period. For easier interpretation, you also can multiply by 100. For example, if a
system has produced a total of 52 winners over 126 trades, the percentage prof-
itable trades is 41.27 percent (52 * 100 / 126). From this, it follows that 58.73 per-
cent [100 41.27, or (126 52) / 126] must be losers or break-even trades.
If the average winner and loser are worth $500 and $400, respectively, and
the historical (or back-tested) track record shows that the system has produced 45
percent profitable trades (and consequently 55 percent losers), then the mathe-
matical expectancy for the system equals $32.5 [(0.45 * 500) (0.55 * 350)].
When looking at these numbers, it’s important to remember that a historical-
ly high percentage of profitable trades doesn’t necessarily mean an equally high
likelihood for the very next trade, or each individual trade, to be a winner. The rea-
son for this is somewhat abstract and philosophical: As soon as any series of words
or numbers result in something that is not random, it contains information. And as
soon as there is information in anything, we can distill it from the background
noise and make it work in our favor.
In the case of a trading system, this is equal to refining the system to make
better use of the nonrandom signals the market gives us. However, the conse-
quence is that the closer we get to distilling all the information, the closer the sys-
tem comes to acting in a random manner. When we have refined the system as
much as we can, but still think we can detect some information, such as seeming-
ly predictable runs of winners and losers, we are still better off assuming that
information is not there. This is because even a very complex and seemingly non-
random series of data still can be the product of randomness—as for example, this
sentence (just kidding).
If we assume nonrandomness when none exists, we run the risk of trading too
aggressively when we shouldn’t, and not aggressively enough when we should,
which over time will result in a less than optimal equity growth. The best way to
avoid this dilemma is to assume randomness and to trade at an equally aggressive
level all the time. Consequently, even if you have more than 50 percent profitable
trades in your testing and historical trading, you are better off not assuming more
than that in your real-life future trading.
In fact, considering that a random entry, at best, has a 50 percent chance of
ending up with a profit (not considering slippage and commission), factoring in
these costs of trading will take the likelihood below the 50 percent level. Exactly
how much lower is hard to estimate and depends on how large these costs of trad-
ing are in relation to the profits and losses produced by the system. Therefore, if
your back testing or historical trading results show a high percentage of winners,
it could be because of two things: Either the system is good enough to overcome
the negative biases stacked against you, or the results so far (whether actual or the
product of back testing) are pure fluke.
Furthermore, assuming a 50 percent chance for the market to move a specif-
ic distance in either direction from the entry point, there still is a larger chance for36 PART 1 How to Evaluate a System