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Kovaryans Matrisi Tahmininin Portföy Seçimine Etkisi: İMKB’de Farklı Yatırım Ufukları İçin Uygulama

Year 2012, Volume: 12 Issue: 3, 311 - 322, 01.07.2012

Abstract

Portföy seçim sürecinde; beklenen getiri vektörü ve kovaryans matrisinin tahmin edilmesi iki önemli girdidir. Bu çalışmada farklı tekniklerin kullanılması ile gerçekleştirilen kovaryans matrisi tahmininin; portföy riski üzerindeki etkisinin araştırılmasına odaklanılmıştır. Portföy seçim işlemi 1986:01-2009:12 dönemleri arasında gerçekleştirilmiştir. Veri seti olarak da bu dönem içinde İMKB’de işlem gören tüm hisse senetlerinin günlük kapanış fiyatları kullanılmıştır. Portföy seçim modeli olarak Markowitz Modeli kullanılmıştır. Yatırım ufku olarak bir gün, bir hafta, on beş gün, bir ay ve bir yıllık periyotlar tercih edilmiştir. Kovaryans tahmin edicileri olarak ise örnek kovaryans tahmin edicisi ile Ledoit ve Wolf(2004) tarafından geliştirilen küçülme tahmin edicisi kullanılmıştır. Araştırma sonucuna göre Ledoit ve Wolf (2004)’ün küçülme tahmin edicisi ile İMKB’de daha düşük riske sahip olan ve daha kolay yönetilebilir portföy seçeneklerine ulaşmak mümkün olmuştur

References

  • Bengtsson, C. ve Holst I. (2002) “On Portfolio Selection: İmproved Covariance Matrix Estimation For Swedish Asset Returns” Working Paper Series.
  • Ceylan, A. ve Korkmaz, T. (1998) Borsada Uygulamalı Portföy Yönetimi 3. Baskı, Bursa, Ekin Kitapevi Yayınları.
  • Clarke, R.,, H. Silva ve S. Thorley (2006), “Minimum Variance Portfolios in the U.S.. Equity Market” Portfolio Management, 33(1):10-24.
  • Disatnik, D. J. ve S. Benninga (2006) “Estimating the Covariance Matrix for Portfolio Optimization” Working Paper Series.
  • Elton, E. ve M. Gruber (1973)“Estimating the Dependence Structure of Share Prıces Implıcatıons for Portfolio Selection” Journal of Finance, 28(5):1203-1232.
  • Elton, E., M. Gruber ve T. Urich (1978) “Are Betas Best?”Journal of Finance, 33(5):1375-1384.
  • Eun, Cheol S. ve Bruce G. Resnick (1984) “Estimating The Correlation Structure of International Share Prices”The Journal of Finace, 39(5):1311-1324.
  • Frost, P. A. ve J. E. Savarino (1986) “An Emprcal Bayes Approach to Efficient Portfolio Selection” The Journal of Financial Quantitative Analysis, 21(3):293- 305.
  • Jagannathan, R. ve T. Ma (2003) “Risk Reduction in Large Portfolios: Why İmposing The Wrong Constrains Helps”Journal of Finance, 58:1651-1683.
  • Jagannathan, R. ve T. Ma. (2000) “Three Methods for Improving the Precision in Covariance Matrix Estimation” Working Paper Series.
  • Jorion, P. (1986) “Bayes-Stein Estimation for Portfolio Analysis, Bayes-Stein Estimation for Portfolio Analysis” Journal of Financial and Quantitative Analysis, 21:279-292.
  • Ledoit, 0. ve M. Wolf (2004) “Honey I Shrunk the Sample Covariance Matrix” Journal of Portfolio Management, 31: 603-621.
  • Ledoit, 0. ve M. Wolf (2003) “Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection” Journal of Empirzcal Finance,10:603-621.
  • Markowitz H. M. (1959) Portfolio Selection: Efcient Diversifcation of Investments, Wiley, Yale University Press.
  • Markowitz H. M.(1956) “The optimization of a quadratic function subject to linear constraints”,Naval Research Logistics Quarterly, 3:111-133.
  • Markowitz H. M.(1987)Mean-Variance Analysis in Portfolio Choice and Capital Markets Blackwell Publishers.
  • Markowitz, H. (1952) “Portfolio Selection”Journal of Finance, 1(7):7-91.
  • Pafka, S. ve 1. Kondor (2004) “Estimated Correlation Matrices And Portfolio Optimization”, Physca A: Statistical Mechanics and Its Applications, 343: 623-634.
  • Stein, C. (1955) “Inadmissibility of the Usual Estimator for the Mean of the Multivariate Normal Distribution” Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1:197-206.

