Testing and Ranking of Asset Pricing Models Using the Grs Statistic

We clear up an ambiguity in Gibbons, Ross and Shanken (1989, GRS hereafter) by providing the correct formula of the GRS test statistic for the multiple factor case and proving its exact F distribution, issues unaddressed in GRS (1989). We theoretically and empirically illustrate the consequences of using the incorrect formula that the ambiguity in GRS leads to – over-rejecting and mis-ranking asset pricing models. We generalize the Sharpe ratio based interpretation of the GRS test to the multiple portfolio case, and note that this paradoxically makes experts in asset pricing studies more susceptible to the incorrect formula. Finally, we also suggest a new approach to ranking competing models, using the GRS statistic p-value