Document Type : Research Paper

Authors

Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran.

Abstract

One of the most important problems in portfolio selection models is the ability to provide the optimal number of each share. Therefore, in some cases, it interferes with portfolio optimization in converting the desired weight per share to the desired number per share, unless the results are an integer. Moreover, by applying the appropriate strategy, it seems possible to discover the optimal stock allocation for significant cases with comparatively large stock value. In this regard, this study presents a multi- objective portfolio selection model considering cardinality, quantity and budget constraints based on a new improved knapsack problem. Value-at-Risk (VaR) is considered as the second objective function of risk assessment in the knapsack-based portfolio selection model. We consider parametric (variance- covariance matrix) and non-parametric (historical) approaches to measure VaR. The study also uses the best GARCH family models to estimate the conditional volatility of return in the variancecovariance matrix, which is based on measuring and comparing different criteria under various types of GARCH family models. Finally, a Non-dominated Sorting Genetic Algorithm II (NSGA II) is planned to solve the problem. An actual portfolio of the Iran stock market is solved to demonstrate the application of the suggested model.

Keywords

Article Title [Persian]

مدل بهینه سازی پرتفوی میانگین _ ارزش در معرض خطر بر مبنای توسعه مدل کوله پشتی:رویکرد پارامتریک و ناپارامتریک

Authors [Persian]

  • فرشته واعظی
  • سید جعفر سجادی
  • احمد ماکویی

گروه مهندسی صنایع، دانشگاه علم و صنعت، تهران، ایران.

Abstract [Persian]

بسیاری از مشکلات بهینه سازی سبد سرمایه گذاری با تخصیص دارایی هایی که قیمت نسبتاً بالایی در بازار دارند ، درگیر هستند. بنابراین ، هنگام مواجهه با مسائل بهینه سازی پرتفوی، باید مقدار صحیح دارایی ها بدست آورده شود. این پژوهش تمرکز در ارائه مدل بهینه سازی سبد سرمایه گذاری چند هدفه میانگین ـ ارزش در معرض خطر بر مبنای مساله کوله پشتی با در نظر گیری گرفتن محدودیت های کاردینالیتی، کمیت و بودجه و متغیرهای گسسته دارد. ارزش در معرض خطر (VaR) به عنوان دومین تابع هدف بر مبنای دو رویکرد متفاوت پارامتریک (ماتریس واریانس کواریانس) و ناپارامتریک (تاریخی) برای ارزیابی ریسک در مدل بهینه سازی سبد سرمایه گذاری مبتنی برمساله کوله پشتی در نظر گرفته شده است. در این راستا، از بهترین تخمین زننده ها مدل های خانواده گارچ برای برآورد نوسانات شرطی بازدهی در ماتریس واریانس- کواریانس بهره گرفته می شود، که مبتنی بر اندازه گیری و مقایسه معیارهای مختلف در انواع مختلف مدل های خانواده گارچ می باشد.در نهایت خروجی های حاصل از حل مدل پیشنهادی چند هدفه بهینه سازی سبد سرمایه گذاری که ریسک آن با این دو رویکرد متفاوت بدست آمده با یکدیگر مقایسه می گردند و رویکرد برتر در اندازه گیری ریسک در مدل پیشنهادی انتخاب و معرفی می شود.. نهایتا با بررسی یک مطالعه موردی واقعی از بازار سهام ایالات متحده، کارکرد مدل و الگوریتم ژنتیک رتبه بندی نامغلوب II بررسی و اعتبار سنجی می شود.

Keywords [Persian]

  • بهینه سازی
  • مدل کوله پشتی
  • توسعه
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