Stokastik baskınlık testi ile portföy optimizasyonu: BIST-30 endeksine uygulanması
Portfolio optimization with stochastic dominance test: An application to BIST-30 index
Yazar: KUTLAY URUN
Danışman: PROF. DR. OKTAY TAŞ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İşletme Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 2016
Konu: Ekonomi = Economics ; Matematik = Mathematics ; Mühendislik Bilimleri = Engineering Sciences

Özet:
Bu çalışmada, Türkiye'deki BIST-30 endeksi, direkt olarak uygulanan Ortalama – Varyans optimizasyonu ve İkinci Dereceden Stokastik Baskınlık Testi ile etkin hisselerden oluşturulan indirgenmiş portföye uygulanan Ortalama – Varyans optimizasyonu; eşit ağırlıklandırma, getiri maksimizasyonu, risk minimizasyonu, Sharpe oranı maksimizasyonu, Treynor oranı maksimizasyonu ve Jensen Alfası maksimizasyonuna göre karşılaştırılmıştır. Bu çalışmada, 01.01.2013–31.12.2015 dönemini kapsayan, günlük, haftalık ve aylık hisse senedi piyasa endeksi kapanış verileri kullanılmıştır. Öncelikli olarak portföy, portföy yönetimi, Geleneksel Portföy Yönetimi, Modern Portföy Yönetimi, portföy yönetim stratejileri, portföy performans ölçütlerinden teorik olarak bahsedilmektedir. Geleneksel Portföy yönteminin dezavantajlarından bahsedilip, sonrasında geliştirilen Modern Portföy yönteminin avantajlarından ve dezavantajlarından bahsedilmektedir.  Daha sonra Stokastik Baskınlık Testi'nden ve geçmişte yapılan çalışmalardan derinlemesine bahsedilip uygulamanın ilk aşaması olan İkinci Dereceden Stokastik Baskınlık Testi'nin nasıl yapıldığından bahsedilmektedir. İkinci Dereceden Stokastik Baskınlık Testi günlük, haftalık ve aylık getiriler baz alınarak yapılmıştır. BIST-30 endeksi günlük, haftalık ve aylık getirilere göre incelendiğinde, endeks bu üç getiri tipine göre de etkin çıkmamaktadır. Üç getiri periyoduna göre etkin çıkan hisseler ise OTKAR, PETKM, TAVHL ve TOASO olmuştur. OTKAR ve TOASO otomotiv, TAVHL ulaştırma, PETKM ise petrokimya sektöründe yer almaktadır. Buna ek olarak da bu üç farklı getiri tipine göre yapılan testin hepsinde her defasında diğer bütün hisseler tarafından domine edilen hisse ise KOZAL olmuştur. KOZAL hissesi ise demir çelik sektörüne ait bir hissedir. Burada daha sonra literatüre yeni bir çalışma olarak 2013, 2014 ve 2015 yıllarını iki yarıya bölerek günlük getirilere İkinci Dereceden Stokastik Baskınlık Testi uygulanmıştır. Burada neredeyse her yarı yılda etkin çıkan hisseler birbirlerinden farklıdır. Bu da BIST-30 endeksinin etkin olmayışının ve ekonomideki sürekli değişkenliğin göstergesidir. Daha sonra ise BIST-30 endeksine ve İkinci Dereceden Stokastik Baskınlık Testi'ne göre etkin çıkan hisselerden oluşturulmuş portföye ortalama – varyans optimizasyonuna göre eşit ağırlıklandırma, getiri maksimizasyonu, risk minimizasyonu, Sharpe oranı maksimizasyonu, Treynor oranı maksimizasyonu ve Jensen Alfası maksimizasyonu uygulanmıştır. BIST-30 endeksine uygulanan optimizasyon sonucuna göre yatırım yapılan hisseler ile, İkinci Dereceden Stokastik Baskınlık Testi'ne göre etkin çıkan hisselerden oluşan indirgenmiş portföye uygulunana optimizasyon sonucunda yatırım yapılan hisseler hemen hemen aynı hisselerdir. Başka bir deyişle İkinci Dereceden Stokastik Baskınlık Testi'ne göre etkin çıkan hisseler, BIST-30 endeksine uygulanan optimizasyon sonucunda yatırım yapılan hisseleri kapsamaktadır. Bu da uygulama sonuçlarının birbirleriyle tutarlı olduğunu göstermektedir. BIST-30 endeksine ve indirgenmiş portföye uygulanan getiri maksimizasyonu, risk minimizasyonu, Sharpe oranı maksimizasyonu, Treynor oranı maksimizasyonu ve Jensen Alfası maksimizasyonunda, her bir optimizasyon türünde iki portföy türünde de hisselere yapılan yatırım oranları oldukça yakındır.  