Portföy seçimi için ortalama-varyans-çarpıklık modeli

Abstract

Bu makalemizde, finansal yatırım araçları arasından optimal portföy seçimi için önce çarpıklığı dikkate alan ortalama-varyans-çarpıklık (MVS) modeli daha sonra iyi çeşitlendirilmiş bir portföy elde edebilmek için entropi ölçüsü ekleyerek oluşturduğumuz ortalama-varyans-çarpıklık-entropi (MVSE) modeli tanıtılmaktadır. MVS ve MVSE’de, geleneksel çarpıklık formüllerinin kullanılması yerine daha dayanıklı ve hesaplanması daha kolay olan Pearson çarpıklık ölçüsü kullanılmıştır. Her iki model, İMKB-30’da yer alan hisse senetleri arasından portföy oluşturmak için kullanılmış ve elde edilen sonuçlar Markowitz’in ortalama-varyans (MV) modeli ile karşılaştırılmıştır. MVS modeli ile, MV modelinden daha etkin portföylerin seçilebileceği gösterilmiştir. 

Keywords

• Markowitz Portföy Teorisi,Ortalama-Varyans,Çarpıklık,Entropi,Portföy Seçimi

Mean-variance-skewness model for portfolio selection

Abstract

In this paper, mean-variance-skewness (MVS) model is proposed first for optimal portfolio selection from financial assets, and then mean-variance-skewness-entopy (MVSE) model by adding entropy measure is proposed in order to obtain well diversified portfolio. In MVS and MVSE, Pearson skewness measure which is robust and easy to calculate than traditional skewness measures is used. Both models are used in IMKB-30 for portfolio selection and the results are compared with Markowitz mean-variance (MV) model. It is showed that more efficient portfolios can be selected by MVS model than MV model. 

Keywords

• Markowitz Portfolio Theory,Mean-Variance,Skewness,Entropy,Portfolio Selection

References

1. H. Markowitz, Portfolio Selection, Journal Of Finance, 7, 77-91, (1952).
2. S.Y. Park, Essays On Entropy Principle With Applications To Econometrics And Finance, University of Illinois, p.51,(2007).
3. P. Jorion, Bayes-stein estimation for portfolio analysis, Journal of Finance and Quantitative Analysis, 21:279-292, (1986).
4. K.B. Anil ve S.Y. Park Optimal Portfolio Optimization Using Maximum Entropy, Econometric Review, 27, 4-6, 484-512, (2008).
5. Y.B. Altaylıgil, Entropi Ölçüsü İle Portföy Seçimi, İ.Ü. Sosyal Bilimler Dergisi, Basım Aşamasında, 2, (2008).
6. P. Samuelson, The fundamental Approximation of Theorem of Portfolio analysis in terms of Means, Variance and higher Moments, Review of Economic Studies, 37, 537-542, (1970).
7. R. Merton, Optimum consumption and portfolio rules in continuous-time model, Journal of Economic Theory, 3, 373-413, (1971).
8. Y. Kroll, H. Levy, H. Markowitz, Mean-variance versus direct utility maximization, Journal of Finance, 39, 42-62, (1984).

9. H.Kono, T. Suzukia, D. Kobayashi, A branch and bound algroritm for solving mean- risk-skewness portfolio models, Optimization Methods and Sofware, (1998).
10. H. Kono, H. Shirakawa, H. Yamazaki, A mean absolute deviation skewness Portfolio Optimization Model, Annals of Operations Research, 45, 205-220, (1993).
11. M. Pornchai, D. Krishnan, H. Shahid ve J. P. Arun, Portfolio selection and skewness Evidence from from international Stock Markets, Journal of Banking and Finance, 21, 143-167, (1997).
12. S. Liu, S.Y. Wang ve W. Qui, Mean-variance-skewness model for portfolio selection with transaction costs, International Journal of Systems Science, Vol. 34, March, (2003).
13. C.R. Harvey, J.C. Liechty, M.W. Liechty, Müller P. Portfolio Selection With Higer Moments, Temmuz, (2004). 20
14. K. Jana, T.K. Roy, S.K. Mazumder, Multi-objective mean-variance-skewness model for Portfolio Optimization, Advanced Modeling and Optimization, 9, 1, (2007).
15. W.F. Sharpe, The Sharpe Ratio, Journal of Portfolio Management, 21, Fall, Issue 1 49-58 (1994).
16. C. Shannon, E. A Mahmematical Theory of Communication, Bell System Technical Journal, 27, 379-423, (1948).
17. J.N. Kapur, H.K. Kesevan, Entropy Optimization Principles with Applications, Academic Press, (1992).
18. EK 1 Portföy seçimi için Mathematica kodu