Nonnormalities and Tests of Asset Pricing Theories




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    • Both authors from College of Business, University of Notre Dame. This research was funded in part by the Herrick Foundation Fund. Data were provided by the Jesse H. Jones Research Data Base. We are grateful to Jay Shanken, Rich Sheehan, and workshop participants at the University of Notre Dame for helpful comments. The manuscript has also benefited from the substantive comments of an anonymous reviewer.


The robustness of the multivariate test of Gibbons, Ross, and Shanken (1986) to nonnormalities in the residual covariance matrix is examined. After considering the relative performance of various tests of normality, simulation techniques are used to determine the effects of nonnormalities on the multivariate test. It is found that, where the sample nonnormalities are severe, the size and/or power of the test can be seriously misstated. However, it is also shown that these extreme sample values may overestimate the population parameters. Hence, we conclude that the multivariate test is reasonably robust with respect to typical levels of nonnormality.