When the assumption of constant risk premiums is relaxed, financial valuation models may be tested, and risk measures estimated without specifying a market index or state variables. This is accomplished by examining the behavior of conditional expected returns. The approach is developed using a single risk premium asset pricing model as an example and then extended to models with multiple risk premiums. The methodology is illustrated using daily return data on the common stocks of the Dow Jones 30. The tests indicate that these returns are consistent with a single, time-varying risk premium.

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.