High interest rate currencies tend to appreciate in the future relative to low interest rate currencies instead of depreciating as uncovered interest parity (UIP) predicts. I construct a model of exchange rate determination in which ambiguity-averse agents face a dynamic filtering problem featuring signals of uncertain precision. Solving a max-min problem, agents act upon a worst-case signal precision and systematically underestimate the hidden state that controls payoffs. Thus, on average, agents next periods perceive positive innovations, which generates an upward re-evaluation of the strategy's profitability and implies ex post departures from UIP. The model also produces predictable expectational errors, negative skewness, and time-series momentum for currency speculation payoffs. (JEL D81, F31, G15)