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Ratios



R-Squared

The R-Squared measure is an indication of how closely correlated a fund is to an index or a benchmark. It can be treated as a percentage, showing what proportion of a fund's movements can be attributed to those of the benchmark. Values for R-Squared range between 0 and 1, with 0 indicating no correlation at all, and 1, rarely, showing a perfect match. Values upwards of 0.7 suggest that the fund's behaviour is increasingly closely linked to its benchmark, whereas the relevance diminishes as R-Squared descends towards 0.5, and starts to disappear altogether below that.
R-Squared is a key ratio, in that other measures of a fund's performance - such as Alpha and Beta - will have been calculated by reference to its benchmark. The weaker the R-Squared correlation, the more unsuitable the benchmark is, and the more unreliable these measures will be in assessing the fund.
Worked Example: Finding an R-squared that fits
R-squared is one of the more important determinants in statistically examining a fund's performance. Many of the other performance measurements are calculated by reference to a fund's benchmark; thus, a strong correlation between the fund and its benchmark is essential if indicators such as Beta are to have any significance and if Alpha is not to be over- or under-stated. In the table that follows, there is a selection of Unit Trusts and/or OEICs from the IA UK All Companies sector. It shows r-squared correlation with this sector as a benchmark, along with the funds' Alphas and Betas over a 3-year period.

Table 13. Ratios table over 36 months against benchmark "UT UK All Companies" (risk free rate at 3.5%) from Unit Trust/OEIC universe
Name Alpha Beta R-Squared
Cavendish Opportunities TR 10.2 1.19 0.63
Fidelity Special Situations TR 5.87 1.06 0.86
Morgan Stanley UK Equity TR -3.38 1.12 0.95
Sector: UT UK All Cos TR 0 1 1

We can see that the Fidelity and Morgan Stanley offerings have high r-squared, and so are strongly correlated with the sector. The Cavendish fund, however, looks weakly linked to its benchmark, and there can be little confidence as a result in its Alpha and Beta figures.
In our next table, we can run the Cavendish fund against a group of alternative benchmarks that could be candidates for a better fit. We know from looking at the fund's principal holdings that there are no identifiable FTSE 100 stocks in its portfolio, so it is possible that the manager is making bets lower down the share listing's pecking order.

Table 14. Ratios table over 36 months against benchmark "Cavendish - Opportunities" (risk free rate at 3.5%) from Unit Trust/OEIC universe
Name Alpha Beta R-Squared
FTSE All Share TR -1.47 0.49 0.47
FTSE-350 Index TR -1.34 0.48 0.45
Cavendish Opportunities TR 0 1 1
Fidelity Special Situations TR 1.67 0.66 0.77
Morgan Stanley UK Equity TR -4.28 0.54 0.5
Sector: UT UK All Cos TR -1.79 0.53 0.63
Sector: UT UK Smaller Cos TR 0.96 0.73 0.87

Here, we have made Cavendish Opportunities the benchmark, and measure how some other sectors and indices align with it. Our strongest correlation is with the UK Smaller Companies sector, and this would seem to bear out the idea that the fund is invested in the SME area of the market. We can now produce a further table, using the new benchmark.

Table 15. Ratios table over 36 months against benchmark "UT UK Smaller Companies" (risk free rate at 3.5%) from Unit Trust/OEIC universe
Name Alpha Beta R-Squared
Cavendish Opportunities TR 1.51 1.2 0.87
Sector: UT UK Smaller Cos TR 0 1 1

This time, the Cavendish fund has a strong r-squared correlation to our substitute benchmark and, while Beta has hardly moved, the Alpha is considerably less than in the original table. Analysts can judge for themselves whether this fund was originally benchmarked inappropriately, but this much-reduced Alpha comes about because the fund is now being measured against a considerably higher-performing sector. Over the 3-year period we are examining, the UK All Companies sector returned 52.87%, while UK Smaller Companies produced 78.68%. So it remains the case that to generate Alpha – outperformance – of 1.51 at this level is still impressive.
Theoretically, there is nothing to stop analysts measuring Alpha against any benchmark they want to use to gauge performance. In this exercise, we have sought to find the most appropriate r-squared fit for the fund, in order to render meaningful its other quantitative characteristics.
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