Markowitz-Based Cardinality Constrained Portfolio Selection Using Asexual Reproduction Optimization (ARO)

Sadeghi Moghadam, Mohammad Reza; Mansouri, Taha; Sheykhizadeh, Morteza

doi:10.22059/ijms.2021.313393.674293

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	Markowitz-Based Cardinality Constrained Portfolio Selection Using Asexual Reproduction Optimization (ARO)
Interdisciplinary Journal of Management Studies (Formerly known as Iranian Journal of Management Studies)
دوره 15، شماره 3، مهر 2022، صفحه 531-548 اصل مقاله (815.06 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22059/ijms.2021.313393.674293
نویسندگان
Mohammad Reza Sadeghi Moghadam^* ¹؛ Taha Mansouri²؛ Morteza Sheykhizadeh³
¹Department of Production and Operation Management, Faculty of Management, University of Tehran, Tehran, Iran
²Department of Computing, Science and Engineering, University of Salford, Greater Manchester, UK
³M.Sc. in Industrial Management, Department of Industrial Management, Faculty of Management, University of Tehran, Tehran, Iran
چکیده
The Markowitz-based portfolio selection turns to an NP-hard problem when considering cardinality constraints. In this case, existing exact solutions like quadratic programming may not be efficient to solve the problem. Many researchers, therefore, used heuristic and metaheuristic approaches in order to deal with the problem. This work presents Asexual Reproduction Optimization (ARO), a model-free metaheuristic algorithm inspired by the asexual reproduction, in order to solve the portfolio optimization problem including cardinality constraint to ensure the investment in a given number of different assets and bounding constraint to limit the proportions of fund invested in each asset. This is the first time that this relatively new metaheuristic is applied in the field of portfolio optimization, and we show that ARO results in better quality solutions in comparison with some of the well-known metaheuristics stated in the literature. To validate our proposed algorithm, we measured the deviation of the obtained results from the standard efficient frontier. We report our computational results on a set of publicly available benchmark test problems relating to five main market indices containing 31, 85, 89, 98, and 225 assets. These results are used in order to test the efficiency of our proposed method in comparison to other existing metaheuristic solutions. The experimental results indicate that ARO outperforms Genetic Algorithm (GA), Tabu Search (TS), Simulated Annealing (SA), and Particle Swarm Optimization (PSO) in most of test problems. In terms of the obtained error, by using ARO, the average error of the aforementioned test problems is reduced by approximately 20 percent of the minimum average error calculated for the above-mentioned algorithms.
کلیدواژه‌ها
portfolio optimization؛ cardinality constraints؛ Markowitz mean-variance model؛ asexual reproduction optimization؛ efficient frontier
عنوان مقاله [English]
انتخاب پورتفولیوی محدود کاردینالیتی مبتنی بر مارکویتز با استفاده از بهینه‌سازی تولید مثل غیرجنسی
نویسندگان [English]
محمدرضا صادقی مقدم¹؛ طاها منصوری²؛ مرتضی شیخی زاده³
¹گروه مدیریت تولید و عملیات، دانشکده مدیریت، دانشگاه تهران، تهران، ایران
²گروه محاسبات، علوم و مهندسی، دانشگاه سالفورد، منچستر بزرگ، بریتانیا
³کارشناسی ارشد مدیریت صنعتی، گروه مدیریت صنعتی، دانشکده مدیریت، دانشگاه تهران، تهران، ایران
چکیده [English]
انتخاب پورتفولیوی مبتنی بر مارکویتز هنگام در نظر گرفتن محدودیت‌های اصلی به یک مسئله با پیچیدیگی محاسباتی سخت تبدیل می‌شود. در این حالت، راه حل های دقیق موجود مانند مدل های برنامه ریزی درجه دوم ممکن است برای حل مشکل کارآمد نباشد. بنابراین بسیاری از محققین از رویکردهای ابتکاری و فراابتکاری برای مقابله با این مشکل استفاده کرده اند. دراین پژوهش، الگوریتم فراابتکاری بهینه سازی بازتولید غیرجنسی (ARO) که از بازتولید غیرجنسی الهام گرفته شده است، به منظور حل مشکل بهینه سازی پورتفولیو از جمله محدودیت کاردینالی برای اطمینان از سرمایه گذاری در تعداد معینی از دارایی های مختلف و محدود ساختن محدودیت ها به منظور منحصر ساختن نسبت های سرمایه گذاری شده هر سهم مورد استفاده قرار گرفته است. این پژوهش اولین مطالعه مربوط به الگوریتم های فراابتکاری می باشد که در زمینه بهینه سازی پورتفولیو پیاده سازی شده است. براساس نتایج پژوهش، ARO در مقایسه با برخی از فراابتکاری های معروف بیان شده در ادبیات، راه حل های با کیفیت بهتری را به ارائه میدهد. برای صحت سنجی الگوریتم پیشنهادی، انحراف نتایج به‌دست‌آمده از مرز کارآمد استاندارد را اندازه‌گیری شده است. بدین منظور با استفاده از داده های مربوط به پنج بازار متشکل از 31، 85، 89، 98، و 225 دارایی که در دسترس عموم قرار دارند دقت مدل مورد ارزیابی قرار گرفت. نتایج پژوهش نشان می‌دهد که ARO از الگوریتم ژنتیک (GA)، جستجوی تابو (TS) ، بازپخت شبیه‌سازی شده (SA) و بهینه‌سازی ازدحام ذرات (PSO) در بیشتر مسائل آزمایشی بهتر عمل می‌کند. از نظر خطای به‌دست‌آمده، با استفاده از ARO، میانگین خطای آزمون مذکور تقریباً کاهش 20 درصدی از حداقل میانگین خطای محاسبه‌شده برای الگوریتم‌های فوق را نشان می دهد.
کلیدواژه‌ها [English]
بهینه‌سازی پورتفولیو, محدودیت‌های کاردینالیتی, مدل میانگین واریانس مارکوویتز, بهینه‌سازی بازتولید غیرجنسی, مرز کارآمد

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Markowitz-Based Cardinality Constrained Portfolio Selection Using Asexual Reproduction Optimization (ARO)