This paper represents the first attempt to apply a stochastic dominance (SD) approach to examine the efficiency of the UK covered warrants market. Our empirical analyses reveal that neither covered warrants nor their underlying shares stochastically dominate the other, indicating the nonexistence of potential arbitrage gains in either wealth or utility, which implies market efficiency. To complement the SD results, we also employ a likelihood ratio (LR) test to examine information efficiency. A bootstrap methodology is developed to correct the size distortion of the LR test. Our findings show that UK covered warrant returns efficiently reflect the return information of the underlying shares.