Utility-based models of asset pricing may be estimated with or without assuming a distribution for security returns; both approaches are developed and compared here. The chief strength of a parametric estimator lies in its computational simplicity and statistical efficiency when the added distributional assumption is true. In contrast, the nonparametric estimator is robust to departures from any particular distribution, and it is more consistent with the spirit underlying utility-based asset pricing models since the distribution of asset returns remains unspecified even in the empirical work. The nonparametric approach turns out to be easy to implement with precision nearly indistinguishable from its parametric counterpart in this particular application. The application shows that log utility is consistent with the data over the period 1926-1981.