طراحی مدل ریاضی متنوع سازی سبد سهام و حل آن با استفاده از الگوریتم ژنتیک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 کارشناس ارشد مدیریت صنعتی، دانشگاه یزد.

2 دانش آموخته دکتری، دانشگاه تربیت مدرس.

3 استادیار، دانشگاه تربیت مدرس.

چکیده

میزان مطلوبیت سرمایه‌گذار از انتخاب مجموعه دارایی‌های سرمایه‌گذاری به‌وسیله معیارهای ریسک و بازده مشخص می‌شود. با توجه به عدم ­اطمینان سرمایه­ گذار نسبت به آینده، یکی از روش‌های مطرح در مباحث سرمایه‌گذاری برای کاهش ریسک، متنوع ­سازی سبد سرمایه‌گذاری است. در این پژوهش علاوه بر معرفی معیار فاصله اقلیدسی به‌عنوان یک معیار اندازه‌گیری تنوع سبد سهام، مدلی چندهدفه برای انتخاب سبد سهام طراحی شده است. مدل ارائه‌شده در این پژوهش درصدد حداکثر­سازی بازدهی و تنوع و حداقل­کردن ریسک غیر‌سیستماتیک سبد سهام است. با توجه به اینکه مدل ارائه‌شده غیرخطی است و از نظر پیچیدگی محاسباتی جزو مسائل «حل­نشدنی چندجمله‌ای سخت» قرار می­گیرد؛ بنابراین پژوهش با توجه به کارایی محاسباتی الگوریتم ژنتیک در بهینه‌سازی، برای حل مدل از الگوریتم ژنتیک استفاده‌ شده است. نتایج اجرای مدل دو­هدفه (بازدهی و تنوع) و سه­هدفه (بازدهی، تنوع و ریسک غیر­سیستماتیک) در تکرارهای متعدد نشان داد که متوسط بازدهی سبدهای سهام انتخاب شده با مدل این پژوهش بالاتر از حد مطلوب است. بررسی شاخص ­های عملکرد سبد سهام نیز نمایانگر کارایی مدل دوهدفه (بازدهی و تنوع) است.

کلیدواژه‌ها

عنوان مقاله [English]

Selection and Solving it with Genetic Algorithms

نویسندگان [English]

  • Moslem Khakbiz 1
  • Abbas Rezaei Pandari 2
  • Mahmoud Dehghan Nayeri 3
1 MSc., University of Yazd.
2 Ph.D., Tarbiat Modares University.
3 Assistant Professor, Tarbiat Modares University.
چکیده [English]

In the selection of a collection of investment assets, the expected utility of investor is determined via risk and return criteria. Regarding the uncertainty of the investor about the future, portfolio diversification is a common path towards risk reduction in investment problem. In this study, not only the Euclidean Distance Criterion (EDI) was introduced to be a measure of portfolio diversification, but also a multi-objective model was designed for portfolio selection. This model intended to maximize the return and diversification of portfolio, and also to minimize non-systematic risk of it.  Since this is a non-linear model and in terms of complexity is among "NP-hard", regarding the computational efficiency of the Genetic Algorithms (GA) in optimization, it was used for solving the model. Results from the implementation of the dual-objective model (return and diversification) and triple-objective model (return, diversification, and non-systematic risk) with multiple-repetition showed that the average return of the portfolio selected by perposed model was higher than the favorable level. Investigation into portfolio performance indices indicates the efficiency of the dual-objective model (return and diversification).

کلیدواژه‌ها [English]

  • Portfolio Selection
  • Diversity Index
  • Genetic Algorithms
  • Expected Return
  • Nonsystematic Risk