The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE

Year 2012, Volume: 12 Issue: 3, 311 - 322, 01.07.2012

Abstract

The expected return vector and covariance matrix estimation are important input on the portfolio selection process. In this study, the use of different techniques to estimate the covariance matrix have been focused on the research of impact on portfolio risk. Portfolio selection process is carried out the periods of 1986:01-2009:12. The daily closing price of all stocks listed on the ISE as data set in this period is used. Markowitz portfolio selection model is used as a model. Investment horizon of one day, a week, for fifteen days, one month and one-year periods were chosen. The sample covariance estimator with the shrinkage estimato rdeveloped by Ledoit and Wolf(2004) as covariance estimators is used. According to the research results, the ISE with a lower risk and more easily managed portfolio options have been able to achieve by shrinkage estimator of Ledoit and Wolf(2004)

References

  • Bengtsson, C. ve Holst I. (2002) “On Portfolio Selection: İmproved Covariance Matrix Estimation For Swedish Asset Returns” Working Paper Series.
  • Ceylan, A. ve Korkmaz, T. (1998) Borsada Uygulamalı Portföy Yönetimi 3. Baskı, Bursa, Ekin Kitapevi Yayınları.
  • Clarke, R.,, H. Silva ve S. Thorley (2006), “Minimum Variance Portfolios in the U.S.. Equity Market” Portfolio Management, 33(1):10-24.
  • Disatnik, D. J. ve S. Benninga (2006) “Estimating the Covariance Matrix for Portfolio Optimization” Working Paper Series.
  • Elton, E. ve M. Gruber (1973)“Estimating the Dependence Structure of Share Prıces Implıcatıons for Portfolio Selection” Journal of Finance, 28(5):1203-1232.
  • Elton, E., M. Gruber ve T. Urich (1978) “Are Betas Best?”Journal of Finance, 33(5):1375-1384.
  • Eun, Cheol S. ve Bruce G. Resnick (1984) “Estimating The Correlation Structure of International Share Prices”The Journal of Finace, 39(5):1311-1324.
  • Frost, P. A. ve J. E. Savarino (1986) “An Emprcal Bayes Approach to Efficient Portfolio Selection” The Journal of Financial Quantitative Analysis, 21(3):293- 305.
  • Jagannathan, R. ve T. Ma (2003) “Risk Reduction in Large Portfolios: Why İmposing The Wrong Constrains Helps”Journal of Finance, 58:1651-1683.
  • Jagannathan, R. ve T. Ma. (2000) “Three Methods for Improving the Precision in Covariance Matrix Estimation” Working Paper Series.
  • Jorion, P. (1986) “Bayes-Stein Estimation for Portfolio Analysis, Bayes-Stein Estimation for Portfolio Analysis” Journal of Financial and Quantitative Analysis, 21:279-292.
  • Ledoit, 0. ve M. Wolf (2004) “Honey I Shrunk the Sample Covariance Matrix” Journal of Portfolio Management, 31: 603-621.
  • Ledoit, 0. ve M. Wolf (2003) “Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection” Journal of Empirzcal Finance,10:603-621.
  • Markowitz H. M. (1959) Portfolio Selection: Efcient Diversifcation of Investments, Wiley, Yale University Press.
  • Markowitz H. M.(1956) “The optimization of a quadratic function subject to linear constraints”,Naval Research Logistics Quarterly, 3:111-133.
  • Markowitz H. M.(1987)Mean-Variance Analysis in Portfolio Choice and Capital Markets Blackwell Publishers.
  • Markowitz, H. (1952) “Portfolio Selection”Journal of Finance, 1(7):7-91.
  • Pafka, S. ve 1. Kondor (2004) “Estimated Correlation Matrices And Portfolio Optimization”, Physca A: Statistical Mechanics and Its Applications, 343: 623-634.
  • Stein, C. (1955) “Inadmissibility of the Usual Estimator for the Mean of the Multivariate Normal Distribution” Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1:197-206.
There are 19 citations in total.

Details

Other ID JA42SK45NZ
Journal Section Research Article
Authors

Gülfen Tuna This is me

Publication Date July 1, 2012
Published in Issue Year 2012 Volume: 12 Issue: 3

Cite

APA Tuna, G. (2012). The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE. Ege Academic Review, 12(3), 311-322.
AMA Tuna G. The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE. ear. July 2012;12(3):311-322.
Chicago Tuna, Gülfen. “The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE”. Ege Academic Review 12, no. 3 (July 2012): 311-22.
EndNote Tuna G (July 1, 2012) The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE. Ege Academic Review 12 3 311–322.
IEEE G. Tuna, “The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE”, ear, vol. 12, no. 3, pp. 311–322, 2012.
ISNAD Tuna, Gülfen. “The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE”. Ege Academic Review 12/3 (July 2012), 311-322.
JAMA Tuna G. The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE. ear. 2012;12:311–322.
MLA Tuna, Gülfen. “The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE”. Ege Academic Review, vol. 12, no. 3, 2012, pp. 311-22.
Vancouver Tuna G. The Effect of Covariance Matrix Estimation on Portfolio Selection Process: The Application for Different Investment Horizons in ISE. ear. 2012;12(3):311-22.