Purpose-This study aims to propose a model-free statistic that tests asymmetric correlations of stock rets,in which stocks move more often with the market when the market goes down than when it goes up,and then empirically analyze the asymmetric correlations of the China stock market and intational stock markets,respectively.Design/methodology/approach-Using empirical likelihood method,this study designs and conducts a model-free test,which converges to x2 distribution under regulated conditions and performs well in the finite sample using bootstrap critical value method.Findings-By analyzing the authors’ model-free test,the authors find that compared with Hong et al.’s test that closely relates to the authors,both of the tests are under rejected using asymptotic critical value.However,using the bootstrap critical value method can greatly improve the performance of the two tests.Second,investigating the power of the two tests,the authors find that the proportion of rejections of the authors’ test is roughly 10-20 percent larger than Hong et al.’s test in mixed copula model setting.The last finding is the authors find evidence of asymmetric for small-cap size portfolios,but no evidence for middle-cap and large-cap size portfolios in the China stock market.Besides,the authors test asymmetric correlations between the USA and Japan,France and the UK;the asymmetric phenomenon exists in intational stock markets,which is similar to Longin and Solnik’s findings,but they are not significant according to both the authors’ test and Hong et al.’s test.Research limitations/implications-The findings in this study suggest that both the authors’test and Hong et al’s test are under rejected using asymptotic critical value.When applying these statistics to test asymmetric correlations,the authors should take care with the choice of critical value.Practical implications-The empirical analysis has a significant practical implication for asset allocation,asset pricing and risk management fields.Originality/value-This study constructs a model-free statistic to test asymmetric correlations using empirical likelihood method for the first time and corrects the size performance by bootstrap method,which improves the performance of Hong et al.’s test.To the authors’ knowledge,this is the first study to test the asymmetric correlations in the China stock market.