Grouping does not produce a wide range of betas. Consequently, cross-sectional tests of the CAPM are bound to lack power. This paper provides a simple way to alleviate the problem by repackaging the data with zero-weight portfolios. When the CAPM is true and the data are repackaged, simulation shows that the average values of the intercept and slope converge to their true values more rapidly and there are striking increases in R 2 and the power of the tests. Empirical results are dramatically different in datasets with and without the zero-weight portfolios. (C) 2009 Elsevier B.V. All rights reserved.