Electronic copy available at: http://ssrn.com/abstract=1973440 Prospect Performance Evaluation: Making a Case for a Non-Asymptotic UMPU Test 1 Zhidong Bai Northeast Normal University, China Yongchang Hui Northeast Normal University, China Wing-Keung Wong 2 Hong Kong Baptist University, Hong Kong Riˇ cardas Zitikis University of Western Ontario, Canada Abstract We propose and develop a mean-variance-ratio (MVR) statistics for comparing the per- formance 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. Keywords: fund management; investment portfolio; assets; Sharpe ratio; mean-variance ratio; hypotheses tests; uniformly most powerful unbiased test. 1 We are grateful to the Editor Eric Renault, Editorial Assistant Nathalie Bannier, an anonymous Associate Editor, and two anonymous Referees for patience, constructive criticism, and suggestions that have resulted in a significant improvement of the manuscript. The authors also thank participants of the Third Symposium on Econometric Theory and Applications (SETA2007) held in Hong Kong for helpful comments. The third author would also like to thank Professors Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. The research is partially supported by the grants from North East Normal University, Hong Kong Baptist University, the Natural Sciences and Engineering Research Council (NSERC) of Canada, and and Research Grants Council of Hong Kong. 2 Corresponding author. Address: Department of Economics and the Institute for Computational Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong. E-mail: awong@hkbu.edu.hk 1