Reward-risk ratio (RR) is a very important stock market definition. In recent years, people extend RR model as distributionally robust reward-risk ratio (DRR) to capture the situation that the investor does not have complete information on the distribution of the underlying uncertainty. In this paper, we study the DRR model where the ambiguity on the distributions is defined through Wassertein metric. Under some moderate conditions, we show that for a fixed ratio, the DRR problem has the tractable reformulation, which motivates us to solve the problem through bisection algorithm. Specifically, we analyze the distributionally robust Sortino-Satchel ratio, Omega ratio and Stable Tail Adjusted Return ratio.