Yatırım fonlarından oluşan portföyün bulanık hedef programlama yaklaşımı ile optimizasyonu
The optimization of a mutual fund portfolio with fuzzy goal programming approach
Yazar: CAN HİÇBEZMEZ
Danışman: DOÇ. DR. ALP ÜSTÜNDAĞ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Endüstri Mühendisliği Ana Bilim Dalı / Mühendislik Yönetimi Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: Ekonomi = Economics ; Endüstri ve Endüstri Mühendisliği = Industrial and Industrial Engineering

Özet:
Küresel ekonominin dinamiklerinin sürekli olarak değiştiği günümüz koşullarında akıllı ve makul bir yatırım aracı bulmak her geçen gün daha da zor bir hal almaktadır. Yatırım araçlarının yapılarında, çeşitlerinde, sayılarında vs. meydana gelen köklü ve hızlı değişimler, gelişmeler yatırımcıların kafasını daha da bulandırmakta ve yatırım yapma cesaretlerini ellerinden almaktadır. Tasarrufların bir yere yatırılamaması da ekonomiyi dolaylı olarak negatif yönde etkilemektedir. Dolayısıyla yatırım yapılması için sağlanan o kadar imkan insanların daha fazla yatırım yapmalarını sağlarken, öte yandan çok dinamik değişimlere sebebiyet verdiğinden ve piyasa dinamiklerini hızla değiştirmelerinden dolayı da insanların güveninin zedelenmesine sebebiyet vermektedir.
Özellikle finansal enstrümanların ve yatırım araçlarının sistemsel anlamda özellikle bireysel yatırımcılar tarafından anlaşılamaması insanların bu alana yoğunlaşmalarını engellemektedir. Ancak günümüz finans piyasalarında en önemli aktörlerden olan portföy yönetim şirketleri, piyasa konusunda uzmanlaşmış profesyonel ekipleriyle yatırım fonlarını ortaya koyarak, bireysel yatırımcıların bilmedikleri bir alanda bilgilendirmeler doğrultusunda daha fazla kazanabilecekleri bir araç sunmaktadırlar. Bu araçlar günümüzün en çok kabul gören yatırım araçlarından biri haline gelmiştir. 
Yatırım fonlarının çokluğu ve pek çok portföy yönetim şirketinin varlığı insanları yatırım fonları konusunda da tereddüte sokmaya başlamıştır. Günümüzde bankaların ve portföy yönetim şirketlerinin en önemli ayağı olan yatırım fonları da artık hisse senedi, tahvil, bono vs. gibi değerlendirmeye tutulmaya ve performans kriterleri ile ölçülmeye başlanmıştır.
Çalışmamızda Türkiye'de yer alan 32 adetlik, hisse senedi yatırım fonu ve karma fonlardan oluşan bir grup menkul kıymetin geçmiş değerlerini inceleyerek yatırım fonlarından oluşan bir portföy oluşturmayı hedeflemekteyiz. Öncelikli olarak literatürde yer alan yatırım fonu performans ölçütleri ve performans ölçüm kriterleri incelenerek Türkiye piyasasına en uygun olanlar değerlendirmeye alınarak bir model oluşturulacaktır. Daha önce çokça kez değerlendirilmiş ve uygulanmış olan ve fon yöneticisinin menkul kıymet seçebilme performansı, zamanlama performansı ve risk bazlı performansını ölçen performans ölçüm kriterlerini daha önceki çalışmalardan farklı olarak gündelik verilerin daha iyi analiz edilebildiği bulanık hedef programlama yöntemi ile çözerek optimal yatırım fonu portföyüne ulaşacağız. Birden fazla model üzerinde yoğunlaşarak her yatırımcı için uygun olabilecek bir model yaratarak, bu doğrultuda performans kriterleri ile model kısıtlarını belirleyerek getiri ve risk değeri herhangi bir yatırımcı için en uygun portföyü oluşturacağız.

Abstract:
With the global economy's dynamics which changes day by day, it is even becoming harder to find a reasonable and fair investment tool because of the changeable environment. The radical and fast changes in the amount, type and structure of these tools are making investors' mind more and more confusing and leading them to get scared to invest money on investment tools. Because of this, people aren't investing much to the investment tools and this situation of not investing savings on investment tools, makes the economy even worse indirectly. So the conflict is, all the tools of investment are for people to have various alternatives and choices to invest their savings, make them confused and scared of investing. This is just a matter of trust, people don't trust the economy, don't trust politics, etc. They don't know what will become next, or which share to invest in, so they don't want to invest their money on investment tools which they don't know what will happen to this investment.
