DEVELOPING A PORTFOLIO OPTIMIZATION MODEL BASED ON LINEAR PROGRAMMING UNDER CERTAIN CONSTRAINTS: AN APPLICATION ON BORSA ISTANBUL 30 INDEX

Öz

The aims of this study are to lend assistance for the account owners who plan to make an investment in the financial markets to make the most accurate investments possible; accordingly, to develop a portfolio selection model and present it with its implementations. Instead of the L2 (standard deviation), risk function which is approached as a risk by Markowitz, the L1 (absolute deviation) risk function was used in the study and the optimal portfolios were trying to be attained. After the data acquired from the index of the Borsa Istanbul 30 index, the portfolio optimization model which is based on linear programming and was developed by Ching-Ter Chang (2005) was embraced in order to create an optimal portfolio. In this model, a new model was proposed by adding a limit on trading volume to reduce the systematic risk of the portfolio with the idea that it is one of the important indicators of the market and that it can create a decision-making risk perception. Thus, it was enabled for the portfolio to contain the equities from the industrial branch in desired numbers in accordance with the desire of the investors by adding the preference constraints on the Chang model. It can be said that this study will be useful for the investors and the finance executives who want to create a portfolio on specific risk and return level.

Anahtar Kelimeler

• Portfolio Optimization,Mean Absolute Deviation,Industry Risk,Trading Volume,Linear Programming,Borsa Istanbul

Belirli Kısıtlar Altında Doğrusal Programlamaya Dayalı Bir Portföy Optimizasyonu Modelinin Geliştirilmesi: Borsa İstanbul 30 Endeksi Üzerine Bir Uygulama

Öz

Bu çalışmanın amacı, finansal piyasalarda yatırım yapmayı düşünen tasarruf sahiplerine optimal yatırım yapma konusunda yol göstermek ve bu doğrultuda bir portföy optimizasyon modeli önermek ve uygulamaları ile birlikte sunmaktır. Çalışmamızda Markowitz’in risk olarak ele aldığı L2 (standart sapma) risk fonksiyonu yerine, L1 (mutlak sapma) risk fonksiyonu kullanılmış ve optimal portföyler elde edilmeye çalışılmıştır. Borsa İstanbul 30 Endeksinden veriler elde edildikten sonra, optimal portföy oluşturmak için doğrusal programlama yaklaşımına dayalı olan Ching-Ter Chang (2005) tarafından geliştirilen portföy optimizasyon modeli ele alınmıştır. Bu modele, portföyün sistematik olmayan riskini azaltmak için endüstri kollarına dağılım ve piyasanın önemli göstergelerinden biri olması ve karar vericide risk algısı yaratabileceği düşüncesiyle işlem hacmi kısıtı eklenerek yeni bir model önerilmiştir. Böylelikle, Chang modeline tercih kısıtları ilave edilerek yatırımcının isteği doğrultusunda portföyün istenen sayıda endüstri kolundan hisse senetlerini içermesi sağlanmıştır. Bu çalışma belirli bir risk ve getiri düzeyinde portföy oluşturmak isteyen finans yöneticilerine ve yatırımcılarına faydalı olacağı söylenebilir.

Anahtar Kelimeler

• Portföy Optimizasyonu,Ortalama Mutlak Sapma,Endüstri Riski,İşlem Hacmi,Doğrusal Programlama,Borsa İstanbul

Kaynakça

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