Mean-Variance Ratio Test For Multiple Assets

The coefficient of variation(CV) statistics and the Sharpe ratio(SR) statistics possess only the asymptotic distribution, one could only obtain their properties for large samples, but not for small samples. However, Mean-Variance ratio could obtain the exact distribution for samples. This paper proposed the multiple Mean-Variance ratio test of which is based on the "Asset Performance Evaluation with Mean-Variance Ratio" of Bai(2008), completing the theory of Mean-Variance Ratio test. For the multiple Mean-Variance Ratio, we can get the k-1 induced separate hypotheses. While accept the multiple Mean-Variance Ratio test, if and only if accept all the separate hypotheses. We could test the each hypothesis applying the Mean-Variance Ratio test. For the significance level of each hypothesis is the level of multiple hypothesis divided by k-1.To demonstrate the superiority of our proposed test over the Mean-Variance Ratio test, this paper illustrate the performance of MSCI state indices of ten countries. MSCI state indices combined by the relatively fixed proportion of every industries, making the indices have strong industry representation. At the same time, MSCI state indices have strongly robustness, objectivity, impartiality, utility, reference, mobility, Openness, etc.. So MSCI indices could get the more objective results.This paper, the Mean-Variance ratio of returns of ten MSCI state indices were tested. Applying the hypothesis of multiple mean variance ratio test, making the multiple test of ten indices induces nine separate hypotheses. Then test each separate hypothesis applying the Mean-Variance ratio test. Reject the most of separate hypotheses of zero hypothesis, implied all the hypotheses are not equation. This imply there exist significant differences among each MSCI index.At the end of the paper, we make the vista for the multiple mean variance ratio test. We wish extend the theory of multiple mean variance ratio test to the sample of any distribution family and more multiple mean variance ratio test, in order to obtain the evaluation of more performance of portfolio.