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.