A generalised method of moments test of mean variance efficiency in the australian stock market

Standard multivariate tests of mean variance efficiency (MVE) have been criticised on the grounds that they require regression residuals to have a multivariate normal distribution. Generally, the existing evidence suggests that the normality assumption is questionable, even for monthly returns. MacKinlay and Richardson (1991) developed a generalised method of moments (GMM) framework which provides tests which are valid under much weaker distributional assumptions. They examined monthly US data formed into size based portfolios, for mean-variance efficiency relative to the Sharpe-Lintner CAPM. They found that inferences regarding mean-variance efficiency can be sensitive to the test considered. In this paper we further investigate their GMM tests using monthly Australian data over the period 1974 to 1994. We extend upon their analysis to consider an alternative version of their GMM test and also to examine a zero-beta version of the CAPM. Similar to the US case, our results also indicate sensitivity of inferences to the tests used. Finally, while we find that the GMM tests generally provide rejection of mean-variance efficiency, tests involving the zero-beta CAPM, particularly when a value-weighted market index is used, prove less prone to rejection.