We address the question of whether various types of speculative investor correctly anticipate future USD/EUR currency movements or whether they tend rather to react to past exchange rate movements. Throughout the analysis, we differentiate between large and small traders, and an upper bound of total speculation. To account for the large number of testable hypotheses, we contrast results obtained from predictive regressions based on individual significance tests with those based on either controlling the false discovery rate (FDR) or the family-wide error rate (FER). While the statistical evidence in favor of a causal relationship from speculative positions to exchange rate movements, and therefore an inefficient Euro futures market, largely collapses if we account for multiple testing, such a pattern does not emerge in the other direction. In addition, findings based on a contemporaneous analysis point to some notable differences between small and large speculators, and a non-linear relationship between USD/EUR movements and changes in the open interest position of large speculators.