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

Yıl 2020, Cilt: 7 Sayı: 1, 115 - 141, 28.02.2020

Mehmet Levent Erdaş

https://doi.org/10.30626/tesamakademi.696299

Cited By: 3

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

• Aksoy, E. E. (2014). Uluslararası portföy yönetimi. Ankara: Detay Publication.
• Bekçioglu, S. (1988). Portföy teorisi ve sermaye piyasaları. Ankara.
• Bozdağ, N., Altan, S. and Duman, S. (2005). Minimax portföy modeli ile Markowitz ortalama-varyans portföy modelinin karşılaştırılması, 7. Ulusal Ekonometri ve İstatistik Sempozyumunda sunulan bildiri, İstanbul.
• Brennan, M. (1971). A note on dividend irrelevance and the Gordon valuation model. The Journal of Finance, 26(5), 1115-1121.
• Chang, C. T. (2005). A modified goal programming approach for the mean-absolute deviation portfolio optimization model. Applied Mathematics and Computation, 171(1), 567-572.
• Çıtak, A. O. S. (2016). Finansal yatırım analizi. İstanbul: Nobel Akademik Publication.
• Cihangir, M., Güzeler, A. K. and Sabuncu, İ. (2008). A Konno and Yamazaki approach to portfolio selection and its applications to IMKB financial sector shares. Gazi University The Journal of Faculty of Economics, 10(3), 125-142.
• Coşkun, M. (2010). Para ve sermaye piyasaları (kurumlar, araçlar ve analiz). Ankara: Detay Publication.
• Elbannan, M. A. (2015). The capital asset pricing model: an overview of the theory. International Journal of Economics and Finance, 7(1), 216-228.
• Ercan, M. K. and Ban, U. (2012). Değere dayalı işletme finansı finansal yönetim. Ankara: Gazi Publication.
• Erdaş, M. L. and Demir, Y. (2016). Developing a portfolio optimization model by fuzzy linear programming method: An application on the Istanbul stock exchange-30 index. Journal of International Social Research, 9(45), 768-789.
• Fama, E. F. and French, K. R. (2004). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25-46.
• Feinstein, C. D. and Thapa, M. N. (1993). Notes: A reformulation of a mean-absolute deviation portfolio optimization model. Management Science, 39(12), 1552-1553.
• Graham, B. and Dodd, D. L. (1934). Security analysis: Principles and technique. New York: McGraw-Hill.
• Gürol, E. and Kılıçoğlu, A. (1994). Business world dictionary. (2. Edition), İstanbul: Cem Publication.
• Karabıyık, L. and Anbar, A. (2010). Sermaye piyasası ve yatırım analizi. Bursa: Ekin Basım Publication.
• Karacabey, A. A. (2007). Risk and investment opportunities in portfolio optimization. European Journal of Finance and Banking Research, 1(1), 1-15.
• Kardiyen, F. (2007). Doğrusal programlama ile portföy optimizasyonu ve IMKB verilerine uygulanması üzerine bir çalışma. Atatürk University The Journal of Faculty of Economics, 21(2), 15-28.
• Kardiyen, F. (2008). The use of mean absolute deviatıon model and Markowitz mean variance model in portfolio optimızation and the application of them in IMKB data. Süleyman Demirel University The Journal of Faculty of Economics, 13(2), 335-350.
• Kayalıdere K. and Aktaş H. (2008). Alternatif portföy seçim modellerinin performanslarının karşılaştırılması İMKB örneği. Dokuz Eylül University The Journal of Institute of Social Sciences, 10(1), 290-312.
• Kıran, B. (2010). Trade volume and return volatility in Istanbul stock exchange. Doğuş University Journal, 11(1), 98-108.
• Kocadağlı, O. and Cinemre, N. (2010). A fuzzy nonlinear model approach with CAPM for portfolio optimization. Istanbul University Journal of the School of Business Administration, 39(2), 359-369.
• Konno, H. and Yamazaki, H. (1991). Mean absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5), 519-531.
• Konno, H. and Wijayanayake, A. (2002). Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints. Journal of Global Optimization Kluwer Academic Publishers, 22, 137-254.
• Konno, H. (2003). Portfolio optimization of small scale fund using mean-absolute deviation model. International Journal of Theoretical and Applied Finance, 6(4), 403-418.
• Konno, H. and Li, J. (2000). Applications of the integrated approach to international portfolio optimization. Asia-Pasific Financial Markets Kluwer Academic Publishers, 7, 121-144.
• Leon, N. K. (2007). An empirical study of relation between stock return volatility and trading volume in the BRVM. African Journal of Business Management, 1(7), 176-184.
• Levy, H. (1983). The capital asset pricing model: Theory and empiricism. Economic Journal, 93, 145- 165.
• Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. The Review of Economics and Statistics, 47(1), 13-37.
• Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
• Özçam, M. (1997). Varlık fiyatlama modelleri aracılığıyla dinamik portföy yönetimi. Ankara: Sermaye Piyasası Kurulu Yayınları Yayın No.104.
• Poyraz, E. (2016). Finansal yönetim. Bursa: Ekin Basım Publication.
• Radoplu, G. (2002). Para ve sermaye piyasaları. Isparta: Tuğra Ofset.
• Ross, S. A. (1976). The abritrage theory of capital asset pricing. Journal of Economic Theory, 13(5), 341-360.
• Roy, A. D. (1952). Safety first and the holding of assets. Econometrica The Econometric Society, 20(3), 431-449.
• Rubinstein, M. (2002). Markowitz’s portfolio selection: A fifty‐year retrospective. The Journal of Finance, LVII(3), 1041-1045.
• Schnabel J. A. (1984). Short sales restrictions and security market line. Journal of Business Research, 12(1), 87-96.
• Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management Science, 9(2), 277-293.
• Simaan, Y. (1997). Estimation risk in portfolio selection: The mean variance model versus the mean absolute deviation model. Management Science, 43(10), 1437-1446.
• Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26(1), 24-36.
• Turnbull, S. M. (1977). Market value and systematic risk. The Journal of Finance, 32(4), 1125-1142.
• Uğurlu, M., Erdaş, M. L. and Eroğlu, A. (2016). A linear programming model suggestion which decreases unsystematic risk in the portfolio management. Cankırı Karatekin University Journal of The Faculty of Economics, 6(1), 147-174.
• Uyar, U. and Kangallı, S. M. (2012). Trade volume constraint on optimal portfolio preference based on Markowitz model. Ege Akademic Review, 12(2), 183-192.
• Williams, J. B. (1938). The theory of investment value. Amsterdam: North Holland Publishing.