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Subject:  Optimizing Blends with Sharpe/(GSD^x) Date:  11/17/2007  6:25 AM
Author:  Zeelotes Number:  203981 of 243423
In the thread The Best Measure for the Best Blend it was suggested that I try testing using a revised Sharpe/GSD. This suggestion came from JeffLandon in post # 203950 and StevnFool in # 203972. I went ahead and had this programmed into my backtester such that I can now test the following:

CAGR / (GSD^x)
CAGR / (UI^x)
CAGR / (UPI^x)
Sharpe / (GSD^x)

x can be set to any value whether positive or negative. To illustrate, let me share a little table I put together that will hopefully make this simpler for those who are a bit challenged by all this -- like me. :)
Sharpe  GSD   Ratio  Parameter x                  Consequence
  1.5   17.6  0.09                Default
  1.5   17.6  6.29       -0.5     GSD Underweighted
  1.5   17.6  3.07      -0.25     GSD Underweighted
  1.5   17.6  1.50        0       GSD Underweighted -- Equal to Sharpe Alone
  1.5   17.6  0.73       0.25     GSD Underweighted
  1.5   17.6  0.36       0.5      GSD Underweighted
  1.5   17.6  0.17       0.75     GSD Underweighted
  1.5   17.6  0.09        1       Sharpe / GSD -- No Weighting
  1.5   17.6  0.04       1.25     GSD Overweighted
  1.5   17.6  0.02       1.5      GSD Overweighted
  1.5   17.6  0.01       1.75     GSD Overweighted
  1.5   17.6  0.00        2       GSD Overweighted
  1.5   17.6  0.00       2.25     GSD Overweighted
  1.5   17.6  0.00       2.5      GSD Overweighted
  1.5   17.6  0.00       2.75     GSD Overweighted

Of course, when GSD is underweighted that means that Sharpe is overweighted and vice versa.

In the test I'm about to share I set it up with the following parameters:
Begin           01/03/1999
End             11/09/2007
Value Line       3 Screens
SIPRO            3 Screens
Ranks                  1-4
Total Held              24
Sort        Sharpe/(GSD^x)

So every year I invest in six screens -- three from VL and three from SIPRO. Each screen has ranks from one to four, resulting in a blend of 24 stocks in all.

The Results of the Backtest

These results show that there is little to no advantage to using this formula compared to just a default of Sharpe/GSD -- which is the 1.00 / 1.00 below. I'd guess the minor difference that there is isn't anything more than noise. The Parameter x on the left is the one for the Value Line screens while the one on the right is for the SIPRO sort.
Parameter x  Parameter x   CAGR    GSD   Sharpe  Ulcer Index
    2.00         1.50     32.23%  15.65   1.75      4.25%
    2.00         1.00     32.23%  15.65   1.75      4.25%
    2.00         2.00     31.70%  15.5    1.73      4.50%
    1.00         1.00     32.26%  15.88   1.73      4.69%
    1.00         1.50     32.26%  15.88   1.73      4.69%
    1.00         2.00     31.73%  15.74   1.71      5.08%
    1.50         1.00     30.27%  15.22   1.69      4.19%
    1.50         1.50     30.27%  15.22   1.69      4.19%
    2.00         0.50     30.98%  15.79   1.67      4.31%
    1.50         2.00     29.78%  15.09   1.67      4.41%
    0.50         1.50     31.15%  16.15   1.65      5.04%
    1.00         0.50     31.03%  16.06   1.65      4.76%
    0.50         1.00     31.15%  16.15   1.65      5.04%
    0.00         1.50     31.97%  16.89   1.63      5.48%
    0.00         1.00     31.97%  16.89   1.63      5.48%
    0.50         2.00     30.60%  16.01   1.63      5.53%
   -0.50         1.00     37.49%  20.47   1.61      7.19%
   -0.50         1.50     37.49%  20.47   1.61      7.19%
    0.00         2.00     31.43%  16.76   1.61      5.90%
    1.50         0.50     29.03%  15.37    1.6      4.26%
   -0.50         2.00     36.86%  20.41   1.59      7.78%
    0.50         0.50     29.94%  16.38   1.57      5.16%
    0.00         0.50     30.76%  17.13   1.55      5.60%
   -0.50         0.50     36.27%  20.85   1.54      7.34%
    1.00         0.00     32.02%  20.49    1.4      5.96%
    2.00         0.00     31.58%  20.12    1.4      5.99%
   -0.50         0.00     37.50%  25.2    1.38      8.31%
    0.00         0.00     32.20%  21.61   1.35      7.34%
    0.50         0.00     31.31%  20.78   1.35      6.10%
    1.50         0.00     29.66%  19.86   1.33      6.02%
   -0.50        -0.50     27.80%  30.46   0.92     14.72%
    2.00        -0.50     22.60%  24.08   0.89     12.25%
    1.00        -0.50     23.07%  24.75   0.89     12.27%
    0.50        -0.50     21.87%  25.18   0.84     13.00%
    0.00        -0.50     22.62%  26.01   0.84     15.77%
    1.50        -0.50     21.08%  23.86   0.83     12.11%

An Alternative Look

Just to be sure, I also did another test.
Begin           01/03/1989
End             11/09/2007
Value Line       5 Screens
Ranks                  1-4
Total Held              20
Sort        Sharpe/(GSD^x)

Parameter x   CAGR    GSD   Sharpe  Ulcer Index
    0.25     33.68%  17.78   1.57      6.35%
    0.00     34.20%  19.85   1.46      8.06%
    1.00     27.32%  15.34   1.45      4.96%
    2.00     26.10%  14.47   1.45      4.90%
    1.75     26.23%  14.66   1.44      4.92%
    1.50     26.22%  14.83   1.43      4.97%
    0.50     28.57%  16.26   1.43      6.32%
    0.75     27.31%  15.84   1.41      5.05%
    1.25     26.26%  15.14    1.4      5.13%
   -0.25     32.03%  21.85   1.27     10.14%
   -0.50     33.61%  27.13   1.14     12.54%

I don't see a mound of toast in this data, but it may be my eyes are a bit blurred at this point in the game. Let me know what the proposers think of these results.
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