MPA in the benchmark test using the S&P 100 index, when compared to other metaheuristic algorithms such as Genetic Algorithm (GA), Tabu Search (TS), Simulated Annealing (SA), Particle Swarm Optimization (PSO), Population-Based Incremental Learning (PBIL), the hybrid of Population-Based Incremental Learning and Differential Evolution (PBIL-DE), and the Adaptive Ranking Multi-Objective Particle Swarm Optimization (ARMOPSO), suggests the notable validity and efficient performance of this algorithm within the portfolio optimization domain. In the numerical example presented, this algorithm effectively circumvented the penalty functions of the problem and adequately interacted with MCS, a novel asset class (projects), and real-world constraints.
Conclusion: The diversification and incorporation of a novel asset class into a portfolio not only mitigates risk but also facilitates the exploitation of opportunities within other investment domains. This research possesses potential utility for stock market participants and organizations engaged in project-based activities that perceive a need for investment within stock markets.
کلیدواژهها [English]
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