Alternative Tests of the Zero-Beta CAPM

Abstract

In this paper I develop an analytical Wald test of the zero-beta capital asset pricing model (CAPM) in a simple iid (independent and identically distributed) setting, and extend the Wald test to the generalized method of moments (GMM) framework that allows for a general form of serial correlation and conditional heteroscedasticity. The size and power of these tests, along with some existing tests, are investigated under normal errors and other alternative distributional specifications. The results show that, under alternative distributional assumptions for the error terms, the proposed Wald and GMM tests have reliable sizes for medium-size samples, while the likelihood ratio test (LRT) tends to reject the efficiency too often, especially when the error terms significantly deviate from normality. However, the LRT is more powerful than both the Wald and GMM tests.

JEL Classification: C13, C53, G14