İkinci derece stokastik baskınlıkta verimlilik testi ve bulanık mantık yaklaşımı ile iki aşamalı bir portföy optimizasyonu

Portfolio management is a 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 years 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 MV optimized portfolios Second Order Stochastic Dominance (SSD) inefficient. In this thesis, a new two step gradual portfolio optimization method is introduced. In the first step of this method SSD inefficient stocks are eliminated after c(n,2) pairwise SSD comparisons of all stocks in the portfolio. At this point, a SSD inefficient stock means that it is second order stochastically dominated by at least one other stock. The second step of this gradual method is the application of the "fuzzy variance" minimization instead of MV. In this second step the future returns of the stocks are predicted with the help of the triangular fuzzy numbers where their centres are the average returns and their left and right deviations are relatively the worst and the best returns of the stocks in the observation period. As an empirical example, this suggested method is applied to the Turkish BIST-30 Index. Once the application is completed, the optimized portfolio of the suggested method is compared with both the MV optimized portfolio and the original BIST-30 portfolio according to most well known performance measurements, Sharpe Ratio (SR) and Treynor Ratio (TR). Detailed performance tests show that this new gradual method has overwhelming superiority over the classical method which requires normal distribution of stock returns that is nearly impossible in real data. In the near future, this novel gradual portfolio optimization method will be applied to other markets of the world to generalize its superiority over the MV.