In this paper the symmetry of daily returns is addressed in eight international stock markets and three spot exchange rates. Tests of symmetry with the sample skewness seem of little value, due to the non-normality of the returns. Under alternative non-normal distributions, the symmetry of the returns cannot be rejected for most markets. Distribution-free procedures do not detect strong asymmetries in most of the series either; however, some differences between returns below the mean and returns over the mean are observed in several markets