Maksimizasyon ve minimizasyon kısıtlarına ve oranların parametrelerine göre hisselere yapılacak yatırımların yüzdeleri değişkenlik göstermektedir. Son olarak tüm bu optimizasyon işlemlerinden elde edilen yatırım oranları, 01/01/2016 – 15/04/2016 tarihleri arasındaki BIST-30 endeks getiri değerlerine uygulandığında en iyi getiri 2015 yılının ikinci yarısına uygulanan optimizasyon işleminden elde edilen yatırım oranları ile elde edilmektedir. Endeks bu süreçte % 22'lik bir büyüme gösterirken, günlük, haftalık ve aylık kapanış değerlerine uygulanan optimizasyondan elde edilen yatırım oranları endeksin altında kalmaktadır. Özetle 2015 yılının son 6 aylık kapanış değerlerine göre yapılan yatırımın, son 3 yıllık kapanış değerlerine göre yapılan yatırımdan daha iyi sonuç verdiği açıkça görülmektedir. Backtesting sonuçlarına göre, en iyi yatırım tahmini veren optimizasyon tipleri sırasıyla Risk Minimizasyonu, Sharpe Oranı Maksimizasyonu, Treynor Oranı Maksimizasyonu, Jensen Alfası Maksimizasyonu ve Getiri Maksimizasyonu olmuştur.

Abstract:
Portfolio management is trillion dollar business in today's financial world where every investor tries to increase the return of his portfolio while at the same time to decrease the risk of it. The classical and 60 yeras old Mean – Variance (MV) portfolio optimization method has become old fashioned since it has some weaknesses which do not satisfy today's financial needs when working with real data. At the core, among other shortcomings, the requirement of normal distributed returns renders the Mean – Variance optimized portfolios Secon Order Stochastic Dominance (SSD) inefficient. In this thesis, compared with a Turkey implemented directly in BIST-30 Index Mean – Variance optimization and Second Order Stochastic Dominance Test with active shares generated from reduced portfolio Mean – Variance optimization; equal weighting, risk minimization, return maximization, Sharpe ratio maximization, Treynor ratio maximization and Jensen's Alpha utilizes. In this study, daily, weekly and monthly stock market index closing data  has been used 01.01.2013 – by 31.12.2015 this covering the period. And mentioned portfolio, portfolio management, Traditional Portfolio Management, Modern Portfolio Management, portfolio management strategies, portfolio performance to meet the criteria of in theory. The disadvantage of the Traditional Portfolio are developed after the method referenced, are the advantages and disadvantages of Modern Portfolio management on both sides. And in addition to this topics, in this chapter, risk neutral investors, risk averse investors and risk seeking investors and decision makers are mentioned. Then in the third chapter mentioned the Stochastic Dominance Test and the depth of the work done in the past, the first phase of the application referenced Second Order Stochastic Dominance Test and First Order Stochastic Dominance Test how committed. First Order Stochastic Dominance Test search an answer this question which is "when can we say that everyone will prefer one investment instrument to another insvetmen instrument?" Secon Order Stochastic Dominance Test tries to find an answer this question which is "when can we say that anyone who is risk averse investor or decision maker will prefer one investment instrument to another investment instrument.  