Tests of informational efficiency of a given market involve testing two hypotheses simultaneously: the first is the hypothesis about the structure determining equilibrium prices or returns, and the second is the hypothesis about the information used in formulating expectations and the ability of agents to set current prices to conform with their expected values. We examine this issue in the context of the foreign exchange market by setting up a simple model of exchange rate determination, and using equilibrium properties of the model to examine market efficiency. The model of exchange rate determination involves monetary equilibrium and rational expectations. By virtue of the latter, equilibrium prices, by definition, 'fully reflect' available information, yet we show that conventional tests of market efficiency would fail when confronted by data generated by such a model. We then proceed to define more restrictive and more appropriate concepts of informational efficiency. We also illustrate and clarify a fundamental misconception with current rational expectations models. We believe that the current models employing the rational expectations hypothesis overemphasize the distinction between monetary and real shocks and underemphasize the distinction between permanent and transitory distinctions. For expectations formation, the conventional efficiency tests, it is the latter distinction that is the essential one.(This abstract was borrowed from another version of this item.)