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Prospect Performance Evaluation: Making a Case for a Non-Asymptotic UMPU TestWing-Keung WongHong Kong Baptist University (HKBU) Ricardas ZitikisUniversity of Western Ontario - Department of Statistical and Actuarial Sciences Zhidong BaiNortheast Normal University Yongchang Huiaffiliation not provided to SSRN December 16, 2011 Abstract: We propose and develop a 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 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.
Number of Pages in PDF File: 31 working papers seriesDate posted: December 16, 2011Suggested CitationContact Information
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