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Subject:  Re: The Best Measure for the Best Blend Date:  11/18/2007  4:50 AM
Author:  Zeelotes Number:  204021 of 253511

In order to enhance everyone's analysis of which measure is the best predictor of future risk-adjusted return, let me take a few minutes to post the exact same data as what you find in the top post of this thread but based on ranks 1-4 instead of ranks 1-10. Keep in mind that this is holding five screens for a total blend of twenty stock positions.

It used to be that we believed Sharpe was the best measure to use for determining a blend. How has that measured faired under all the testing you've done?

As I posted a day or two ago, the Sharpe does not tend to come out on top with any of the means we have to evaluate a blend. Let me share the same table again, but this time with ranks 1-4 included.
             1-10      1-4
Sharpe Position Position
CAGR 11 9
GSD 5 6
Sharpe 6 6
UI 5 8
Win Ratio 5 3
Drawdown 5 10

What this shows more than anything else, is simply that there are better tools available for blend selection.
What is the best measure for finding the highest future CAGR? In other words, which measure is most predictive of future CAGR?

Jensen and Alpha came out on top with ranks 1-10, but this time GSD is the top CAGR finder. This is most definitely counter-intuitive, since what this is saying is that we find the best screens by sorting on GSD in descending order. In other words, the highest GSD screens produce the highest CAGR. GSD was in position #5 for ranks 1-10, but it shoots to first position when only twenty stocks are held.
 RANKS 1-4                                 
CAGR Minimum Maximum Median Average
GSD 28.65% 47.69% 46.31% 43.34%
Treynor 40.61% 46.82% 43.99% 44.02%
UP 30.20% 43.71% 43.54% 40.35%
Alpha 34.27% 41.73% 39.99% 39.47%
DD 28.96% 42.81% 39.76% 37.73%
Jensen 30.47% 40.68% 39.30% 38.34%
UPI 28.49% 36.15% 35.05% 34.02%
CAGR/GSD 27.92% 35.35% 32.16% 31.35%
Sharpe 27.64% 34.09% 31.94% 31.40%
Sortino 25.77% 35.28% 31.53% 30.92%
UPR 24.02% 35.05% 31.18% 30.92%
Beta 24.85% 32.21% 30.50% 30.13%
CAGR/UPI 23.10% 33.74% 29.36% 28.95%
CAGR/UI 26.17% 32.33% 29.10% 28.82%
Correlation 21.47% 31.14% 29.09% 28.02%
UI 21.52% 30.28% 27.54% 27.17%
Sharpe/GSD 24.41% 30.67% 27.32% 26.89%
GSD Ratio 19.18% 39.10% 26.41% 26.88%
Trough # 19.09% 32.80% 24.30% 23.79%

But our goal is risk-adjusted return, not raw return, so what is the best measure for finding the highest Sharpe Ratio?

Treynor pushes Sharpe/GSD out of first place when ranks 1-4 are employed. What is interesting is that there is a pretty big difference between the median Treynor and either Sharpe/GSD or CAGR/GSD.
  Sharpe     Minimum  Maximum  Median  Average
Treynor 1.32 1.73 1.66 1.64
CAGR/GSD 0.87 1.55 1.47 1.37
Sharpe/GSD 1.07 1.53 1.44 1.39
UPR 0.93 1.49 1.39 1.34
UPI 1.00 1.43 1.38 1.33
Sharpe 0.91 1.44 1.35 1.28
GSD 0.83 1.38 1.34 1.25
Sortino 1.00 1.42 1.33 1.26
CAGR/UI 0.91 1.25 1.24 1.19
UP 0.84 1.20 1.20 1.11
Alpha 1.02 1.25 1.19 1.17
Jensen 0.92 1.20 1.14 1.13
Correlation 0.82 1.21 1.14 1.08
DD 0.83 1.21 1.13 1.07
GSD Ratio 0.72 1.36 0.98 0.99
CAGR/UPI 0.76 1.11 0.93 0.92
UI 0.70 0.97 0.91 0.89
Beta 0.67 0.84 0.80 0.79
Trough # 0.58 0.86 0.75 0.71

What measure comes out on top for Ulcer Index?

I consider the UI one of the most important tools for evaluating a blend. A low value with this measure will make a huge difference in real-time use of the blend chosen, at least that has been my experience since Mungo first suggested the measure. Based on this I'd say Treynor is a very reasonable option rather than Sharpe/GSD.
    UI       Minimum  Maximum  Median  Average
Sharpe/GSD 4.67% 5.55% 4.96% 5.02%
CAGR/GSD 6.25% 17.98% 6.76% 7.58%
Treynor 6.61% 8.05% 6.87% 7.00%
UPR 6.64% 12.33% 7.01% 7.32%
CAGR/UI 6.81% 18.41% 7.77% 8.35%
UPI 6.95% 13.10% 7.83% 8.02%
Sortino 7.47% 16.99% 8.07% 9.15%
Sharpe 7.81% 18.10% 8.13% 8.95%
Correlation 7.27% 18.94% 8.22% 9.29%
UI 11.20% 17.90% 11.46% 12.40%
CAGR/UPI 11.10% 14.62% 12.13% 12.39%
GSD 11.89% 22.07% 12.81% 14.05%
Jensen 12.43% 22.71% 13.14% 14.01%
Alpha 11.85% 21.20% 13.15% 13.90%
GSD Ratio 7.03% 21.10% 16.07% 15.67%
DD 15.97% 24.30% 16.12% 17.81%
UP 16.26% 25.37% 16.29% 18.03%
Trough # 18.83% 39.42% 19.98% 23.60%
Beta 29.57% 37.30% 34.55% 34.53%

Which measure chooses screens with a high win ratio?

