We study in a bivariate framework the statistical properties of the variance ratio test and t-statistic based on long period returns. Following Richardson and Stock (1989)with their approach K/T ¬ k, we show that the asymptotic distributions of those statistics are non-standard. Under the null hypothesis of market efficiency, we show in finite sample that our approximations are adequate as in Richardson and Stock (1989). Under various alternative hypotheses, the asymptotic power of the variance ratio test, as a function of k, increases up to some value, and then decreases. On the other hand, the power of the test based on the t-statistic decreases with k.