It is prominently stated in the literature that local asymptotic power properties serve as a useful indicator for the performance of residual‐based no‐cointegration tests in finite samples. However, this article comes to an opposing conclusion. In particular, we show that Breitung's (2002, Journal of Econometrics 108, 343–363) nonparameteric variance ratio unit root test applied to regression residuals serves as a no‐cointegration test but is inferior to its competitors from a local asymptotic power perspective. Nevertheless, in finite samples, the variance ratio test has good size properties, competitive power, and the convenience of being tuning parameter free. In general, we find that short‐run dynamics in the error process can have considerably larger detrimental effects on the performance of residual‐based no‐cointegration tests in finite samples than changes in the only nuisance parameter affecting local asymptotic power of the tests. The results serve as a warning for practitioners and lead to interesting directions for future research.