This tells us what percent of the screens employed each year produced a winning return. It is pretty impressive to find a win ratio about 85%. I doubt there are too many here who have had this level of success in picking screens to use for their investing.
 Win Ratio   Minimum  Maximum  Median  Average
CAGR/GSD 80% 92% 91% 90%
Sortino 82% 92% 91% 90%
Sharpe 79% 91% 88% 88%
Treynor 86% 92% 88% 89%
Sharpe/GSD 83% 87% 86% 86%
UPR 78% 88% 84% 84%
GSD 74% 86% 83% 83%
UP 75% 83% 83% 81%
Alpha 81% 85% 82% 83%
CAGR/UI 80% 85% 82% 82%
Correlation 71% 84% 82% 80%
UPI 81% 86% 82% 82%
DD 75% 84% 81% 80%
GSD Ratio 77% 89% 81% 81%
Jensen 80% 83% 80% 81%
UI 69% 83% 77% 76%
CAGR/UPI 67% 79% 76% 76%
Beta 68% 77% 73% 73%
Trough # 64% 75% 71% 71%

When it comes to the maximum daily drawdown, which of the measures is able to avoid drawdowns the best?

  Drawdown   Minimum  Maximum  Median  Average
Sharpe/GSD -26% -24% -24% -24%
CAGR/UI -57% -26% -28% -30%
UPR -50% -27% -28% -29%
UPI -47% -24% -29% -29%
Treynor -38% -28% -31% -31%
Correlation -55% -33% -33% -35%
CAGR/GSD -59% -35% -35% -36%
CAGR/UPI -44% -37% -38% -39%
Sortino -56% -38% -38% -40%
Sharpe -59% -38% -38% -40%
UI -47% -39% -39% -40%
GSD -66% -40% -41% -45%
Jensen -66% -40% -43% -45%
Alpha -63% -40% -43% -45%
DD -68% -44% -44% -48%
UP -70% -46% -48% -51%
Trough # -80% -52% -54% -60%
GSD Ratio -64% -30% -63% -57%
Beta -78% -71% -75% -76%

Which of the measures you used actually produced a backtest with the lowest GSD?

I only wish that Treynor came out a bit better on this one. But if it did, the Sharpe on the Treynor would really be out in the stratosphere.
    GSD      Minimum  Maximum  Median  Average
Sharpe/GSD 14.54 20.73 15.34 15.66
CAGR/GSD 17.63 30.87 17.85 19.58
UPR 17.79 24.69 18.87 19.44
CAGR/UI 19.75 28.23 19.98 20.98
Sortino 19.63 28.43 20.20 21.10
Sharpe 19.66 29.78 20.29 21.38
UPI 20.87 26.07 21.79 22.16
Treynor 20.96 27.02 21.86 22.18
Correlation 22.01 28.74 22.22 22.90
GSD Ratio 19.54 26.30 24.06 23.85
UI 27.72 32.54 28.12 28.77
CAGR/UPI 27.96 31.51 29.58 29.75
GSD 31.08 38.64 31.39 32.16
Alpha 28.69 32.42 31.87 31.25
Jensen 30.84 32.53 32.11 31.90
Trough # 31.81 41.23 33.04 34.72
DD 33.02 38.53 33.14 33.82
UP 34.28 39.24 34.36 35.31
Beta 41.06 43.30 41.74 41.93

What about the Treynor as an option instead of Sharpe/GSD?

Here I've prepared a table with Sharpe, Treynor and Sharpe/GSD laid out side by side, and their position rank among all the measures for each of the factors we use to evalute the results. I'm confident that there is a huge difference in opinion regarding how to best use all of this data, but I for one, based on this data alone, would lean toward the Treynor as the best measure. One other factor why I think so is that when you look at the annual returns it wins every year and has an average win of over 50% CAGR. Pretty impressive! The only year where it really did not do great is 1990. In fact, when I take all the yearly returns and sort by the percent of years that were positive so that those with 100% winning are at the top, and then sort by average yearly return, Treynor takes the top twelve positions. Pretty amazing!
             1-10      1-4                        1-10      1-4                         1-10      1-4
Sharpe Position Position Treynor Position Position Sharpe/GSD Position Position
CAGR 11 9 CAGR 4 2 CAGR 19 17
GSD 5 6 GSD 7 8 GSD 1 1
Sharpe 6 6 Sharpe 2 1 Sharpe 1 3
UI 5 8 UI 8 3 UI 1 1
Win Ratio 5 3 Win Ratio 7 4 Win Ratio 1 5
Drawdown 5 10 Drawdown 6 5 Drawdown 1 1

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