We clear up an ambiguity in the statement of the GRS statistic by providing the correct formula of the GRS statistic and the first proof of its F-distribution in the general multiple-factor case. Casual generalization of the Sharpe-ratio-based interpretation of the single-factor GRS statistic to the multiple-portfolio case makes experts in asset pricing studies susceptible to an incorrect formula. We illustrate the consequences of using the incorrect formulas that the ambiguity in GRS leads to—over-rejecting and misranking asset pricing models. In addition, we suggest a new approach to ranking models using the GRS statistic p-value.
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Kamstra et al. (2024) studied this question.
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