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Sharpe and to the Point
By Craig L. Israelsen
From Financial Planning - October 2001. Reprinted with Permission.
he Sharpe Ratio is a "compact" statistic for simultaneously considering risk and return. It is compact in that its calculation is (1) very straight-forward and (2) it does not involve obscure variables. Devised by William Sharpe, it is calculated (as shown below) by dividing the excess return of an asset by its standard deviation of return. Excess return is typically calculated by subtracting the T-bill rate of return from the asset being analyzed. The higher the Sharpe ratio the better.
As described by Morningstar, the Sharpe Ratio is a measure which calculates the amount of "reward per unit of risk." Equating risk with standard deviation of return is not a perfect approach, inasmuch as returns that deviate above the mean are seldom viewed by investors as a "bad thing." Nevertheless, the Sharpe Ratio represents a well-accepted and highly useful statistic in the analysis of investment assets. Morningstar calculates the Sharpe Ratio and includes it in its Principia Pro software.
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Asset Return minus T-bill rate
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Sharpe Ratio =
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Asset Standard Deviation of Return
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How is the Sharpe Ratio useful in mutual fund analysis? First, as with many statistics, it is only useful when comparing similar funds. For instance, the Sharpe Ratio of a money market fund will be much higher than an excellent equity growth fund. But the comparison is meaningless because those two funds have virtually nothing in common. Secondly, the Sharpe Ratio might be most meaningfully used when we have some idea how it relates to other important measures of mutual fund performance.
With these two guidelines in mind, this study examined distinct groups of equity mutual funds (grouped by market cap) to examine how the Sharpe Ratio might be correlated with other relevant equity fund characteristics, such as total return, standard deviation of return, tax efficiency, Morningstar "Star" rating, alpha, beta, 12 month yield, bear market % rank (the lower the score the better), turnover ratio, length of manager tenure, expense ratio, and total net assets. The raw data in this article are as of June 30, 2001 and were obtained from Morningstar Principia Pro. Only non-index, U.S. equity funds with at least 3 years of performance and with the same manager were included in this study. There were 803 large cap funds, 351 mid cap funds, and 247 small cap funds which met the criteria. Morningstar defines a bear market as a month in which the S&P 500 loses more than 3%.
Figure 1 shows the results of the large cap funds. The 803 large cap funds were ranked by 3 year Sharpe Ratio from high to low (recall that a high Sharpe ratio is better). Then the funds were divided into deciles and averages for each variable within each decile were calculated. The 1st decile are the 10% of funds which the highest Sharpe ratios, and so on. The other variables included in this analysis were thought to have a possible correlation with the Sharpe Ratio. Some demonstrated that, while some did not. (A research note: It is often just as interesting to discover which variables do NOT behave as hypothesized compared to those that do).
Large Cap Equity Funds
From Figure 1 it can be seen that the Sharpe Ratio average (80 funds per decile among the large cap funds) is highest in the first decile and progressively declines to the 10th decile. No surprise, because the data were sorted by Sharpe Ratio from high to low. Next, we observe the 3 year total return averages exhibit a similar linear trend from 1st to 10th decile. As 3 year total return declines so does the Sharpe ratio. Not too surprising. Next, are the decile averages for the 3 year standard deviation of return. No clear correlation with Sharpe ratio emerges. In fact, the funds in the upper deciles (1st though 4th) have higher standard deviations on average than the lowest 4 deciles. This is unexpected inasmuch as a lower standard deviation (other things being equal) gives rise to a higher Sharpe Ratio. But, other things aren't equal. Clearly, when observing the two components of the Sharpe Ratio - total return and standard deviation of return - it is return which appears to be the primary driver of the Sharpe Ratio.
Another characteristic of equity funds which appears to have a strong correlation with the Sharpe Ratio is tax efficiency. Funds with high Sharpe ratios appear to be more tax efficient and vice versa. The same is true for their Star Rating and alpha coefficient. Beta, on the other hand, does not demonstrate a stable relationship with the Sharpe ratio. If there is a relationship, it would be that higher Sharpe ratios are correlated with lower beta coefficients. Large cap funds with higher dividend yields tended to have higher Sharpe ratios during the 3 year period ending June 30, 2001. The progression of bear market % rank average scores from low to high suggests that funds which withstand bear markets better (decline less than their peers) tend to be those funds with higher Sharpe ratios. The correlation between turnover ratio and the Sharpe ratio is unclear. The hypothesis that funds with higher Sharpe ratios would have lower turnover ratios is not validated by these results. The same was true for manager tenure. It was thought that higher Sharpe ratios would correlate with greater managerial tenure, but these results cannot support that idea. There is only weak evidence, comparing the 1st and 10th decile averages only, to support the idea that higher Sharpe ratios are correlated to funds with lower expense ratios. Finally, the data support the assertion that funds with greater net assets tend to have higher Sharpe ratios. In summary, large cap funds with higher Sharpe ratios tended to have higher return, higher tax efficiency, a higher Star rating, higher alpha score, somewhat higher yield, lower bear market score (which is good), and greater total net assets.
