On comparing zero-alpha tests across multifactor asset pricing models

Evaluating competing multifactor asset pricing models involves comparing the statistical significance of their mean pricing errors (alphas). Unfortunately, this comparison favors imprecisely estimated models because p-values tend to be higher in more noisy models. To avoid false impressions of relative success at tests for zero mean pricing errors, we develop a notion of comparative p-values and suggest comparing these instead of the raw p-values. This comparison gives more precisely estimated models a fairer chance or, equivalently, quantifies how much easier it is for imprecisely estimated models, by comparison, to pass the test.