Way of the turtle

Table 12-2
Robustness of CAGR% versus RAR%
CAGR% RAR%
System
06/06 11/06
%
06/06
11/06
%
ATR CBO 
52.4% 
48.7% 
–7.0% 
54.7% 
55.0% 
0.5%
Bollinger CBO 
40.7% 
36.7% 
–9.8% 
40.4% 
40.7% 
0.6%
Donchian Trend 
27.2% 
25.8%
–5.2% 
28.0% 
26.7% 
–4.6%
Donchian Time 
47.2% 
4% 
–0.4% 
45.4% 
44.8% 
–1.4%
Dual Moving
50.3% 
42.4%
–15.7% 
55.0% 
53.6% 
–2.6% 
Average
Triple Moving
41.6% 
36.0%
–13.5% 
41.3% 
40.8% 
–1.2% 
Average
Average 

–8.6%
–1.4% 
Copyright 2006 Trading Blox, LLC. All rights reserved worldwide.
190
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Way of the Turtle

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The RAR% changed less than a sixth as much as the CAGR%
over this time period. This demonstrates that the RAR% measure
is much more robust than CAGR%, meaning that it will be more
stable over time during actual trading. The same holds true for the
risk/reward measure R-cubed compared with its less robust cousin
the MAR ratio. Table 12-3 lists the percentage changes in R-cubed
compared with the percentage change in the MAR ratio for these
systems.
Table 12-3
Robustness of 
R-Cubed versus the MAR Ratio
MAR Ratio 
System
06/06
11/06
%
R
4
06/06
11/06
%
ATR CBO 
1.35 
1.25 
–7.4% 
3.72 
3.67 
–1.4% 
Bollinger CBO 
1.29 
1.17 
–9.3% 
3.48 
3.31 
–4.9% 
Donchian Trend 
0.76 
0.72 
–5.3% 
1.32 
1.17 
–11.4% 
Donchian Time 
1.17 
1.17 
–0.0% 
2.15 
2.09 
–2.8% 
Dual Moving
1.29 
0.77 
–40.3% 
4.69 
3.96 
–15.6% 
Average
Triple Moving
1.32 
0.86 
–34.9% 
3.27 
2.87 
–12.2% 
Average
Average 

–16.2% –8.0% 
Copyright 2006 Trading Blox, LLC. All rights reserved worldwide.
The R-cubed measure changed about half as much as the MAR
ratio did for the period indicated. 
Robust measures are also less susceptible to the effect of luck
than nonrobust measures are. For example, a trader who hap-
pened to be on vacation and avoided the largest drawdown for a
particular type of trading would show a relatively higher MAR
On Solid Ground
•
191

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ratio compared with his peers; this would be shown with R-cubed,
since that single event will not have as large an effect on the R-
cubed measure. You are more likely to get good test results that
come from lack rather than repeating market behavior which can
be exploited by a trader when you are using nonrobust measures,
and that is yet another reason to use those that are robust.
Using robust measures also helps you avoid overfitting because
they are less likely to show large changes caused by small numbers
of events. Consider the effect of the rules added to improve our
Dual Moving Average system in the discussion on overfitting. The
rule that was added to cut down the size of the drawdown
improved CAGR% from 41.4 percent to 45.7 percent (10.3 per-
cent) and the MAR ratio from 0.74 to 1.17 (60 percent). In con-
trast, the robust measure RAR% changes from 53.5 percent to
53.75, or only 0.4 percent; likewise, the robust risk/reward meas-
ure R-cubed changes from 3.29 to 3.86, only 17.3 percent. Robust
measures are less likely to show major improvement from changes
in a small number of trades. Therefore, since curve fitting gener-
ally benefits only a small number of trades, when you use robust
measures, you are less likely to see major improvements in per-
formance from curve fitting.
Let’s consider a few other factors that affect the reliability of
backtests for predicting system performance in the future.