The Sharpe and DRT(RFR, 2) ranks of each company, on five year (1984-1989) and ten year (1984-1994) bases, are reported respectively in tables 7.14, and 7.15. Tables 7.14, and 7.15 provide the same results in rank order.
Due to the negativity problem discussed in section 4.4.1, the computation of a meaningful set of annual Sharpe measures was impossible. As the blank spaces in tables B.7, and B.8 testify, their computation on a rolling five year basis still proved problematic. As the objective of this chapter is to compare the DRT and Sharpe measures, focus was laid on the five year period (1984-1989) as it had the greatest number of valid Sharpe measures. Tables B.9 on page 258, and B.10 provide the comparable DRT(RFR, 2) measures and rankings respectively.
The results are presented in tables 7.14, and 7.15 and show the significant difference in ranking, between the two measures. However, due to sample size and the lack of positive Sharpe measures, results of the Wilcoxon signed ranks test failed to provide evidence of statistically significant differences in the ranks between the two models. However, given consideration to the relative rankings expected under the two measures i.e. similar results would be expected from both measures if rankings were confined to quartiles, the correlation between the two measures was low. This suggested that the two measures provide very different rankings. Specifically in the five year study, the Spearman rank order correlation for the difference between the Sharpe measure and the DRT(RFR, 2) measure is - 0.90, the Kendal τ-0.74 and the Gamma correlation - 0.74. This is supported by figure 7.13, which plots the correlation between the two measures.
As table 7.16, the Wilcoxon signed ranks test again failed to provide evidence of statistically significant differences in the ranks when κ was varied using the
DRT(RFR, κ) measure.22 However, the matrix of DRT correlation plots in figure 7.14, disputes this. Varying κ is shown to significantly alter the rank of companies.
Although of little power, the Wilcoxon signed ranks test was also applied to the rolling DRT(RFR, 2) 5 year ranks contained in table B.10. The results are presented in table B.11, and suggest that the rolling 5 year DRT measures were reasonably stable over the period.
Finally, the DRT(RFR, ƙ) ranks of each company on a ten year (1984-1994) bases are reported in table 7.17. Table B.12 provides the geometric means, standard deviations and ten year DRT(RFR, ƙ) measures, while their alphabetical ranking is contained in table B.13.
22In an effort to assess the power of the Wilcoxon signed ranks test on sample sizes of 50, a simple bootstrapping procedure (without replacement) was used to construct 1,000 ranks from 1 to 50. The Wilcoxon signed ranks test failed in all cases to provide evidence of statistically significant difference in any of the ranks; the average p-value was 0.624. Although used on samples of this size, these results question the validity of its application.