Way of the turtle

186
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Way of the Turtle

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CAGR% was almost 30 times more sensitive to the change in the
end dates.
The monthly average return used in the Sharpe ratio is also sen-
sitive to these changes because we are removing three bad months
from the end of the tests, and that affects the average return,
although the average return is affected less than the CAGR%. A
better measure to use in the numerator would be the RAR%.
As was noted earlier, the maximum drawdown component of the
MAR ratio is also sensitive to changes in start and end dates. If the
largest drawdown is on either end of the test, the performance
measure MAR will be affected considerably. The maximum draw-
down is a single point on an equity curve, and so you are missing
out on some valuable additional data. A better measure is one that
includes more drawdowns. A system that had five large drawdowns
of 32 percent, 34 percent, 35 percent, 35 percent, and 36 percent
would be harder to trade than would a system that had drawdowns
of 20 percent, 25 percent, 26 percent, 29 percent, and 36 percent.
Further, the extent of the drawdown is only one dimension: All
30 percent drawdowns are not the same. I would not mind a draw-
On Solid Ground
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187
The Effect of Start and End Date Changes on RAR%
Original Test Dates
Revised Test Dates
Figure 12-2
The Effect of Changes in the Start and End Dates on RAR%

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down that lasted only two months before recovering to new highs
nearly as much as I would mind one that took two years to reach
new highs. The recovery time or the length of the drawdown itself
is also very important. 
R-Cubed: A New Risk/Reward Measure
To take all these factors into account, I have created a new
risk/reward measure that I call the robust risk/reward ratio (RRRR).
I also like to call it R-cubed since I still have a bit of the nerdy engi-
neer in me and tend to do these sorts of things. R-cubed uses RAR%
in the numerator and a new measure I call the length-adjusted aver-
age maximum drawdown in the denominator. There are two com-
ponents to this measure: the average maximum drawdown and the
length adjustment.
The average maximum drawdown is computed by taking the five
largest drawdowns and dividing by 5. The length adjustment is
made by taking the average maximum drawdown length in days
and dividing it by 365 and then multiplying that number by the
average maximum drawdown. The average maximum drawdown
length is computed by using the same algorithm, that is, taking the
five longest drawdowns and dividing by 5. So, if the RAR% was 50
percent and the average maximum drawdown was 25 percent and
the average maximum drawdown length was one year, or 365 days,
you would have an R-cubed value of 2.0, which comes from 50 per-
cent/(25 percent 

 365/365). R-cubed is a risk/reward measure that
accounts for risk from both a severity perspective and a duration
perspective. It does this by using measures that are less sensitive to
changes in the start and end dates. The measure is more robust