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.

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.

A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier. Several intuitive interpretations of the test are provided, including a simple mean-standard deviation geometric explanation. A univariate test, equivalent to our multivariate-based method, is derived, and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected. Empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics.