Low Power of Alpha Tests When Factors Are Constructed From Sorted Portfolios

When factors for asset pricing are constructed from a set of sorted portfolios, statistical tests of factor model alphas can suffer from low power. The low power arises because alpha can be decomposed into a sum of two parts, where each part is equal to zero under the null of a correct factor model. If the values of the two parts under the alternative hypothesis are nonzero, differ in sign, and have approximately equal magnitudes, they offset which results in a high probability of not rejecting a false model. Thus, insignificant alpha tests can be misleading when factors are constructed from sorted portfolios. This paper uses the parts of alpha to derive new test statistics that have high power when the traditional alpha test lacks power.