Stochastic dominance algorithms with application to mutual fund performance evaluation

While the possibility for investment A to dominate investment B under the first- and second-order stochastic dominance framework can be tested only at the points of jumps in the probabilities of the distributions, the comparison at interior points is also essential under third-order, due to the non-linearity in the difference in the third-order stochastic dominance integral. Furthermore, it was established that the quantile approach used to test for the first- and second-order dominance does not work under the third-order. If these points are overlooked, it is possible to conclude that an investment is third-order inefficient when it is actually efficient. Also, an inefficient investment may not be relegated to the inefficient set. In this work, to test for third-order efficiency, we derive the expressions for the functions essential for testing the possibility of third-order stochastic dominance at the interior points and arrive at their restrictions on the common grid of the pairwise investments under consideration. We also develop a program to determine the efficient funds and the funds superior and inferior to the benchmark indices at a fast pace. We find that the size of the efficient set reduces drastically under third-order. Also, several funds are found to be superior to the indices under second- and third-order.