than necessary losses or smaller than necessary profits. The formula to calculate
the standard deviation follows:
s Sqrt[(N * Sum(Xi^2 ) Sum(Xi)^2 ) / N * (N 1)]
Where:
NNumber of trades
XiResult of trade Xi, for i 1 to N
If the return from a trading system is normally distributed, about 68 percent of
the individual outcomes will be within one standard deviation of the mean, and
about 95 percent will be within two standard deviations of the mean (1.96 standard
deviations to be exact). For example, if the average profit for a trading system is
$500, and the standard deviation is $700, then we can say that the profit for 68 per-
cent of all trades falls somewhere in the interval of $200 (500 700) to $1,200
(500 700), and that the profit for 95 percent of all trades falls somewhere in the
interval of $900 (500 2 * 700) to $1,900 (500 2 * 700). If, on the other hand,
the one standard deviation boundary lies at $900, the outcome for 68 percent off all
trades falls somewhere in the interval of $400 (500 800) to $1,400 (500 900).
We can see that the wider the standard deviation boundaries, the more dis-
persed the trades; and the more dispersed the trades, the less sure we can be about
the outcome of each individual trade. (Note that a large percentage of all trades
falls into negative territory. It is virtually impossible to build a system that can
keep its lower one standard deviation boundary in positive territory, with the
results measured on a per-trade basis.)
If taking on risk means taking on uncertainty about an unknown future or the
outcome of a specific event, then if we can be absolutely certain about the out-
come of a specific trade, no matter if we know whether it will be a winner or a
loser, we take no risk. (More about the distinction between risk and loss is in
Chapter 5: “Drawdown and Losses.”) Consequently, the less sure we are about the
outcome, the more risk we’re assuming, no matter if the outcome can be either
negative and positive.
Note that, using the formula above, the standard deviation will be smaller the
larger the denominator is in relation to the numerator, which happens with an
increasing number of trades. This is also an important reason why a system should
work on (or at least be tested on) as many markets as possible, because the more
hypothetical trades we have, the more certain we can be about the outcome of each
individual trade.
Finally, you probably have heard the old saying that the larger the profits you
want to make, the larger the risks you need to assume. This is because the standard
deviation most likely will increase with the value of the average trade. This doesn’t
always have to be the case, but most often it will. The trick, then, is to try to mod-
ify the system so that the standard deviation at least increases at a slower rate than24 PART 1 How to Evaluate a System