We now have a plethora of measures. Some are absolute, others relative. Some of the relative measures provide ranks within the set of all equity funds, others within a set of funds in a narrower equity category. In this section we take as given the use of the nine diversified equity categories. More specifically, we assume that an investor plans to allocate funds among these categories, then choose one or more funds from each category based on a single performance measure. Since such a procedure is almost certainly suboptimal we do not endorse it. However, this sort of hierarchic taxonomic approach explicitly or implicitly motivates the use of performance measures for ranking funds within investment categories.
In this spirit we analyze the rankings of funds within categories based on five different measures:
Excess Return Sharpe Ratios
Morningstar Category Risk-adjusted Ratings
Morningstar Overall (Star) Risk-adjusted Ratings
Style Analysis Selection Means
Style Analysis Selection Sharpe Ratios
For each performance measure, a list of all 1,286 funds was then prepared, with each fund's percentile within its category listed. Then the lists were compared with one another to determine the correlations between the rankings based on different measures. The table below provides the resulting correlation coefficients:
ERSR msCRAR msRAR MnSelRet SelSR Excess Return Sharpe Ratio (ERSR) 1.000 0.986 0.945 0.831 0.744 Category Risk-adjusted rating (msCRAR) 0.986 1.000 0.957 0.829 0.735 Star Risk-adjusted Rating (msRAR) 0.945 0.957 1.000 0.790 0.694 Selection Mean (MnSelRet) 0.831 0.829 0.790 1.000 0.940 Selection Sharpe Ratio (SelSR) 0.744 0.735 0.694 0.940 1.000
Note that rankings based on selection means and selection Sharpe ratios were fairly similar (the correlation coefficient was 0.940). This provides at least some solace to those who wish to take selection risk into account, but not to the full extent associated with the selection Sharpe ratio.
As seen in earlier comparisons, rankings within categories based on Excess Return Sharpe Ratios, Category Risk-adjusted Ratings and Overall (Star) Risk-adjusted Ratings were fairly similar, as shown by the correlation coefficients in the upper left hand (3x3) portion of the table, all of which are greater than 0.945.
If one assumes that the best measure for ranking funds is either the selection mean or the selection Sharpe Ratio but wishes to use one of the two Morningstar rankings as a surrogate, the choice appears to be relatively clear. The Category Risk-adjusted Rating is more highly correlated with each of the style-based measures than is the Overall (Star) Risk-adjusted Rating (0.829 versus 0.790 for the mean selection return and 0.735 versus 0.694 for the selection Sharpe ratio). However these correlations are far from perfect. The following figures provide more detailed comparisons of the rankings based on the Morningstar Category measures with (1) those based on Style analysis-based mean selection returns and (2) style analysis-based selection Sharpe ratios.
Category Rating versus Style analysis Mean Selection Return
Category Rating versus Style analysis Selection Sharpe Ratio
As can be seen, limiting one's attention to, say, funds with Category ratings of 5 wouldl exclude a significant number of funds with large historic mean selection returns and/or selection Sharpe ratios. Moreover, the set of funds with Category ratings of 5 would include some funds with less-than-stellar historic mean selection returns and/or selection Sharpe ratios.
