This study investigated a method for constructing portfolios by applying the concept of stochastic dominance, in contrast to the Mean-Variance approach commonly used for selecting investment stocks in the stock market. Specifically, it sought a method to systematically search for optimal weights to construct a portfolio that second-order stochastically dominates a reference probability distribution (KOSPI). As the weights of each portfolio changed, the first derivatives of the differences in the integrated cumulative distribution functions of the two probability distributions were analytically derived, and an algorithm was developed using the derivative technique. This algorithm was applied to actual data from the Korean and U.S. stock markets to test its efficiency, yielding considerably encouraging results.