Mid Cap Equity Funds
Mid cap funds (shown in Figure 2) which higher Sharpe ratios tended to be those with higher returns, higher tax efficiency, higher Star rating, higher alpha, lower dividend yield, and higher net assets. As was the case among large cap funds, there is weak evidence that funds with higher Sharpe ratios may tend to have lower beta coefficients. There appears to be some correlation, though weak, between better bear market performance and higher Sharpe ratios. Standard deviation of return, turnover ratio, length of manager tenure, and expense ratio did not demonstrate clear correlations to the Sharpe ratio among mid cap funds.
Small Cap Equity Funds
Small cap funds (Figure 3) demonstrated correlations similar to mid cap funds. Higher Sharpe ratios were linked to funds with higher return, higher tax efficiency, higher Star rating, higher alpha, lower yield, and superior bear market performance. Unlike mid cap funds, there was a reasonably strong correlation between higher Sharpe ratio and higher standard deviation of return. As with large cap funds, this finding is counter intuitive because a high standard deviation of return is a penalty when calculating the Sharpe ratio, not a benefit. The supporting data for beta, turnover ratio, and net assets only exists in the contrast between 1st and 10th decile averages. Funds with the highest Sharpe ratios had larger betas, lower turnover ratios, and far fewer net assets compared to funds with the lowest Sharpe ratios. Once again, manager tenure and expense ratio data did not present compelling correlations to the Sharpe ratio.
Overall, several consistent findings emerge from this analysis of the Sharpe ratio and its correlates across each of the three market cap groups. Funds with higher Sharpe ratios: (1) have higher return but not necessarily lower standard deviations of return, (2) are clearly more tax efficient, (3) have higher Star ratings and alpha coefficients, and (4) tend to have superior performance during bear markets.
Figure 1. Large Cap U.S. Equity Funds Ranked by Sharpe Ratio (per decile).
Only non-index, distinct funds with at least 3 years performance data (as of 6/30/01) under the same manager.
80 Funds per decile
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Decile
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Sharpe Ratio
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Total Return
3 Yr
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Std Dev
3 Yr
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Tax Efficiency
3 Yr
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Star Rating
3 Yr
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Best Fit Alpha
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Best Fit Beta
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12 Mo Yield
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Bear Mkt % Rank
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Turnover Ratio
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Manager Tenure
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Expense Ratio
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Net Assets $MM
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1st
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0.44
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13.61
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21.65
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80.06
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4.45
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9.00
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0.73
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1.17
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28.61
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89.6
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7.54
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1.15
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2,326
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2nd
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0.23
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10.23
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24.12
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77.26
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4.05
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6.19
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0.81
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1.24
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36.93
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85.0
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6.70
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1.12
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2,613
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3rd
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0.13
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8.07
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25.54
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70.62
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3.60
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4.69
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0.85
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1.00
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46.43
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83.8
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6.43
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1.03
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1,922
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4th
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0.05
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6.37
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23.68
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72.28
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3.19
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3.21
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0.88
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0.73
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45.93
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72.8
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7.24
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1.20
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2,557
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5th
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-0.01
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5.15
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22.76
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67.39
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2.93
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2.29
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0.91
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0.75
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46.60
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80.5
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5.54
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1.15
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2,226
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6th
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-0.06
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4.13
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21.45
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59.29
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2.76
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0.88
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0.86
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0.94
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43.85
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68.2
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6.03
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1.15
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2,623
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7th
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-0.11
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3.28
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20.35
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50.55
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2.60
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-0.38
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0.87
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0.86
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47.27
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67.7
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5.85
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1.13
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877
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8th
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-0.18
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1.95
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22.35
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51.55
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2.31
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-0.39
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0.96
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0.74
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53.09
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72.5
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6.48
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1.15
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554
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9th
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-0.26
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0.88
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19.39
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40.45
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2.11
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-2.83
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0.87
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0.89
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47.69
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73.0
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5.75
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1.17
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647
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10th
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-0.49
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-2.45
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18.97
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21.20
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1.69
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-5.80
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0.84
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0.99
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46.99
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101.2
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7.47
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1.49
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524
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Figure 2. Mid Cap U.S. Equity Funds Ranked by Sharpe Ratio (per decile).
