A variety of financial models are cast as nonlinear parameter restrictions on multivariate regression models, and the framework seems well suited for empirical purposes. Aside from eliminating the errors-in-the-variables problem which has plagued a number of past studies, the suggested methodology increases the precision of estimated risk premiums by as much as 76%. In addition, the approach leads naturally to a likelihood ratio test of the parameter restrictions as a test for a financial model. This testing framework has considerable power over past test statistics. With no additional variable beyond β, the substantive content of the CAPM is rejected for the period 1926–1975 with a significance level less than 0.001.

When testing portfolio efficiency, empiricists usually perform tests using subperiods and aggregate the results in some manner. Although the power of individual subperiod tests has been studied previously, little is known about the power of the aggregate test. Power is evaluated here through simulations using two different aggregation techniques. Aggregate power is substantially higher than that for a single subperiod. For example, in one scenario the aggregate power is 0.77 over a sixty-year period, but only 0.17 for each five-year subperiod. In addition, the level of power depends on the method of aggregation.

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.