Way of the turtle

200
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Way of the Turtle

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stand the nature of the fission characteristics of uranium without
having to be able to predict exactly what each atom would do at
each point.
Alternative Trading Universes
The markets are even more complex than nuclear fission reactions.
Markets are composed of the actions of thousands of people who
make decisions on the basis of their own history and brain chem-
istry, which are much less predictable than neutrons are. Fortu-
nately, as Feynman did with uranium analysis, we can use random
numbers to get a better feel for the potential characteristics of a
trading system even though we cannot predict what the future will
bring. We can examine a set of alternative trading universes that
represent a potential way in which history might have unfolded if
things had been slightly different.
There are two common ways to use Monte Carlo methods to
generate these alternative trading universes:
• Trade scrambling: Randomly changing the order and start
dates of the trades from an actual simulation and then using
the percentage gain or loss from the trades to adjust equity
by using the new scrambled trade order
• Equity curve scrambling: Building new equity curves by
assembling random portions of the original equity curve 
Of these two approaches, equity curve scrambling generates
more realistic alternative equity curves because Monte Carlo sim-
ulation with random trade reordering tends to understate the pos-
sibility of drawdowns.
On Solid Ground
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201

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The periods of maximum drawdown invariably occur at the tail
end of large trends or periods of positive equity increases. At those
times, markets tend to correlate more highly than they normally
do. This is true for futures and stocks. At the end of a large trend
when it breaks down and reverses, it seems that everything moves
against you at once; even markets that normally do not seem cor-
related become so on those volatile days when a large trend dis-
integrates.
Because trade scrambling removes the connection between
trades and dates, it also removes the effect on the equity curve
of many trades simultaneously reversing. This means that your
drawdowns show up with less magnitude and frequency in
Monte Carlo simulation than they will in real life. Take a look
at the moves in gold and silver in the spring of 2006. If you hap-
pened to test a trend-following system that traded both of those
markets, scrambling the trades would mean that your draw-
downs for those two markets would happen at different times,
effectively reducing the effect of each separate drawdown. In
fact, this effect extended to a few other relatively unlikely mar-
kets, such as sugar; there was a significant period of drawdown
in the sugar market during the 20-day period from mid-May to
mid-June 2006, the same period in which gold and silver were
declining. Thus, trade scrambling is inferior because it under-
states the drawdowns one is likely to encounter in trading long-
term and medium-term systems.
Another example of this phenomenon is the one-day draw-
down in the 1987 U.S. stock market crash. On they day of the
large opening gap in eurodollars, many markets that normally
were not correlated also gapped strongly against my positions.