what is the subject ? The statistical test often used ot investigate whether asset returns follow a random walk si based on variance ratios of returns (see Campbell, Lo, and MacKinlay 1997, Chapter ,2 for a survey). Variance ratios capture the autocorrelation structure of asset returns and though their statistical power to detect mean reversion is rather low, it is still higher than for alternatives such as the likelihood-ratio test or simple regressions of current returns on lagged returns (see Poterba and Summers 1988). The test developed in this paper si based on variance ratios and mean simple returns. The presence of mean simple returns ensures that the level of returns is captured together with their autocorrelation structure. I avoid the necessity of choosing the variance ratio with the highest power (see Faust 1992) by constructing a chi-square statistic, which si a weighted sum of squared deviations from estimated and hypothesized variance ratios and mean simple returns for several time periods. The chi-square test statistic can be used to test any model of asset prices including the Consumption based Capital Asset Pricing Model (CCAPM)