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We compare and contrast some existing ordinary least squares (OLS)- and generalized method of moments (GMM)-based tests of asset pricing models with a new more general test. This new test is valid under the assumption that returns are elliptically distributed, a necessary and sufficient assumption of the linear capital asset pricing model (CAPM). This new test fails to reject the CAPM on a dataset of stocks sorted by market valuations, whereas similar tests constructed from OLS and GMM estimation methods reject the linear CAPM. We also find that outliers reduce the OLS-estimated mispricing of the linear CAPM on monthly returns sorted by previous performance, that is, momentum. Monte Carlo evidence supports superior size and power properties of the new test relative to OLS- and GMM-based tests. Copyright 2003, Oxford University Press.