Conditional heteroskedasticity is frequently found in the prediction errors of linear exchange rate models. It is not clear whether such conditional heteroskedasticity is a characteristic of the true data-generating process, or whether it indicates misspecification associated with linear conditional-mean representations. We address this issue by estimating nonparametrically the conditional-mean functions of ten major nominal dollar spot rates, 1973–1987, which are used to produce in-sample and out-of-sample nonparametric forecasts. Our findings bode poorly for recent conjectures that exchange rates contain nonlinearities exploitable for enhanced point prediction.