A Decision Support System Application for Portfolio Optimization

Yıl 2020, Cilt: 25 Sayı: 3, 1345 - 1358, 31.12.2020

Aslı Sebatlı-sağlam , Fatih Çavdur

https://doi.org/10.17482/uumfd.532966

Cited By: 1

Öz

In this study, a decision support system for portfolio optimization is developed. The application is developed on a spreadsheet environment frequently used in daily life. Using the developed system, the Markowitz mean-variance model is solved based on the problem parameters entered by the user. The resulted optimal portfolio is presented using the graphical user interface of the spreadsheet environment. A dataset including the daily closure prices of the 30 companies in the Dow Jones Industrial Average Index between the years of 2009 and 2018 is used for the implementation of the system. The optimal portfolios for different required-return rates are obtained and the results are analyzed using the developed decision support system. Development of a flexible and easy-to-use portfolio optimization tool running in a spreadsheet environment and allowing investors constructing optimal portfolios without dealing with the mathematical details of the Markowitz mean-variance model constitute the most important contribution of the study.

Anahtar Kelimeler

Portfolio optimization, Markowitz mean-variance model, Mathematical programming, Quadratic programming, Decision support systems

PORTFÖY OPTİMİZASYONU İÇİN BİR KARAR DESTEK SİSTEMİ UYGULAMASI

Öz

Bu çalışmada, Markowitz ortalama-varyans modeli kullanılarak portföy optimizasyonu için kişisel bilgisayarda çalışan bir karar destek sistemi sunulmaktadır. Uygulama, günlük hayatta sıklıkla kullanılan bir elektronik tablolama yazılımı ortamında geliştirilmiştir. Geliştirilen sistem ile girilen parametrelere bağlı olarak Markowitz ortalama-varyans modeli çözdürülmektedir. Elde edilen optimal portföy, elektronik tablolama ortamının grafiksel arayüzü kullanılarak sunulmaktadır. Sistemin uygulaması için 2009-2018 yılları arasındaki Dow Jones Borsası Endüstri Endeksi’nde yer alan 30 firmanın günlük kapanış fiyatlarını içeren bir veri kümesi kullanılmıştır. Geliştirilen karar destek sistemi kullanılarak farklı beklenen getiri oranları için optimal portföyler elde edilmiş ve sonuçlar analiz edilmiştir. Esnek ve kullanımı kolay şekilde bir elektronik tablolama yazılımı ortamında çalışabilen ve Markowitz ortalama-varyans modelinin matematiksel detaylarına hakim olmayı gerektirmeksizin yatırımcıların optimal portföyler oluşturmalarına olanak sağlayan bir portföy optimizasyonu aracının geliştirilmiş olması çalışmanın en önemli katkısını oluşturmaktadır.

Anahtar Kelimeler

Portföy optimizasyonu, Markowitz ortalama-varyans modeli, Matematiksel programlama, Kuadratik programlama, Karar destek sistemleri

