Portfolio Optimization Problem with Markowitz's Mean-Variance Framework under Practical Constraints Using an Improved Genetic Algorithm
Subject Areas :
Mostafa Shabani
1
,
Hossein Ghanbari
2
,
Emran Mohammadi
3
1 - MSc in Industrial Engineering, Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
2 - PhD Candidate in Industrial Engineering, Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
3 - University of Science and Technology
Keywords: Portfolio optimization Mean-Variance model Improved genetic algorithm Cardinality constraint,
Abstract :
Objective: The selection of an optimal investment portfolio is a pivotal concern within investment management, representing a focal point of extensive scholarly research and serving as a foundational framework for practitioners in the capital market. Originating from the seminal contributions of Harry Markowitz and the development of the mean-variance model, this area has garnered considerable attention. Despite the theoretical intricacies and the significant role of the mean-variance optimization model, it faces skepticism among participants in the capital market. A primary obstacle lies in the simplistic assumptions inherent in the classical mean-variance model, where optimal portfolios are constructed without imposing constraints on stock diversity or specifying the allocation percentages for each stock. Consequently, achieving a more comprehensive and realistic portfolio necessitates considering additional influential factors beyond risk and return in the modeling process. To address this gap, this study introduces an advanced mean-variance investment portfolio optimization model that integrates practical constraints such as cardinality constraints and upper and lower bounds. Methodology: By incorporating these constraints, the conventional quadratic optimization model is transformed into a mixed-integer quadratic problem, requiring the utilization of meta-heuristic algorithms. In this context, the research utilizes the genetic algorithm, recognized as a pragmatic meta-heuristic algorithm for navigating highly complex mathematical models. To enhance the efficiency of the genetic algorithm, the study introduces and employs a novel intersection operator, aiming to generate superior solutions within the genetic algorithm's framework. Conclusion: The effectiveness of the proposed methodology is evaluated using well-established databases in the meta-heuristics literature. The findings of this research highlight the remarkable efficiency and effectiveness of the proposed approach in addressing the challenges associated with portfolio optimization within the context of mean-variance models.
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