Testing the Semi Strong form of Market Efficiency

• Significance tests of Sharpe Ratios of property portfolio's
  

To test the significant differences in the Sharpe ratios of selected properties against the total sample, Londerville (1998) imposed a statistical test developed by Jobson and Korkie (1981), in which the following hypothesis is to be tested.


According to Jobson and Korkie (1981) the following transformations to the sample differences in the Sharpe ratio provide an improvement of the estimations, especially for smaller samples.


They find that with this transformed difference, the asymptotic distribution is normal, with the mean as Sh and the variance as defined below (Jobson & Korkie, 1981).
And the proposed test statistic for these property portfolio's is Where the transformed difference is divided by the square root of the variance, which approximates the z statistic (Jobson & Korkie 1981). This z-test is used to test the significant differences in the Sharpe ratio when compared to the total portfolio. The results of z-tests for each identified group of properties against the total sample of properties within the same time period is shown in the table below. With the null hypothesis that the transformed mean is zero, the z statistics show that both property portfolios yield statistically significant Sharpe ratios. But before conclusions can be made about these significant differences in returns, the efficiency of the hedonic pricing model needs to be discussed.