Way of the turtle

–23.7% 
1991 to 2000 
280 
1.8 
–0.5 
58.5% 
58.8% 
0.6% 
5.60 
5.32 
–5.0% 
1993 to 2002
260
1.7
–0.7
58.5%
59.3%
1.4%
7.68
3.94
–5.0%
1995 to 2004
290
1.7
–0.6
63.9%
57.7%
–8.3%
5.53
3.90
–29.5%
1997 to 2006
290
1.7
–0.6
55.1%
N/A
N/A
3.90
N/A
N/A
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198
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broad range. I then picked the optimal setting on the basis of the
optimal position, generally near the point where the maximum R-
cubed value was achieved. I ran this optimization for five separate
10-year tests. Table12-4 shows the performance of the rolling opti-
mization for the year after the period indicated.
As you can see from the table, performance varies greatly from
the tested value for each rolling period. Further, the optimal val-
ues are different for each time period tested. This illustrates the
imprecision of the testing process and the variability one will
encounter in making the transition from testing to actual trading.
Monte Carlo Simulation
Monte Carlo simulation is one way to determine the robustness of
a system and answer questions such as: “What if the past had been
just slightly different?” and “What might the future bring?” You
could think of it as a way to generate slightly different alternative
universes by using the data from the series of events that represent
the actual past price data. 
The term Monte Carlo simulation refers to a general class of
methods that use random numbers to investigate a particular phe-
nomenon. It is most useful with phenomena that are impossible or
difficult to describe with mathematical precision. The name Monte
Carlo comes from the city in Monaco that is famous for gambling
casinos since those casinos offer many games whose outcomes are
determined by random events: roulette, craps, blackjack, and the
like. The method was used during the Manhattan Project by the
scientists who created the atomic bomb, and its name comes from
that era. 
On Solid Ground
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199

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Those scientists were trying to determine the fission character-
istics of uranium so that they could determine how much uranium
mass would be necessary to make an atomic bomb. Enriched ura-
nium was incredibly expensive, and so they could not afford to be
wrong in their assessment or they would waste months of time, not
to mention money, if the bomb didn’t explode because there was
not enough uranium. Similarly, if they overestimated and ended
up using more uranium than they needed, it would add months to
the schedule for testing. Unfortunately, the complex interactions
of uranium atoms inside a bomb were impossible to model accu-
rately with the methods of that period and would have required
computing resources that were unavailable until recent times. 
To determine the amount of fissionable uranium required, they
needed to know what percentage of the neutrons emitted by an
atom splitting would result in another atom splitting. The famous
physicist Richard Feynman had the insight that they could deter-
mine the characteristics of the interactions of particular single neu-
tron by using a team of mathematicians and then could determine
whether that neutron was absorbed by another nucleus or split
another atom. Feynman realized that they could use random num-
bers to represent the various types of neutrons that would be emit-
ted when an atom split. If that was done thousands of times, they
would be able to look at an accurate distribution of the fission
characteristics of uranium that would allow them to determine
how much material would be needed. Feynman knew that
although he could not predict the future because the process was
too complex, he could take the parts of the problem he did under-
stand and, using random numbers to simulate neutron properties,
obtain the answer to the problem anyway. So, he could under-