GÜVEN SAYILGAN, Değer.Arma MUT

Portföy optimizasyonunda alt kısmi moment ve yarı-varyans ölçütlerinin kullanılması

Portföy optimizasyonu, esas olarak getirinin maksimize edilmesi ve riskin minimize edilmesinin hedeflendiği çok amaçlı bir optimizasyon problemidir. Problemin çözümü sonucunda elde edilecek sonuçların geçerliliği açısından, bu problemin parametrelerinin doğru olarak tanımlanması önem taşımaktadır.Çeşitli araştırmacılar tarafından yatırımcıların risk algısını daha iyi temsil ettikleri belirtilen kayıp riski ölçütlerinin arasında bulunan yarı-varyans ve alt kısmi moment ölçütleri kullanılarak portföy optimizasyonu uygulamasının gerçekleştirildiği bu çalışmada, pareto etkin portföylerin elde edilmesi için sezgisel hesaplama tekniklerinden birisi olan genetik algoritmaların kullanılması tercih edilmiştir. Geliştirilen uygulama, İstanbul Menkul Kıymetler Borsası (İMKB) 100 endeksine kayıtlı hisse senetlerinin geçmiş verileriyle test edilmiş ve elde edilen etkin sınırların elde edilmesi beklenen sonuçlarla uyum içerisinde bulunduğu gözlenmiştir.

Uses of variance and lower partial moment measures for portfolio optimization

Portfolio optimization is mainly a multi-objective optimization problem that aims to maximize expected return while minimizing risk. It is important to define the meaning of these parameters accurately, in terms of validity that is acquired by the solution of the problem. In this study, portfolio optimization is implemented through two downside risk measures, semi-variance and lower partial moment, which are stated by researchers to be better representation for investors risk perception. Genetic algorithms, which are among the heuristic computational methods, are used to achieve pareto-efficient portfolios. The implementation is tested by historical data of the shares that are authorized to Istanbul Stock Exchange (ISE) 100 Index, and it is observed that the efficient portfolios achieved by the implementation are consistent with expected results.

