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When estimates of variances are used to make asset allocation decisions, underestimates of population variances lead to lower expected utility than equivalent overestimates: a utility-based criterion is asymmetric, unlike standard criteria such as mean squared error. To illustrate how to estimate a utility-based criterion, we use five bilateral weekly dollar exchange rates, 1973–1989, and the corresponding pair of Eurodeposit rates. Of homoskedastic, GARCH, autoregressive and non-parametric models for the conditional variance of each exchange rate, GARCH models tend to produce the highest utility, on average. A mean squared error criterion also favors GARCH, but not as sharply.