Second-Order Stochastic Dominance Test  is made on the basis daily, weekly and monthly benefits. When we analyze the daily closing values of the BIST-30 index; ARCLK, BIMAS, EREGL, FROTO, KCHOL, OTKAR, PETKM, TAVHL, TCELL, TOASO, TUPRS and ULKER are selected efficient shares. After the MV optimization which is applied to daily returns, at the return maximization EREGL, OTKAR, TAVHL, TOASO and ULKER; at the risk minimization OTKAR and TAVHL; at the Sharpe ratio maximization EREGL, OTKAR, TAVHL, TOASO and ULKER; at the Treynor ratio maximization EREGL, OTKAR, TAVHL and ULKER; at the Jensen's Alpha maximization EREGL, OTKAR, TAVHL, TOASO and ULKER are selected in our portfolio. Secondly, when we analyze weekly closing values of BIST-30 index; BIMAS, ENKAI, EREGL, OTKAR, PETKM, TAVHL, TOASO, TUPRS and ULKER are selected efficient shares. After the MV optimization which is applied to weekly returns, at the return maximization OTKAR, TAVHL, TOASO and ULKER; at the risk minimization OTKAR and TAVHL; at the Sharpe ratio maximization EREGL, OTKAR, PETKM, TAVHL, TOASO and ULKER; at the Treynor ratio maximization OTKAR, TAVHL and ULKER; at the Jensen's Alpha maximization EREGL, OTKAR, TAVHL, TOASO and ULKER are selected in our portfolio. Lastly, when we analyze the monthly closing values of BIST-30 index; ENKAI, OTKAR, PETKM, TAVHL and TOASO are selected efficient shares. After the MV optimization which is applied to monthly returns, at the return maximization OTKAR, PETKM, TAVHL and TOASO; at the risk minimization OTKAR; at the Sharpe ratio maximization OTKAR, PETKM, TAVHL and TOASO; at the Treynor ratio maximization ENKAI, OTKAR, PETKM, TAVHL and TOASO; at the Jensen's Alpha maximization OTKAR, PETKM, TAVHL and TOASO are selected in our portfolio. Second Order Stochastic Dominance  BIST-30 index is not efficient also according to the type of these three return according to the daily, weekly and monthly returns were examined. According to three return period is efficient has been the shares OTKAR, PETKM, TAVHL and TOASO. Located in the industry OTKAR and TOASO automotive, TAVHL transportation and PETKM petrochemical. In addition, these three distinct return type according to all the test done and each time has been the dominate share KOZAL. KOZAL stock is a stock that belongs to the iron and steel industry. As a new study here later literature has been applied by half a Second Order Stochastic Dominance Test interested in daily return 2013, 2014 and 2015 by dividing the two halves. Here the active shares nearly every half year is different from each other. The shares are efficient according to the daily closing value of the first six months of 2013 are as follows; ARCLK, BIMAS, CCOLA, EREGL, KCHOL, OTKAR, PETKM, TAVHL, TCELL, TTKOM and ULKER. After the MV optmization which is applied to daily closing value of the first six months of 2013, at the return maximization BIMAS, CCOLA, OTKAR, TAVHL, TCELL, TTKOM and ULKER; at the risk minimization OTKAR; at the Sharpe ratio maximization CCOLA, OTKAR, TAVHL and ULKER; at the Treynor ratio maximization CCOLA, OTKAR, TAVHL, TCELL, TTKOM and ULKER; at the Jensen's Alpha mazimization BIMAS, CCOLA, OTKAR, TAVHL, TCELL, TTKOM and ULKER are selected in our portfolio. The shares are efficient according to the daily closing value of the second six months of 2013 are as follows; BIMAS, ENKAI, KCHOL, PETKM, SISE, TAVHL, TCELL and ULKER. After the MV optmization which is applied to daily closing value of the second six months of 2013, at the return maximization ENKAI, SISE, TAVHL and ULKER; at the risk minimization ENKAI and TAVHL; at the Sharpe ratio maximization ENKAI and TAVHL; at the Treynor ratio maximization ENKAI, TAVHL and ULKER; at the Jensen's Alpha maximization ENKAI, SISE, TAVHL and ULKER are selected in our portfolio. The shares are efficient according to the daily closing value of the first six months of 2014 are as follows; EREGL and KRDMD. After the MV optmization which is applied to daily closing value of the first six months of 2014, at the return maximization EREGL and KRDMD; at the risk minimization KRDMD; at the Sharpe ratio maximization EREGL and KRDMD; at the Treynor ratio maximization EREGL; at the Jensen's Alpha maximization EREGL and KRDMD are selected in our portfolio. The shares are