This paper is to examine the performance of stock and bond with the applications of Almost Stochastic Dominance (ASD). Besides that, with the new version issued by Tzeng et al (2013), this paper will use Almost Second-order Stochastic Dominance as one of decision rules to evaluate the performance between these two commodities. Furthermore, Generalized Almost Second Stochastic Dominance (GASSD) will be taken as a tool to testify the existence of the hierarchy property. At last, single industry index will be used to see whether there is a ASD relationship with bond. All the process will follow the same steps as the overall stock index.