Prospect Performance Evaluation: Making a Case for a Non-asymptotic UMPU Test
提出均值方差比统计量用于比较投资前景绩效，在非渐近框架下证明其具有一致最大功效无偏性，并通过韩国和新加坡股票数据展示其在小样本中优于夏普比率检验。
We propose and develop mean-variance-ratio (MVR) statistics for comparing the performance of prospects (e.g., investment portfolios, assets, etc.) after the effect of the background risk has been mitigated. We investigate the performance of the statistics in large and small samples and show that in the non-asymptotic framework, the MVR statistic produces a uniformly most powerful unbiased (UMPU) test. We discuss the applicability of the MVR test in the case of large samples and illustrate its superiority in the case of small samples by analyzing Korea and Singapore stock returns after the impact of the American stock returns (which we view as the background risk) has been deducted. We find, in particular, that when samples are small, the MVR statistic can detect differences in asset performances while the Sharpe ratio test, which is the mean-standard-deviation-ratio statistic, may not be able to do so.