Öz
The effectiveness of the mean variance model, which is
based on the assumption that the historical returns are normally distributed,
falls when the series of stock returns do not follow a normal distribution. In order to increase the efficiency of the
model and to cover the properties of the return series’ distribution better,
higher order moments are added to the model. Mean variance model and its
variants are often facing another problem, corner solutions that models often
produce. Entropy function is used to prevent accumulation in
certain stocks and to increase natural diversity. Entropy functions, however,
can be far from the decision maker's point of view and can also produce results
that dominate other objective functions. In the study, a new mean-variance-skewness-kurtosis-fuzzy entropy
portfolio selection model with a new defined fuzzy entropy has been proposed to
overcome the problems mentioned and experiments was performed on two real data
sets to show the effectiveness of the proposed model with using various
portfolio objectives and preferences of decision makers. Entropy and fuzzy entropy
are compared in basis of portfolio models which have higher moments. Results
present that proposed fuzzy entropy approach is better-suited especially with
higher-moment portfolio models.
Anahtar Kelimeler
Portfolio optimization higher order moments entropy fuzzy entropy
Kaynakça
- Aracioglu, B., Demircan, F. ve Soyuer, H. (2011). Mean-Variance-Skewness-Kurtosis Approach to Portfolio Optimization: An Application in Istanbul Stock Exchange. Ege Akademik Bakis, 11, 9-17.
- Arditti, F. D., ve Levy, H. (1975). Portfolio efficiency analysis in three moments: the multiperiod case. The Journal of Finance, 30(3), 797-809.
- Bera, A. K., ve Park, S. Y. (2008). Optimal portfolio diversification using the maximum entropy principle. Econometric Reviews, 27(4-6), 484-512.
- BIST web site. Available online:https://datastore.borsaistanbul.com/ (accessed on 17 March 2016)
- Chunhachinda, P., Dandapani, K., Hamid, S., ve Prakash, A. J. (1997). Portfolio selection and skewness: Evidence from international stock markets. Journal of Banking & Finance, 21(2), 143-167.
- De Luca, A., ve Termini, S. (1972). A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and control, 20(4), 301-312.
- DeMiguel, V., Garlappi, L., ve Uppal, R. (2009). Optimal versus naive diversification: How ineffi-cient is the 1/N portfolio strategy?. Review of Financial Studies, 22(5), 1915-1953.
- Harvey, C. R., Liechty, J. C., Liechty, M. W., ve Müller, P. (2010). Portfolio selection with higher moments. Quantitative Finance, 10(5), 469-485.
- Huang, X. (2012). An entropy method for diversified fuzzy portfolio selection. International Journal of Fuzzy Systems, 14(1), 160-165.
- Jana, P., Roy, T. K., ve Mazumder, S. K. (2007). Multi-objective mean-variance-skewness model for portfolio optimization. Advanced Modeling and Optimization, 9(1), 181-193.
- Joshi, D., ve Kumar, S. (2014). Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making. Egyptian informatics journal, 15(2), 97-104.
- Jurczenko, E., Maillet, B. B., ve Merlin, P. (2005). Hedge funds portfolio selection with higher-order moments: a non-parametric mean-variance-skewness-kurtosis efficient frontier. Available at SSRN 676904.
- Kemalbay, G., Özkut, C. M., ve Franko, C. (2011). Portfolio selection with higher moments: A polynomial goal programming approach to ISE-30 index. Ekonometri ve Istatistik Dergisi, (13), 41-61.
- KennethFrench’swebsite. Available online: http: //mba.tuck.dartmouth.edu /pages /faculty /ken.french /index.html (accessed on 1 August 2016)
- Konno, H., ve Suzuki, K. I. (1995). A mean-variance-skewness portfolio optimization model. Journal of the Operations Research Society of Japan, 38(2), 173-187.
- Kosko, B. (1986). Fuzzy entropy and conditioning. Information sciences, 40(2), 165-174.
- Lai, K. K., Yu, L., ve Wang, S. (2006, June). Mean-variance-skewness-kurtosis-based portfolio op-timization. In Computer and Computational Sciences, 2006. IMSCCS'06. First Internation-al Multi-Symposiums on (Vol. 2, pp. 292-297). IEEE.
- Levy, H. (1974). The rationale of the mean-standard deviation analysis: Comment. The American Economic Review, 64(3), 434-441.
- Liu, S. Y. W. S., Wang, S. Y., ve Qiu, W. 2. (2003). Mean-variance-skewness model for portfolio selection with transaction costs. International Journal of Systems Science, 34(4), 255-262.
- Maringer, D., ve Parpas, P. (2009). Global optimization of higher order moments in portfolio selection. Journal of Global Optimization, 43(2-3), 219-230.
- Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
- Markowitz, H. M. (1991). Foundations of portfolio theory. The journal of finance, 46(2), 469-477.
- Mhiri, M., ve Prigent, J. L. (2010). International portfolio optimization with higher moments. International Journal of Economics and Finance, 2(5), 157.