مراجع

1. Agarwal, M. (2015). Developments in Mean-Variance Efficient Portfolio Selection. Published by Palgrave Macmillan.
2. Akbari, M., Zandieh, M., & Dorri, B. (2012). Scheduling part-time and mixed-skilled workers using genetic algorithm approach, Journal of Industrial Management Perspective, 7, 87-102, (In Persian).
3. Aslan, O., Kantar, M.Y. Usta, I. (2015). Genetic Algorithms for Solving Portfolio Allocation Models based on Relative-Entropy, Mean and Variance. Journal of Scientific Research and Development 2 (12), 7-12.
4. Carmichael, B., & Koumou, G. B., & Moran, K. (2015). Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy.CIRANO (Center for Interuniversity Researchand Analysis of Organizations) Working Papers.
5. Chang, Tun J., & Yang, S. C., & Chang, K. J. (2009). Portfolio optimization Problems in Different Risk Measures Using Genetic Algorithm. Expert Systems with Applications, 36 (7), 10529-10537.
6. Diyarbakırlıoğlu, E., & Satman, M. H. (2013). The Maximum Diversification Index. Journal of Asset Management, 14(6), 400-409.
7. El hachloufi, M., & Guennoun, Z., & Hamza, F. (2012). Stocks Portfolio Optimization Using Classification and Genetic Algorithms. Applied Mathematical Sciences, 6, pp. 4673-4684.
8. Eom, C., & Kim, Y. H., & Park, J., & Kaizoji, T. (2015). Effects of the Market Factor on Portfolio Diversification: The Case of Market Crashes. Investment Analysts Journal, 44(1), 71-83.
9. Farzi, S., & Shavazi, A. R., & Pandari, A. R. (2013). Using quantum-behaved particle swarm optimization for portfolio selection problem. International Arab Journal of Information Technology, 10(2), 111-119.
10. Francis, J. C., Kim, D. (2013). Modern Portfolio Theory: Foundations, Analysis, and New Developments. John Wiley & Sons.
11. Garkaz, M., & Abasi, E. & Moghadasi, M. (2010). Selecting and Optimizing the Portfolio Using the Genetic Algorithm Based on Different Definitions of Risk Portfolio, Journal of Industrial Management, 5(11), 115-136.
12. Hattingh, j.j. (2004).Portfolio management: The use of alternative investments for the purpose of diversification. Thesis. Rand Afrikaans University, Johannesburg.
13. Jones, C. P. (2008). Investments: Analysis and management, translation to Persian by Reza Tehrani, Asgar Noorbakhsh, Negah Danesh, Iran.
14. Kirchner, U., & Zunckel, C. (2011). Measuring Portfolio Diversification, arXiv.org Quantitative Finance Paper, No. 1102.4722.
15. Moutameni, A., & Sharifi, S.A. (2012). Propounding a Model for Portfolio Selection in Stock Exchange by Using of MCDM (Case Study: 50 Better Companies), Journal of Industrial Management Perspective, 5, 73-89, (In Persian).
16. Oh, K. J., & Kim, T. Y., & Min, S. (2005). Using Genetic Algorithm to Support Portfolio Optimization for Index Fund Management. Expert Systems with Application, 28(2), 371-379.
17. Oyenubi, A. (2016). Diversification Measures and the Optimal Number of Stocks in a Portfolio: An Information Theoretic Explanation. Computational Economics, 1.
18. Pandari, A.R., & Azar, A., & Shavazi, A.R. (2012). Genetic algorithms for portfolio selection problem with non-linear objectives. African Journal of Business Management, 6, 6209-6216.
19. Parque, V., & Mabu, S., & Hirasawa, K., (2009). Global portfolio diversification by genetic relation algorithm. ICROS-SICE International Joint Conference (ICCAS-SICE 2009). 2567-2572.
20. Rahnama, R.F., & Nikoomaram, H., & Toloie, E.A., & Lotfi, H.F., & Bayat, M. (2015). Reviewing the efficiency of portfolio optimization based on a stable model with classical optimization in risk prediction and portfolio returns, Financial engineering and securities management, 6(22), 29-60.
21. Ravindran, A. (2009). Operations Research Methodologies. CRC Press Taylor & Francis Group.
22. Reily, F.K., & Brown, K.C. 2012. Investment analysis and portfolio management. 10th edition. South- Western College Publication
23. Rudin, A. M., & Morgan, S. (2006). A Portfolio Diversification Index. The Journal of Portfolio Management, 32(2), 81-89.
24. Shahrabadi, A. & Bashiri, N. (2015). Investment Management in the Stock Exchange, Exchange Sharing Publishing. (In Persian).
25. Sharpe, William F., Gordon J. Alexander. 1990. Investments. Fourth Edition, Prentice-Hall.
26. Stirling, A. (2006). On the economics and analysis of diversity.SPRU ElectronicWorking Paper, Number 28. University of Sussex.
27. Stirling, A. (2007). A general framework for analysing diversity in science, technology and society. Journal of the Royal Society Interface.
28. Taghizadeh, R., & Fazli, S. (2011). Corporate Performance Measurement Method using Grey Relation Analysis and Fuzzy TOPSIS, Journal of Industrial Management Perspective, 2, 125-150, (In Persian).
29. Terra, C. (2015), Principles of International Finance and Open Economy Macroeconomics: Theories, Applications, and Policies. Elsevier Academic Press.
30. Yibing, C., & Yong, S., & Xianhua W., & Lingling, Z. (2014). How Does Credit Portfolio Diversification Affect Banks’ Return and Risk? Evidence from Chinese Listed Commercial Banks. Technological and Economic Development of Economy, 20(2), 332–352.

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