Asset Performance Evaluation with the Mean-Variance Ratio

Abstract

Asset performance evaluation is one of the most important areas in investment analysis. In order to compare the performance among assets, several statistics have been developed; and among them, the Sharpe-ratio statistic is the most prevalent. However, the major limitation of the Sharpe-ratio statistic is that its distribution is only valid asymptotically, but not valid for small samples. Nevertheless, it is important in finance to test the performance among assets for small samples. To serve this purpose, we first provide theoretical reasoning and then develop both one-sided and two-sided mean-variance-ratio statistics to evaluate the performance among the assets for small samples. In this paper we further prove that our proposed statistics provide uniformly most powerful unbiased tests. We illustrate the superiority of our proposed test over the traditional Sharpe-ratio test by applying both tests to analyze the performance of funds from Commodity Trading Advisors. Our findings show that while the traditional Sharpe-ratio test concludes most of the CTA funds being analyzed as being indistinguishable in their performance, our proposed statistics show that some funds outperform the others. On the other hand, when we apply the Sharpe-ratio statistic on some other funds, we find that the statistic indicates that one fund is significantly outperforming another fund even though the difference between the two funds is insignificantly different from zero and/or even changes directions. However, when our proposed mean-variance-ratio statistic is applied, we could detect the change in the difference. This shows the superiority of our proposed statistic in revealing short term performance and in return, enables investors to make better decisions about their investments.