بهینه‌سازی سبد سهام چنددوره‌ای با استفاده از آنتروپی امکانی و الگوریتم ازدحام ذرات

نوع مقاله : مقاله پژوهشی

نویسندگان

1 کارشناس ارشد، گروه مدیریت، دانشکده علوم اداری و اقتصاد، دانشگاه فردوسی مشهد.

2 دانشیار، گروه مدیریت، دانشکده علوم اداری و اقتصاد، دانشگاه فردوسی مشهد.

3 دانشیار، گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه فردوسی مشهد.

چکیده

در این پژوهش، انتخاب سبد سهام چند دوره­ای درحالت عدم­‌قطعیت و با درنظرگرفتن هزینه­‌های معاملاتی، مدل‌سازی و حل شد. به‌منظور انتخاب سبد سهام چنددوره‌­ای با چهار معیار بازده، ریسک، درجه تنوع­‌بخشی سبد سهام و هزینه معاملاتی، یک مدل میانگین-نیم‌­واریانس-آنتروپی امکانی معرفی شد. در این مدل سطح بازده با مقدار میانگین امکانی بازده، سطح ریسک با نیم­‌واریانس امکانی پایینی بازده و درجه تنوع­‌پذیری سبد سهام به‌وسیله آنتروپی امکانی محاسبه شد. برای درنظرگرفتن عدم‌­قطعیت در مدل پیشنهادی، از نظریه فازی استفاده شده و بازده سهام، عدد فازی ذوزنقه‌­ای درنظرگرفته شد. باتوجه به پیچیدگی محاسباتی مسئله، الگوریتم بهینه­‌سازی ازدحام ذرات چندهدفه برای حل مدل به‌­کار رفت. به‌منظور ارزیابی عملکرد مدل پیشنهادشده، مدلی مشابه، مشتمل بر آنتروپی تناسبی، مدل‌سازی و حل شد و نتایج آن با مدل آنتروپی امکانی مقایسه شد. نتایج نشان داد که مدل آنتروپی امکانی از مدل آنتروپی تناسبی بهتر است؛ زیرا مرز کارایی بهتری ارائه می­‌دهد. با توجه به پرتفوهای بهینه به‌­دست­‌آمده از یک بار اجرای الگوریتم روی مدل آنتروپی امکانی در دوره­‌ی زمانی سوم، بیشترین درصد سهام انتخاب­‌شده در سبد بهینه سرمایه­‌گذار ریسک‌­پذیر، ریسک­‌گریز و بی‌­تفاوت نسبت به ریسک، به‌­ترتیب کگل، حکشتی و شخارک هستند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

The Multi-period Portfolio Optimization Using Possibilistic Entropy and Particle Swarm Optimization(PSO)

نویسندگان [English]

  • Marzieh Mazheri Zaveh 1
  • Amir Mohammad Fakoor Saghih 2
  • Omid Soleimani Fard 3
1 Master's degree, Department of Management, Faculty of Economics and Administrative Sciences, Ferdowsi University of Mashhad.
2 Associate Professor, Department of Management, Faculty of Economics and Administrative Sciences,Ferdowsi University of Mashhad.
3 Associate Professor, Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad.
چکیده [English]

In this research, multi-period stock portfolio selection was modeled and solved under uncertainty and considering transaction costs. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection by taking into account four criteria viz., return, risk, diversification degree of portfolio and transaction cost was introduced. In this model, the return level by the possibilistic mean value of return, the risk level by the lower possibilistic semivariance of return, and the diversification degree of portfolio was quantified by the possibilistic entropy. We used fuzzy theory in order to consider uncertainty in proposed model and considered asset returns as trapezoidal fuzzy numbers. MOPSO algorithm was used to solve the model. In order to evaluate the proposed models performance, a similar model including proportional entropy was modeled and solved and its results were compared with the possibilistic entropy model. The results of this comparison showed that the possibilistic entropy model is better than the proportional entropy model because it provides better efficiency frontier. Regarding the optimized portfolios in one-time implementation of the algorithm on the possibilistic entropy model in third-time period, the highest percentage of stocks selected in the optimal portfolio of risk seeker, risk averse and risk neutral investor is respectively kagol,hakeshti and shekhark.

کلیدواژه‌ها [English]

  • Multi-Period Portfolio
  • Multi Objective Particle Swarm Optimization (MOPSO)
  • Possibilistic Entropy
  • Proportional Entropy
  • Terminal Wealth

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