A Test Of The Performance Difference Of Two Portfolios

Portfolio performance evaluation is one of the most important areas in investment analysis. In order to compare the different performance among portfolios several statistics have been applied to this question. In this thesis different performance measure will be introduced. Among them we know Sharpe ratio is the most prevalent one. However, Sharpe ratio can not be observed directly, they must be estimated from the return serials. Then a method which is frequently used is to compare portfolios' sample Sharpe ratio without considering this measure's precision. Although some papers such as Jobson and Korkie (1981) has checked Sharpe and Treynor measure's statistical properties under large samples, the small sample property can still not be exactly known when we do not have the big sample. In this thesis we derive a new measure to compare portfolio performance, and then do a test about that. We study the independent identical distribution returns by considering two portfolios which are also independent and follow normal distribution respectively. Under that assumption we claim that our performance measure test is a uniformly most powerful unbiased (UMPU) test. Using our performance measure we compared the old economy and new economy stocks as proxied by the S&P500 index and two technology stock indices respectively.