Only non-index, distinct funds with at least 3 years performance data (as of 6/30/01) under the same manager.
35 Funds per decile
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Decile
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Sharpe Ratio
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Total Return
3 Yr
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Std Dev
3 Yr
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Tax Efficiency
3 Yr
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Star Rating
3 Yr
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Best Fit Alpha
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Best Fit Beta
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12 Mo Yield
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Bear Mkt % Rank
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Turnover Ratio
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Manager Tenure
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Expense Ratio
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Net Assets $MM
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1st
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0.79
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22.90
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26.82
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85.05
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5.00
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17.17
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0.72
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0.73
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22.76
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142.7
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6.74
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1.33
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795
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2nd
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0.44
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17.64
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32.32
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79.95
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4.89
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13.27
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0.85
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0.74
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40.21
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77.0
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7.34
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1.27
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836
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3rd
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0.32
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13.80
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30.71
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78.15
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4.40
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8.58
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0.84
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0.74
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46.74
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125.3
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6.11
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1.38
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440
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4th
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0.25
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13.66
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38.62
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78.42
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4.23
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9.23
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1.01
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0.42
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56.92
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92.0
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5.69
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1.35
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1,044
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5th
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0.18
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11.53
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39.39
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78.84
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3.94
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9.08
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1.09
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0.71
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51.42
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125.3
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4.71
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1.33
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700
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6th
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0.12
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8.61
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32.47
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67.25
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3.63
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4.61
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0.92
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1.27
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46.33
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90.8
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6.71
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1.16
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638
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7th
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0.08
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7.59
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35.62
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70.95
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3.34
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4.48
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1.07
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1.22
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56.16
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88.6
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6.17
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1.14
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764
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8th
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0.00
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5.37
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37.98
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63.66
|
2.60
|
2.13
|
1.09
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0.49
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65.77
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113.8
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6.09
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1.44
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235
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9th
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-0.12
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2.65
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28.03
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41.49
|
2.29
|
-2.29
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0.96
|
1.47
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47.81
|
112.8
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6.46
|
1.35
|
171
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10th
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-0.38
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-2.06
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24.62
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37.54
|
1.81
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-7.42
|
0.79
|
1.37
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43.81
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120.9
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8.11
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1.44
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342
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Figure 3. Small Cap U.S. Equity Funds Ranked by Sharpe Ratio (per decile).
Only non-index, distinct funds with at least 3 years performance data (as of 6/30/01) under the same manager.
25 Funds per decile
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Decile
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Sharpe Ratio
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Total Return
3 Yr
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Std Dev
3 Yr
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Tax Efficiency
3 Yr
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Star Rating
3 Yr
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Best Fit Alpha
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Best Fit Beta
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12 Mo Yield
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Bear Mkt % Rank
|
Turnover Ratio
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Manager Tenure
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Expense Ratio
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Net Assets $MM
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1st
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0.77
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31.84
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38.66
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88.86
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5.00
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26.61
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0.89
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0.15
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25.25
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116.0
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4.36
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1.56
|
289
|
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2nd
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0.43
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18.55
|
34.07
|
82.85
|
4.84
|
12.39
|
0.91
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0.13
|
39.50
|
104.8
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6.48
|
1.34
|
631
|
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3rd
|
0.32
|
15.14
|
35.74
|
84.67
|
4.64
|
10.12
|
0.93
|
0.27
|
55.07
|
99.6
|
5.28
|
1.52
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542
|
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4th
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0.24
|
11.64
|
31.03
|
78.81
|
4.08
|
6.30
|
0.89
|
0.48
|
43.94
|
92.4
|
6.36
|
1.32
|
509
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5th
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0.18
|
10.61
|
33.52
|
78.01
|
3.96
|
6.31
|
0.94
|
0.78
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49.53
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90.2
|
6.68
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1.31
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358
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6th
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0.11
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8.83
|
36.06
|
73.15
|
3.48
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5.53
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0.90
|
0.62
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43.28
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137.1
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6.92
|
1.42
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452
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7th
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0.04
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6.44
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34.30
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70.62
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2.84
|
2.49
|
1.03
|
0.40
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64.35
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113.0
|
5.32
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1.41
|
166
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8th
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-0.05
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4.32
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27.69
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66.20
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2.60
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-0.98
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0.89
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0.57
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45.71
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84.8
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6.64
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1.36
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653
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9th
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-0.21
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0.44
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27.97
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68.96
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2.04
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-4.61
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0.91
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0.75
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52.87
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102.7
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5.88
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2.14
|
115
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10th
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-0.51
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-5.62
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25.38
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50.76
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1.41
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-9.47
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0.70
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0.71
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45.00
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174.7
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6.95
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1.66
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57
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