This paper is a response to the literature that tests for cointegration between national stock market indices. It argues that apparent findings of cointegration in other studies may often be due to the use of asymptotic, rather than small-sample, critical values. In fact, economic theory suggests that cointegration is unlikely to be observed in efficient markets. However, this paper finds some evidence for the long-horizon predictability of relative returns, and the existence of “winner-loser” reversals across 16 national equity markets. A conclusion is that national stock market indices include a common world component and two country-specific components, one permanent and one transitory.