Publication: Kuadratik programlama ile portföy optimizasyonu ve İMKB’de bir uygulama
Abstract
KUADRATİK PROGRAMLAMA İLE PORTFÖY OPTİMİZASYONU VE İMKB'DE BİR UYGULAMA Portföy optimizasyonu, mevcut fonların menkul kıymet, tahvil gibi varlıklara yatırılması sürecidir. Portföy teorisinin temel amacı, yatırımların çeşitli finansal varlıklar arasında en uygun şekilde dağıtılmasıdır.. Kuadratik formdaki Markowitz ortalama varyans modeli, yatırımcıların bu dağıtımı risk ve getiriyi göz önünde bulundurarak gerçekleştirmesine imkan sağlayan kantitatif bir yöntemdir. Bu çalışmada, Markowitz kuadratik programlama ile portföy seçim modelinin İMKB 30 endeksinde yer alan hisse senetlerine uygulaması yapılmış ve farklı beklenen getiri düzeylerinde minimum riske sahip etkin portföylerin elde edilmesi amaçlanmıştır. Çalışmanın ilk kısmında, İMKB 30 endeksinde yer alan hisse senetlerinin Ocak 2003-Aralık 2004 arasındaki 24 aylık getiri oranları kullanılarak beklenen getiri ve varyans-kovaryans matrisi elde edilmiştir. Daha sonra model LINGO Sonuç olarak, portföy ağırlıkları ve aynı risk düzeyinde daha yüksek beklenen getiriye, aynı beklenen getiri düzeyinde daha düşük riske sahip optimum portföyler bulunmuştur. Name and Surname : Gökhan Çolakoğlu Field : Econometrics Programme : Operations Research Supervisor : Prof. Dr. İbrahim Doğan Degree Awarded and Date : Master - July 2005 Portfolio Optimization, Quadratic Programming, ISE
PORTFOLIO OPTIMIZATION BY QUADRATIC PROGRAMMING AND AN APPLICATION OF ISE Portfolio optimization is the process of investing existent funds into stocks, bonds, etc. The fundamental goal of portfolio theory is to optimally allocate investments between different financial assets. Mean variance model of Markowitz, which is in the form of quadratic programming, is a quantitative method which will allow investors to make this allocation by considering risk and return. In this study, Markowitz portfolio selection model is applied to the stocks of ISE 30 index and the goal is to obtain efficient portfolios with the minimum risk subject to different level of expected returns. In the first part of the study, expected returns and variance-covariance matrices were obtained by using 24 months rates of return of ISE 30 index stocks during january 2003-September 2004. Then the model was solved by LINGO programme. Finally, portfolio weights and optimum portfolios with expected return greater than any other with the same risk level, and lesser risk than any other with the same return level were determined.
PORTFOLIO OPTIMIZATION BY QUADRATIC PROGRAMMING AND AN APPLICATION OF ISE Portfolio optimization is the process of investing existent funds into stocks, bonds, etc. The fundamental goal of portfolio theory is to optimally allocate investments between different financial assets. Mean variance model of Markowitz, which is in the form of quadratic programming, is a quantitative method which will allow investors to make this allocation by considering risk and return. In this study, Markowitz portfolio selection model is applied to the stocks of ISE 30 index and the goal is to obtain efficient portfolios with the minimum risk subject to different level of expected returns. In the first part of the study, expected returns and variance-covariance matrices were obtained by using 24 months rates of return of ISE 30 index stocks during january 2003-September 2004. Then the model was solved by LINGO programme. Finally, portfolio weights and optimum portfolios with expected return greater than any other with the same risk level, and lesser risk than any other with the same return level were determined.