- Özkan, M.M. (2003). Bulanık Hedef Programlama. Bursa: Ekin Kitapevi.
- Qin, Z., Li, X., ve Ji, X. (2009). Portfolio selection based on fuzzy cross-entropy. Journal of Computational and Applied mathematics, 228(1), 139-149.
- Pala, O., ve Aksaraylı, M. (2016). Bulanik Hedef Programlama Tabanli Yüksek Dereceden Momentlerle Bist 30 Endeksinde Portföy Seçimi. Sosyal Bilimler Metinleri Dergisi. (ICOMEP16, Özel Sayı) 98-113.
- Samuelson, P. A. (1970). The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. The Review of Economic Studies, 37(4), 537-542.
- Shannon, C. E. (1948). A mathematical theory of communication. Bell System. Technical. Journal. 27, 379–423.
- Simkowitz, M. A., ve Beedles, W. L. (1978). Diversification in a three-moment world. Journal of Financial and Quantitative Analysis, 13(05), 927-941.
- Singleton, J. C., ve Wingender, J. (1986). Skewness persistence in common stock returns. Journal of Financial and Quantitative Analysis, 21(03), 335-341.
- Steinbach, M. C. (2001). Markowitz revisited: Mean-variance models in financial portfolio analysis. SIAM review, 43(1), 31-85.
- Usta, I., ve Kantar, Y. M. (2011). Mean-variance-skewness-entropy measures: A multi-objective approach for portfolio selection. Entropy, 13(1), 117-133.
- Wang, S., ve Xia, Y. (2012). Portfolio selection and asset pricing (Vol. 514). Springer Science & Business Media.
- Yager, R. R. (1995). Measures of entropy and fuzziness related to aggregation operators. Information Sciences, 82(3-4), 147-166.
- Yu, J. R., Lee, W. Y., ve Chiou, W. J. P. (2014). Diversified portfolios with different entropy measures. Applied Mathematics and Computation, 241, 47-63.
- Zhou, R., Cai, R., ve Tong, G. (2013). Applications of entropy in finance: A review. Entropy, 15(11), 4909-4931.
Öz
Tarihsel
getirilerin normal dağıldığı varsayımına dayanan ortalama varyans modelinin
etkinliği, hisse senetleri getiri serileri normal dağılım göstermediğinde
düşmektedir. Modelin etkinliğini artırmak ve getiri serilerinin dağılışını daha
iyi modele aktarabilmek için yüksek dereceden momentler modele eklenmektedir.
Ortalama varyans modeli ve varyantlarının bir başka karşılaştığı problem ise
modellerin sıklıkla ürettiği köşe çözümlerdir. Belirli hisse senetlerine
yığılmayı önlemek ve doğal çeşitliliği artırmak için entropi fonksiyonu
kullanılmaktadır. Fakat entropi fonksiyonları karar vericinin bakış açısından
uzak ve diğer amaç fonksiyonlarına baskınlık kuran sonuçlar üretebilmektedir.
Çalışmada, değinilen sorunları aşmak için yeni bir bulanık entropi
tanımlanmış, yeni bir ortalama-varyans-çarpıklık-basıklık-bulanık
entropi portföy seçim modeli önerilmiş ve önerilen modelin etkililiğini
göstermek için, iki gerçek veri seti üzerindeki deneyler, çeşitli portföy
hedefleri ve karar vericilerin tercihleri kullanılarak gerçekleştirilmiştir.
Entropi ve bulanık entropi, amaç fonksiyonu olarak yüksek momentleri içeren
portföy modelleri açısından karşılaştırılmıştır. Bulgular, önerilen bulanık
entropi yaklaşımının, özellikle yüksek dereceden momentli portföy modelleri
için daha uygun olduğunu göstermektedir.
Anahtar Kelimeler
portföy optimizasyonu yüksek dereceden momentler entropi bulanık entropi
Kaynakça
- Aracioglu, B., Demircan, F. ve Soyuer, H. (2011). Mean-Variance-Skewness-Kurtosis Approach to Portfolio Optimization: An Application in Istanbul Stock Exchange. Ege Akademik Bakis, 11, 9-17.
- Arditti, F. D., ve Levy, H. (1975). Portfolio efficiency analysis in three moments: the multiperiod case. The Journal of Finance, 30(3), 797-809.
- Bera, A. K., ve Park, S. Y. (2008). Optimal portfolio diversification using the maximum entropy principle. Econometric Reviews, 27(4-6), 484-512.
- BIST web site. Available online:https://datastore.borsaistanbul.com/ (accessed on 17 March 2016)
- Chunhachinda, P., Dandapani, K., Hamid, S., ve Prakash, A. J. (1997). Portfolio selection and skewness: Evidence from international stock markets. Journal of Banking & Finance, 21(2), 143-167.
- De Luca, A., ve Termini, S. (1972). A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and control, 20(4), 301-312.
- DeMiguel, V., Garlappi, L., ve Uppal, R. (2009). Optimal versus naive diversification: How ineffi-cient is the 1/N portfolio strategy?. Review of Financial Studies, 22(5), 1915-1953.
