Abstract
The finite sample performance of the Wald, GMM and Likelihood Ratio (LR) tests of multivariate asset pricing tests have been investigated in several studies on the US financial markets. This paper extends this analysis in two important ways. Firstly, considering the fact that the Wald test is not invariant to alternative non-linear formulation of the null hypothesis the paper investigates whether alternative forms of the Wald and GMM tests result in considerable difference in size and power. Secondly, the paper extends the analysis to the emerging market data. Emerging markets provide an interesting practical laboratory to test asset pricing models. The characteristics of emerging markets are different from the well developed markets of US, Japan and Europe. It is found that the asymptotic Wald and GMM tests based on Chi-Square critical values result in considerable size distortions. The bootstrap tests yield the correct sizes. Multiplicative from of bootstrap GMM test appears to outperform the LR test when the returns deviate from normality and when the deviations from the asset pricing model are smaller. Application of the bootstrap tests to the data from the Karachi Stock Exchange strongly supports the zero-beta CAPM. However the low power of the multivariate tests warrants a careful interpretation of the results.
Highlights
Asset pricing models and their empirical tests constitute a major component of the finance literature
As the deviations from the asset pricing tests increase the ability of the Likelihood Ratio (LR) tests to detect the difference increase rapidly compared to the other tests
The Wald tests with the two non-linear formulations results in numerically smaller values of the test statistics compared to the LR test which in turn is smaller in value to the GMM tests
Summary
Asset pricing models and their empirical tests constitute a major component of the finance literature. Univariate testing of the Capital Asset Pricing Model (CAPM) introduced by Fama and MacBeth (1973) employed a two-stage test procedure. This two-step procedure has been criticized on two concerns. Asset pricing tests in particular and econometric methods in general that involve estimation or testing in stages are shown to lack efficiency and are less powerful. Affleck-Graves and Bradfield (1993) conclude through simulations that frequent rejection of CAPM tests or equivalently non-rejection of hypothesis that there is no positive linear relationship between beta and returns is due to the low power of the univariate tests associated with smaller sample sizes. According to Shanken (1996) the statistical properties of multi-stage tests are difficult to assess
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