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In this paper, we study predictability of exchange rates and explore determinants of its dynamics over time. We model the admissible amount of predictability in two ways, each corresponding in a stylized manner to a broad class of rational currency pricing models, namely those under which the marginal currency trader can diversify away currency risk and alternative specifications under which this possibility is precluded. Under the null of Rational Expectations, we find strong evidence against the former class of models but little evidence against the latter, except that predictability itself is predictable. Our results pose a challenge to Fama's (1970) Efficient Market Hypothesis, but are consistent with microstructure models of foreign exchange markets in which a capital-constrained undiversified marginal currency trader seeks reward for total risk instead of systematic risk alone and sluggish risk-capital mobility drives predictable time-variation in currency predictability.