Especially financial instruments and investment tools, which personel investors don't actually understand or follow the economical incidents, are not good choices for regular investors to invest in without a professional advice or something else. But today, one of the most important figures in the economy, portfolio management companies, present something much more efficient for regular investors which will lead them to trust the knowledge and experience of the company and invest their savings in much more profitable way, the mutual funds. With their experienced crew in economical developments, they can lead people to earn much from their savings and make people trust in them because of their experience and knowledge and big portfolios. The mutual funds have become one of the most important tools in the world of economy.
After having mutual funds, people started to earn money just because of the fact that they know the fund has so many investors and can buy and sell securities according to the sudden changes in the economy. But after the trend of mutual funds, it's become even harder to choose which mutual fund and which investment company to invest in. All of the companies are big, all of the funds seem to be profitable, but why some of them go bankrupt suddenly? Why did the economy struggle and some of the big investment companies declared bankruptcy? These are the questions in personel investors' mind. These incidents scared people again. They still need some trustworthy stuff in these companies to continue investing. The companies have to prove themselves to the customers after all.
So with all of these instruments of mutual funds, we have to find the most profitable portfolio composed of mutual funds by taking into account their risk levels and returns in a specific period of time. In this study we will find the optimal portfolio according to investors' needs in Turkish financial market. 
The mutual funds started to become the most popular instrument of finance and in the last 30 years the experts started to study on comparing the mutual funds according to some performance criteria. 
In this study we aim to find the most suitable portfolio for each investor. In order to generate a mathematical model of optimization, we first examine the performance criteria of mutual funds and which fit the Turkish market best. 
The performance criteria are divided in four parts, the criteria considering total risk, the criteria considering systematical risk, the criteria considering the fund manager's ability of choosing the right securities in the market and the criteria considering the fund manager's ability on timing. After examining these criteria, we set up a model with them and find the optimal portfolio with the help of the model. 
As a model it must fit the natural environment of financial economics and must be dynamic just like the market. That's why the study suggests the fuzzy goal programming model to solve the portfolio selection and optimization problem. 
We choose the criteria for the model as Jensen's alpha criteria and Treynor & Mazuy's alpha criteria for selectivity ability, Fama criteria and Treynor & Mazuy's Gama criteria for timing, Treynor Ratio, Appraisal ratio for the measure of systematical risk criteria and Sharpe ratio and Sortino ratio for the measure of total risk. So it's been chosen two criteria from each main criteria. 
In the literature there are so many ways considered to portfolio optimization problems. But it's usually used with the Markowitz method, who found the modern portfolio theory to get the optimal portfolio. There are very rare studies that only take into account the performance criteria. 
In the studies of portfolio optimization it's usually chosen the standard deviation, beta coefficient and return rate of the fund as criteria of the problem and solve it according to these criteria. But in our study we didn't consider them as criteria for choosing the portfolio. They are the tools which will make us calculate the criteria and evaluate the optimal portfolio.
In this study we will take into account 32 mutual funds, which some of them are mixed funds and some of them are equities mutual fund. The historical data for these 32 funds is taken for 2 years 2012 – 2013 and we examine these values according to the criteria of the ones chosen. 
By taking into account equities mutual funds and mixed funds, which are the one of the riskiest mutual funds and shares in the economy, we will examine the risk limit of the mutual funds and their greater returns. Also the benchmark metric taken into consideration is BIST 100 which is the index of the most valuable 100 companies in Istanbul Stock Exchange. So having equities mutual funds as our investment tool makes it easier to compare and gives us healthier results for the optimization of the portfolio.
In our study, to get a reasonable solution we are departing the standard model into some other models. Because there is not only one kind of investors. For example there can be some investors who likes taking risks, there are some who hates, there are some who wants a balanced etc. That's why after solving the standard model, we will add some other constraints to run the model again. For example for the investors who like taking risk, there is a model where the benchmark index of BIST 100 can be added to the model, a model that finds the same risk level with the benchmark with a better level of return etc. For the investors don't like to invest in a risky position, we can add the risk free rate, economical repo, to the model and get a riskless portfolio. Also there is another model where the investor can choose his/her level of return desired to the model and get the portfolio according to it. For the investors don't want to invest all of their money to less mutual funds and want to fiversify them, we can put limits of maximum percentage of the mutual fund's ratio in the portfolio and the portfolio will be safer. 
So the aim is to find the optimal portfolio but not for one kind of investors, but for all kinds of investors. After finding the optimal portfolio we will examine the values of portfolio and evaluate it according to its average rate of return, risk measure of standard deviation and risk measure of beta coefficient. After examining, the optimality of the solutions and the user friendly part of the system will be interpreted.
According to the latest economical developments the behaviours of the mutual funds are so changeable and resulting in being risky. The risk level of the mutual funds must be balanced with the expected return of it. The performance criteria are trying to evaluate these measures and evaluate the mutual funds, with their risk levels, expected return, market performance (benchmark index) and risk free rate. After all the eight measures of performance will led us know which portfolio is the best for whom.