- Harvey, C. R., Liechty, J. C., Liechty, M. W., ve Müller, P. (2010). Portfolio selection with higher moments. Quantitative Finance, 10(5), 469-485.
- Huang, X. (2012). An entropy method for diversified fuzzy portfolio selection. International Journal of Fuzzy Systems, 14(1), 160-165.
- Jana, P., Roy, T. K., ve Mazumder, S. K. (2007). Multi-objective mean-variance-skewness model for portfolio optimization. Advanced Modeling and Optimization, 9(1), 181-193.
- Joshi, D., ve Kumar, S. (2014). Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making. Egyptian informatics journal, 15(2), 97-104.
- Jurczenko, E., Maillet, B. B., ve Merlin, P. (2005). Hedge funds portfolio selection with higher-order moments: a non-parametric mean-variance-skewness-kurtosis efficient frontier. Available at SSRN 676904.
- Kemalbay, G., Özkut, C. M., ve Franko, C. (2011). Portfolio selection with higher moments: A polynomial goal programming approach to ISE-30 index. Ekonometri ve Istatistik Dergisi, (13), 41-61.
- KennethFrench’swebsite. Available online: http: //mba.tuck.dartmouth.edu /pages /faculty /ken.french /index.html (accessed on 1 August 2016)
- Konno, H., ve Suzuki, K. I. (1995). A mean-variance-skewness portfolio optimization model. Journal of the Operations Research Society of Japan, 38(2), 173-187.
- Kosko, B. (1986). Fuzzy entropy and conditioning. Information sciences, 40(2), 165-174.
- Lai, K. K., Yu, L., ve Wang, S. (2006, June). Mean-variance-skewness-kurtosis-based portfolio op-timization. In Computer and Computational Sciences, 2006. IMSCCS'06. First Internation-al Multi-Symposiums on (Vol. 2, pp. 292-297). IEEE.
- Levy, H. (1974). The rationale of the mean-standard deviation analysis: Comment. The American Economic Review, 64(3), 434-441.
- Liu, S. Y. W. S., Wang, S. Y., ve Qiu, W. 2. (2003). Mean-variance-skewness model for portfolio selection with transaction costs. International Journal of Systems Science, 34(4), 255-262.
- Maringer, D., ve Parpas, P. (2009). Global optimization of higher order moments in portfolio selection. Journal of Global Optimization, 43(2-3), 219-230.
- Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
- Markowitz, H. M. (1991). Foundations of portfolio theory. The journal of finance, 46(2), 469-477.
- Mhiri, M., ve Prigent, J. L. (2010). International portfolio optimization with higher moments. International Journal of Economics and Finance, 2(5), 157.
- Özkan, M.M. (2003). Bulanık Hedef Programlama. Bursa: Ekin Kitapevi.
- Qin, Z., Li, X., ve Ji, X. (2009). Portfolio selection based on fuzzy cross-entropy. Journal of Computational and Applied mathematics, 228(1), 139-149.
- Pala, O., ve Aksaraylı, M. (2016). Bulanik Hedef Programlama Tabanli Yüksek Dereceden Momentlerle Bist 30 Endeksinde Portföy Seçimi. Sosyal Bilimler Metinleri Dergisi. (ICOMEP16, Özel Sayı) 98-113.
- Samuelson, P. A. (1970). The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. The Review of Economic Studies, 37(4), 537-542.
- Shannon, C. E. (1948). A mathematical theory of communication. Bell System. Technical. Journal. 27, 379–423.
- Simkowitz, M. A., ve Beedles, W. L. (1978). Diversification in a three-moment world. Journal of Financial and Quantitative Analysis, 13(05), 927-941.
- Singleton, J. C., ve Wingender, J. (1986). Skewness persistence in common stock returns. Journal of Financial and Quantitative Analysis, 21(03), 335-341.
- Steinbach, M. C. (2001). Markowitz revisited: Mean-variance models in financial portfolio analysis. SIAM review, 43(1), 31-85.
- Usta, I., ve Kantar, Y. M. (2011). Mean-variance-skewness-entropy measures: A multi-objective approach for portfolio selection. Entropy, 13(1), 117-133.
- Wang, S., ve Xia, Y. (2012). Portfolio selection and asset pricing (Vol. 514). Springer Science & Business Media.
- Yager, R. R. (1995). Measures of entropy and fuzziness related to aggregation operators. Information Sciences, 82(3-4), 147-166.
- Yu, J. R., Lee, W. Y., ve Chiou, W. J. P. (2014). Diversified portfolios with different entropy measures. Applied Mathematics and Computation, 241, 47-63.
- Zhou, R., Cai, R., ve Tong, G. (2013). Applications of entropy in finance: A review. Entropy, 15(11), 4909-4931.
Ayrıntılar
| Bölüm | MAKALELER |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 18 Ocak 2018 |
| Yayımlandığı Sayı | Yıl 2018 18. EYİ Özel Sayısı |
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