بهینه‌سازی سبد سرمایه‌گذاری مبتنی بر رویکرد میانگین-واریانس مارکویتز تحت محدودیت‌های کاربردی با استفاده از یک الگوریتم ژنتیک بهبودیافته
محورهای موضوعی :
مصطفی شبانی
1
,
حسین قنبری
2
,
عمران محمدی
3
1 - کارشناسی ارشد مهندسی صنایع، دانشکده مهندسی صنایع، دانشگاه علم و صنعت ایران، تهران، ایران
2 - دانشجوی دکتری مهندسی صنایع، دانشکده مهندسی صنایع، دانشگاه علم و صنعت ایران، تهران، ایران
3 - دانشیار، دانشکده مهندسی صنایع، دانشگاه علم و صنعت ایران، تهران، ایران
کلید واژه: : بهینه‌سازی سبد سرمایه‌گذاری, مدل میانگین-واریانس, الگوریتم ژنتیک بهبودیافته, محدودیت کاردینالیتی,
چکیده مقاله :
هدف و ضرورت: انتخاب سبد سرمایه‌گذاری بهینه، یکی از مسائل مهم در زمینه مدیریت سرمایه‌گذاری می‌باشد که با تحقیقات پیشگامانه هری مارکویتز و ارائه‌ی مدل میانگین-واریانس به یک حوزه داغ تحقیقاتی برای پژوهشگران و یک چارچوب مناسب برای فعالان بازارهای سرمایه تبدیل گردیده است. علی‌رغم ظرافت نظری و اهمیت مدل بهینه‌سازی میانگین-واریانس، این رویکرد با شک و تردید در میان فعالان بازارهای سرمایه مورد استفاده قرار می‌گیرد. یکی از دلایل اصلی این مشکل این است که سبدهای بهینه تشکیل شده با استفاده از مدل کلاسیک میانگین-واریانس شامل مفروضات بسیار ساده‌ای نظیر تشکیل سبد سرمایه‌گذاری بدون درنظرگرفتن محدودیتی برای تنوع سهام انتخاب شده یا درصد سرمایه‌گذاری شده در هر سهم می‌باشد. به همین منظور برای تشکیل یک سبد کارا و واقع‌گرایانه باید سایر عوامل تأثیرگذار برای سرمایه‌گذاران علاوه بر ریسک و بازدهی در مدل‌سازی در نظر گرفته شود. در همین راستا این مطالعه به ارائه یک مدل بهینه‌سازی سبد سرمایه‌گذاری توسعه‌یافته میانگین-واریانس با درنظرگرفتن محدودیت‌های کاربردی از قبیل محدودیت کاردینالیتی و محدودیت‌های سقف و کف می‌پردازد. روش شناسی: درنظرگرفتن این محدودیت‌ها در مدل‌سازی ریاضی، مدل بهینه‌سازی درجه دو سنتی را به یک مسئله درجه دوم عدد صحیح مختلط تبدیل می‌کند که برای مواجه با آن نیازمند به‌کارگیری الگوریتم‌های فراابتکاری می‌باشد. به همین منظور این پژوهش از الگوریتم ژنتیک به‌عنوان یکی از کاربردی‌ترین الگوریتم‌های فراابتکاری برای حل مدل‌های ریاضی با درجه پیچیدگی بالا استفاده می‌کند و به جهت افزایش کارایی این الگوریتم در این مطالعه یک عملگر تقاطع نوین برای تولید جواب‌های بهتر در ساختار الگوریتم ژنتیک معرفی و استفاده می‌گردد. یافته‌ها و نتیجه‌گیری: کارایی رویکرد پیشنهادی در پایگاه‌های داده معروف در حوزه ادبیات فراابتکاری مورد ارزیابی قرار گرفت. نتایج حاصل از این پژوهش بیانگر کارایی و اثربخشی بالای رویکرد پیشنهادی می‌باشد.
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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