بهینه‌سازی سبد سرمایه‌گذاری مبتنی بر رویکرد میانگین-واریانس مارکویتز تحت محدودیت‌های کاربردی با استفاده از یک الگوریتم ژنتیک بهبودیافته
الموضوعات :
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
الکلمات المفتاحية: : بهینه‌سازی سبد سرمایه‌گذاری, مدل میانگین-واریانس, الگوریتم ژنتیک بهبودیافته, محدودیت کاردینالیتی,
ملخص المقالة :
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.
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