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1. Ait-Sahalia, Y. ve Brandt, M. (2001). Variable Selection for Portfolio Choice. Journal of Finance, 54, 1297–1351.
2. Bawa, V. S. (1975). Optimal, Rules For Ordering Uncertain Prospects. Journal of Financial Economics, 2(1), 95–121.
3. Bawa, V. S. ve Lindenberg, E. B. (1977). Capital Market Equilibrium in a Mean Lower Partial Moment Framework. Journal of Financial Economics, 5(2), 189–200.
4. Bawa, V. S., Lindenberg, E. B. ve Rafsky, L. C. (1979). An Efficient Algorithm to Determine Stochastic Dominance Admissible Sets. Management Science, 25(7),609–622.
5. Benartzi, S. ve Thaler, R.. (1995). Myopic Loss Aversion and The Equity Premium Puzzle. Quarterly Journal of Economics, 110, 73–92.
6. Berkelaar, Arjan B., Kouwenberg R. ve Post T. (2004). Optimal Portfolio Choice Under Loss Aversion. The Review of Economics and Statistics, 86(4), 973–987.
7. Chen, D., Chen, C. ve Chen, J. (2007). Downside risk measures and equity returns in the NYSE. Applied Economics, 41(8), 1055–1070.
8. Coutino-Gomez, C. A., Torres-Jimenez, J. ve Villarreal-Antelo, B. M. (2003). Heuristic Methods for Portfolio Selection at the Mexican Stock Exchange. İçinde, Emilio Corchado ve Hujun Yin. (Editörler), Intelligent Data Engineering and Automated Learning. New York: Springer Berlin/Heidelberg.
9. Davidson, R. (2008). Stochastic Dominance. İçinde, Steven N. Durlauf ve Lawrence E. Blume (Editörler), The New Palgrave Dictionary of Economics (2nd Ed.).Basingstoke: Palgrave Macmillan.
10. Dreo, J., Petrowski, A., Siarry, P. ve Taillard, E. (2006). Metaheuristics for Hard Optimization. New York: Springer Berlin/Heidelberg.
11. Estrada, J. (2008). Mean-Semivariance Optimization: A Heuristic Approach. Journal of Applied Finance, Spring/Summer 2008, 57–72.
12. Fernández, A. ve Gómez, S. (2007). Portfolio selection using neural networks.Computers & Operations Research, 34(4), 1177–1191.
13. Fishburn, P. C. (1977). Mean-Risk Analysis with Risk Associated with Below-Target Returns. The American Economic Review, 67(2), 116–126.
14. Friedman, M. ve Savage, L. P. (1948). The Utility Analysis of Choices involving Risk. Journal of Political Economy, 56(4), 279–304.
15. Gomes, F. J. (2005). Portfolio Choice and Trading Volume With Loss-Averse Investors.Journal of Business, 78(2), 675–706.
16. Grootveld, H. ve Hallerbach, W. (1999). Variance vs. downside risk: Is there really that much difference?. European Journal of Operational Research, 114(2),304–319.
17. Groner, R., Groner, M. ve Bischof, W. F. (1983). Approaches to Heuristics: A Historical Review. İçinde, Walter F. Bischof, Marina Groner ve Rudolf Groner (Editörler), Methods of Heuristics. Londra: Lawrence Erlbaum Associates.
18. Hadar, J. ve Russell, W. R. (1969). Rules for Ordering Uncertain Prospects. The American Economic Review, 59(1), 25–34.
19. Hogan, W. W. ve Warren, J. M. (1972). Computation of the Efficient Boundry in the E-S Portfolio Selection Model. Journal of Financial and Quantitative Analysis,7(4), 1881–1896.
20. Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. Michigan:University of Michigan Press.
21. Holton, G. A. (2004). Defining Risk. Financial Analyst Journal, 60(6), 19-25.
22. İMKB web sitesi, Aylık Fiyat ve Getiri Verileri, 1986 - 2008/12, http://www.imkb.gov.tr/Data/StocksData.aspx (Eriflim tarihi: 03.05.2009)
23. İMKB web sitesi, 2000 Yılından İtibaren Endekslerde Bulunan fiirketler (İMKB Ulusal-30, İMKB Ulusal-50 ve İMKB-100 için), 2009, http://www.imkb.gov.tr/Data/StocksData.aspx (Eriflim tarihi: 03.05.2009)
24. İMKB web sitesi, Tahvil ve Bono Piyasası Günlük Bültenleri, 02.01.2009, http://www.imkb.gov.tr/Data/BondsandBillsData.aspx (Erişim tarihi: 25.05.2009)
25. Jarrow, R. ve Zhao, F. (2006). Downside Loss Aversion and Portfolio Management.Management Science, 52(4), 558?566.
26. Jensen, M. C., Black, F. ve Scholes, M. (1972). The Capital Asset Pricing Model:Some Empirical Tests. İçinde, Michael C. Jensen (Editör), Studies in the Theory of Capital Markets. New York: Praeger Publishers Inc.
27. Knight, F. H. (1921). Risk, Uncertainty, and Profit, Hart, Schaffner, and Marx Prize Essays, no. 31. Boston and New York: Houghton Mifflin.
28. Kraus, A. ve Litzenberger, R. H. (1976). Skewness Preference and the Valuation of Risk Assets. The Journal of Finance, 31(4), 1085–1100.
29. Lin, C. ve Liu, Y. (2008). Genetic Algorithms for Portfolio Selection Problems with Minimum Transaction Lots. European Journal of Operational Research,185(1), 393–404.
30. Markowitz, H. M. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.
31. Markowitz, H. M. (1956). The Optimization of a Quadratic Function Subject to Linear Constraints. Naval Research Logistics Quarterly, 3(1-2), 111–133.
32. Markowitz, H. M. (1959). Portfolio Selection, Efficient Diversification of Investment.New York: Yale University Press.
33. Markowitz, H. M. (1991). Foundations of Portfolio Theory. The Journal of Finance,46(2), 469–477.
34. Markowitz, H. M., Todd, P., Xu, G. ve Yamane, Y. (1993). Computation of mean semivariance efficient sets by the Critical Line Algorithm. Annals of Operations Research, 45(1), 307–317.
35. Nawrocki, D. N. (1991). Optimal Algorithms And Lower Partial Moment: Ex- Post Results. Applied Economics, 23, 465–470.
36. Nawrocki, D. N. (1999). A Brief History of Downside Risk Measures. Journal of Investing, 8(3), 9–25.
37. von Neumann, J. ve Morgenstern, O. (1943). Theory of Games and Economic Behavior (Commemorative Edition) (Princeton Classic Editions). Princeton University Press.
38. Pratt, J. W. (1964). Risk Aversion in the Small and in the Large. Econometrica,32(1/2), 122–136.
39. Price, K., Price, B. ve Nantell, T. J. (1982). Variance and Lower Partial Moment Measures of Systematic Risk: Some Analytical and Empirical Results. The Journal of Finance, 37(3), 843–855.
40. Roy, A. D. (1952). Safety First and the Holding of Assets. Econometrica, 20(3),431–449.
41. Rudolph, G. (1994). Convergence Analysis of Canonical Genetic Algorithms. IEEE Transactions on Neural Networks, 5(1), 96–101.
42. Saha, A. (1993). Expo-power Utility: A Flexible Form for Absolute and Relative Risk Aversion. American Journal of Agricultural Economics, 75, 905–913.
43. Sharpe, W. F. (1994). The Sharpe Ratio, The Journal of Portfolio Management, 21(1), 49–58.
44. Sharpe, W. F., Alexander, G. J. ve Bailey, J. V. (1999). Investments. New York:Prentice Hall.
45. Sortino, F. A. ve Price, L. N. (1994). Performance Measurement in a Downside Risk Framework. The Journal of Investing, 3(3), 59–94.
46. Türk Dil Kurumu (TDK) web sitesi, Büyük Türkçe Sözlük, http://tdkterim. gov.tr/bts/ (Erişim tarihi: 23.03.2009)