Test for fractional degree stochastic dominance with applications to stock preferences for China and the United States

Jianli Wang, Xiong Xiong, Lin Zhou and Xu Guo

Abstract

The concept of stochastic dominance plays a critical role in many economic and financial studies. However, the classical integer-degree stochastic dominance does not allow for local risk attitudes. In a 2020 paper, Huang, Tzeng and Zhao propose the concept of fractional degree stochastic dominance, which encompasses integer-degree stochastic dominance. They derive the integral conditions for fractional degree stochastic dominance. In this paper we develop the test statistics for fractional degree stochastic dominance based on a reformulation of the integral conditions. The test statistics’ asymptotic distributions are obtained and a bootstrap method for determining the critical values of the tests is also introduced. We further explore the stock preferences of the Chinese and US markets to illustrate the applicability of the test statistics for fractional degree stochastic dominance developed here.