Kaynakça

• 1. Algarvio, H., Lopes, F., Sousa, J. and Lagarto, J. (2017) Multi-agent electricity markets: Retailer portfolio optimization using Markowitz theory, Electric Power Systems Research, 148, 282-294. doi: 10.1016/j.epsr.2017.02.031
• 2. Bernoulli, D. (1954) Exposition of a new theory on the measurement of risk, Econometrica,22(1), 23-36. doi: 10.2307/1909829
• 3. Cornuejols, G. and Tütüncü, R. (2006) Optimization methods in finance (Vol. 5), Cambridge University Press.
• 4. Derigs, U. and Nickel, N.H. (2003) Meta-heuristic based decision support for portfolio optimization with a case study on tracking error minimization in passive portfolio management, OR Spectrum, 25(3), 345-378. doi: 10.1007/s00291-003-0127-5
• 5. Doerner, K., Gutjahr, W.J., Hartl, R.F., Strauss, C. and Stummer, C. (2004) Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection, Annals of operations research, 131(1-4), 79-99. doi: 10.1023/B:ANOR.0000039513.99038.c6
• 6. Ertenlice, O. and Kalayci, C.B. (2018) A survey of swarm intelligence for portfolio optimization: Algorithms and applications, Swarm and evolutionary computation, 39, 36-52. doi: 10.1016/j.swevo.2018.01.009
• 7. Fisher, I. (1906) The nature of capital and income, The Macmillan Company.
• 8. Yahoo Finance, (2018). Dow Jones Industrial Average. Erişim Adresi: https://finance.yahoo.com/ (Erişim tarihi: 01.03.2018)
• 9. Jalota, H., Thakur, M. and Mittal, G. (2017) A credibilistic decision support system for portfolio optimization, Applied Soft Computing, 59, 512-528. doi: 10.1016/j.asoc.2017.05.054
• 10. Kalayci, C.B., Ertenlice, O. and Akbay, M.A. (2019) A comprehensive review of deterministic models and applications for mean-variance portfolio optimization, Expert Systems with Applications, 125, 345-368. doi: 10.1016/j.eswa.2019.02.011
• 11. Kellner, F. and Utz, S. (2019) Sustainability in supplier selection and order allocation: Combining integer variables with Markowitz portfolio theory, Journal of Cleaner Production, 214, 462-474. doi: 10.1016/j.jclepro.2018.12.315
• 12. Konno, H. (1990) Piecewise linear risk function and portfolio optimization, Journal of the Operations Research Society of Japan, 33(2), 139-156. doi: 10.15807/jorsj.33.139
• 13. Konno, H. and Yamazaki, H. (1991) Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management science, 37(5), 519-531. doi: 10.1287/mnsc.37.5.519
• 14. Li, H.Q. and Yi, Z.H. (2019) Portfolio selection with coherent Investor’s expectations under uncertainty, Expert Systems with Applications, 133, 49-58. doi: 10.1016/j.eswa.2019.05.008
• 15. Lwin, K.T., Qu, R. and MacCarthy, B.L. (2017) Mean-VaR portfolio optimization: A nonparametric approach, European Journal of Operational Research, 260(2), 751-766. doi: 10.1016/j.ejor.2017.01.005
• 16. Mansini, R., Ogryczak, W. and Speranza, M.G. (2014) Twenty years of linear programming based portfolio optimization, European Journal of Operational Research, 234(2), 518-535. doi: 10.1016/j.ejor.2013.08.035
• 17. Markowitz, H. (1952) Portfolio selection, The journal of finance, 7(1), 77-91. doi: 10.2307/2975974
• 18. Markowitz, H.M. (1991) Foundations of portfolio theory, The journal of finance, 46(2), 469-477. doi: 10.1111/j.1540-6261.1991.tb02669.x
• 19. Markowitz, H.M. (1999) The early history of portfolio theory: 1600-1960, Financial analysts journal, 55(4), 5-16. doi: 10.2469/faj.v55.n4.2281
• 20. Marschak, J. (1938) Money and the Theory of Assets, Econometrica, Journal of the Econometric Society, 6, 311-325. doi: 10.2307/1905409
• 21. Michaud, R.O. (1989) The Markowitz optimization enigma: Is ‘optimized’optimal?, Financial Analysts Journal, 45(1), 31-42. doi: 10.2469/faj.v45.n1.31
• 22. Pardalos, P. M., Sandström, M. and Zopounidis, C. (1994) On the use of optimization models for portfolio selection: A review and some computational results, Computational Economics, 7(4), 227-244. doi: 10.1007/BF01299454
• 23. Pouya, A.R., Solimanpur, M. and Rezaee, M.J. (2016) Solving multi-objective portfolio optimization problem using invasive weed optimization, Swarm and Evolutionary Computation, 28, 42-57. doi: 10.1016/j.swevo.2016.01.001
• 24. Power D.J. and Sharda R. (2009) Decision Support Systems, Springer Handbook of Automation, Nof, S.Y. (Ed.) Springer Science & Business Media, Berlin, Heidelberg, 1539-1548. doi: 10.1007/978-3-540-78831-7
• 25. Rockafellar, R.T. and Uryasev, S. (2000) Optimization of conditional value-at-risk, Journal of risk, 2, 21-42. doi: 10.21314/JOR.2000.038
• 26. Rockafellar, R.T. and Uryasev, S. (2002) Conditional value-at-risk for general loss distributions, Journal of banking & finance, 26(7), 1443-1471. doi: 10.1016/S0378- 4266(02)00271-6
• 27. Roy, A.D. (1952) Safety first and the holding of assets, Econometrica: Journal of the econometric society, 431-449. doi: 10.2307/1907413
• 28. Rubinstein, M. (2002) Markowitz's “Portfolio Selection”: A Fifty Year Retrospective, The journal of finance, 57(3), 1041-1045. doi: 10.1111/1540-6261.00453
• 29. Santos-Alamillos, F.J., Thomaidis, N.S., Usaola-García, J., Ruiz-Arias, J.A. and PozoVázquez, D. (2017) Exploring the mean-variance portfolio optimization approach for planning wind repowering actions in Spain, Renewable Energy, 106, 335-342. doi: 10.1016/j.renene.2017.01.041
• 30. Sprague Jr, R.H. and Carlson, E.D. (1982) Building effective decision support systems, Prentice Hall Professional Technical Reference. doi: 10.1016/0167-8051(82)90033-X
• 31. Tobin, J. (1958) Liquidity preference as behavior towards risk, The review of economic studies, 25(2), 65-86. doi: 10.2307/2296205
• 32. Williams, J.B. (1938) The Theory of Investment Value, Cambridge, Mass., Harvard University Press.
• 33. Xidonas, P., Mavrotas, G., Zopounidis, C. and Psarras, J. (2011) IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection, European Journal of Operational Research, 210(2), 398-409. doi: 10.1016/j.ejor.2010.08.028
• 34. Zhang, Y., Li, X. and Guo, S. (2018) Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature, Fuzzy Optimization and Decision Making, 17(2), 125-158. doi: 10.1007/s10700-017-9266-z
• 35. Zopounidis, C., Godefroid, M. and Hurson, C. (1995) Designing a multicriteria decision support system for portfolio selection and management, Advances in stochastic modelling and data analysis, Janssen, J., Skiadas, C.H. and Zopounidis, C. (Ed.) Springer, Dordrecht, 261-292. doi: 10.1007/978-94-017-0663-6_17