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

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

Keywords

• Kovaryans tahmini, portföy seçimi, küçülme tahmin edicisi, örnek kovaryans tahmin edicisi, yatırım ufku

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

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)

Keywords

• Covariance estimation, portfolio selection, shrinkage estimator, sample covariance estimator, ınvestment horizon

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