The unintended consequences of grouping in tests of asset pricing models
We identify a number of unintended consequences of grouping when the capital asset pricing model is true and when it is false. When the model is true, grouping may cause fundamental problems with the most basic capital asset pricing and cross-sectional regression relationships. For example, with traditional grouping, the market portfolio is super-efficient––unless securities in each group are value weighted. Yet, when the model is grossly false, grouping may cause the model to appear to be absolutely correct. Ironically, the only way this can occur is when securities in each group are value weighted. To make matters worse, when the model is false, the slope of a cross-sectional regression of expected returns on betas fitted to grouped data may be either steeper or flatter than when the regression is fitted to ungrouped data. In other words, grouping may exacerbate the very problem it was meant to alleviate.