Portfolio optimization is one of the most important steps in asset allocation procedure. Having optimized portfolios with Markowitz Mean-Variance, recently Stochastic Dominance method is taking place as a preliminary test in efficient asset allocation procedure. In some studies, it is even used as an alternative method to replace mean-variance theory in portfolio selection. In this research, distribution-based Stochastic Dominance method applied to discover the dominant individual stocks of DJIA and BIST-30 indices. We conducted Second-order Stochastic Dominance (SSD) method with various weighting logic Equal, Simple and Logarithmic. This paper concerns about two concepts; firstly, investigating market  efficiency with SSD in one emerging and one developed market, Borsa Istanbul and New York Stock Exchange, respectively. Secondly, the impact of different weighting methods in dominant portfolios. Results illustrate that, there are differences in dominant portfolios with various weighting methods. Further, NYSE seems more efficient market than BIST.