efficient according to the daily closing value of the second six months of 2014 are as follows; FROTO, KCHOL, OTKAR, PETKM, SISE, THYAO and TTKOM. After the MV optmization which is applied to daily closing value of the second six months of 2014, at the return maximization FROTO, KCHOL, OTKAR, PETKM, SISE and THYAO; at the risk minimization OTKAR; at the Sharpe ratio maximization FROTO, OTKAR, PETKM, SISE and THYAO; at the Treynor ratio maximization FROTO, KCHOL, OTKAR, PETKM, SISE and THYAO; at the Jensen's Alpha maximization FROTO, KCHOL, OTKAR, PETKM, SISE and THYAO are selected in our portfolio.  The shares are efficient according to the daily closing value of the first six months of 2015 are as follows; ARCLK, DOAS, ENKAI, FROTO, KCHOL, KOZAL, TAVHL and TUPRS. After the MV optmization which is applied to daily closing value of the first six months of 2015, at the return maximization DOAS, ENKAI, KOZAL, TAVHL and TUPRS; at the risk minimization DOAS and KOZAL; at the Sharpe ratio maximization DOAS, ENKAI, KOZAL, TAVHL and TUPRS; at the Treynor ratio maximization DOAS, ENKAI, KOZAL and TAVHL; at the Jensen's Alpha maximization DOAS, ENKAI, KOZAL, TAVHL and TUPRS are selected in our portfolio.  The shares are efficient according to the daily closing value of the second six months of 2015 are as follows; BIMAS and PETKM. After the MV optmization which is applied to daily closing value of the second six months of 2015, at the return maximization BIMAS and PETKM; at the risk minimization PETKM; at the Sharpe ratio maximization PETKM; at the Treynor ratio maximization BIMAS and PETKM; at the Jensen's Alpha maximization BIMAS and PETKM are selected in our portfolio. This is indicative of the continuous variability in the economy and the lack of efficient for BIST-30 index. Then the BIST-30 index and the Second Order Stochastic Dominance Test the efficient shares, according to the  portfolio is created from Mean – Variance optimization, equal weighting, risk minimization, return mazimization, Sharpe ratio maximization, Treynor ratio maximization and Jensen's Alpha maximization. BIST-30 index according to the results of optimization applied to investment shares that are made as a result of the reduced portfolio with applied optimization invested shares are shares almost the same. In the other words, according to Second Order Stochastic Dominance Tests the efficient shares, BIST-30 index as a result of optimization applied to cover the invested stocks. This is consistent with each other of the results of the application. Finally BIST-30 index and reduced risk minimization, maximization of return, applied portfolio Sharpe ratio maximization, Treynor ratio maximization and Jensen Alpha maximization, each type of a type of two portfolio optimization in investment ratios into shares. The percent of investments into shares varies of the maximization and minimization according to the parameters, and restricted rates. Finally, we applied the investment ratio which are gotten from the application to BIST-30 index's return value which are between 01/01/2016 – 15/04/2016. After this backtesting, the best result are gotten from according to the daily closing value of the second half of the 2015's investment ratio which is 33,39 % average return. BIST-30 index grow 22 percent between this date. But the portfolio wihch is created from 2015's second half index return grow an about 34 percent. According to the result of backtesting, optimization types that best investment estimated respectively, risk minimization has 22,30 % average return, Sharpe ratio maximization has 20,73 % average return, Treynor ratio maximization has 19,12 % average return, Jensen's Alpha maximization has 17,92 % average return and return maximization has 17,52 % average return.