144 THE HANDBOOK OF PORTFOLIO MATHEMATICS
assume that there is a maximum drawdown that we can expect is simply an
illusion. The idea is propagated for a trader’s peace of mind. Statistically,
it has no significance. If we are trading on a fixed fractional basis (where
the drawdown is also a function of when it happens—i.e., how big the
account was when the drawdown started), then drawdown is absolutely
meaningless.
Third, the drawdown under fixed fraction is not the drawdown we
would encounter on a constant contract basis (i.e., nonreinvestment). This
was demonstrated in the previous chapter. Fourth and finally, in this exer-
cise we are trying to discern only how much to commit to the next trade, not
the next sequence of trades. Drawdown is a sequence of trades—should the
maximum drawdown occur on one trade, then that one trade would also be
the biggest losing trade.
If you want to measure the downside of a system, then you should
look at the biggest losing trade, since drawdown is arbitrary and, in effect,
meaningless. This becomes even more so when you are considering fixed
fractional (i.e., reinvestment of returns) trading. Many traders try to “limit
their drawdown” either consciously (as when they are designing trading
systems) or subconsciously. This is understandable, as drawdown is the
trader’s nemesis. Yet we see that, as a result of its arbitrary nature, draw-
down is uncontrollable. What is controllable, at least to an extent, is the
largest loss. As you have seen, optimalfis a function of the largest loss.
It is possible to control your largest loss by many techniques, such as only
day-trading, using options, and so on. The point here is that you can control
your largest loss as well as your frequency of large losses (at least to some
extent).
It is important to note at this point that the drawdown you can expect
with fixed fractional trading, as a percentage retracement of your account
equity, historically would have been at least as much asfpercent. In other
words, iffis .55, then your drawdown would have been at least 55% of your
equity (leaving you with 45% at one point). This is so because if you are trad-
ing at the optimalf, as soon as your biggest loss is hit, you would experience
the drawdown equivalent tof. Again, assumingffor a system is .55, and
assuming that translates into trading one contract for every $10,000, your
biggest loss would be $5,500. As should by now be obvious, when the biggest
loss was encountered (again we’re speaking historically, i.e., about what
would have happened), you would have lost $5,500 for each contract you had
on, and you would have had one contract on for every $10,000 in the account.
Therefore, at that point your drawdown would have been 55% of equity. How-
ever, it is possible that the drawdown would continue, that the next trade or
series of trades would draw your account down even more. Therefore, the
better a system, the higher thef. The higher thef, generally the higher the
drawdown, since the drawdown (as a percentage) can never be any less than