over time, resulting in a data series that is far from being representative of the way
the stock actually traded at the time, before the splits took place.
The efficiency of a system is mainly measured via the average profit per trade
in normalized terms. It is better to look at the average profit per trade, rather than
the final net profit, because it is the final net profit that is a function of the out-
comes of the many trades, instead of the other way around. The average profit per
trade is also called the mathematical expectancy of the system. From this, it follows
that for a system to be profitable, the mathematical expectancy must be positive.
However, because the outcome of any individual trade most likely will not
be the same as for the average trade, it also is important to know how much all
trades are likely to deviate from the average trade. This measure is called the stan-
dard deviation and is a measure of the risk involved in trading the system. The
higher the standard deviation, the less sure we can be of the outcome of any indi-
vidual trade, and the riskier the system. Dividing the average profit per trade by
the standard deviation of all trades gives us the risk-adjusted return. The higher
the risk-adjusted return, the higher the average profit in relation to the risk of
trading the system.
It also is good to know the normalized values of a system’s average winner
and loser. In the best of worlds, the losers only have one size—that of the stop
loss—which makes the average loser equal to the largest loser. Knowing this, we
can calculate a system’s true risk–reward relationship and experiment with differ-
ent types of profit-taking techniques, such as profit targets and trailing stops, to
create a trade profile that suits our needs.
Managing your trades this way also means that most trades should fall with-
in a few very distinct categories, the two most obvious being the maximum winner
and the maximum loser. The distribution of your trades should not follow the reg-
ular normal distribution, which implies that the outcomes are random. The month-
ly results, however, could follow a normal distribution around a positive mean.
Knowing the size of the average winners and losers also makes it possible to
calculate a realistic number of trades to get out of a drawdown. Adding the aver-
age time spent in a trade to this equation also makes it possible to calculate a real-
istic time horizon for the same dilemma.
Talking about drawdown, it is a sad but true fact that your worst drawdown
is always still to come. No matter how severe your worst historical drawdown is
today, if you only stay in the game long enough, another drawdown will occur that
will surpass it, both in time and in magnitude. From this, it also follows that if you
only stay in the game long enough, you will encounter a drawdown that will be
deep or long enough to take you out of the game completely.
The only thing we can do about this is to make the likelihood for these draw-
downs as small as possible, so that, statistically speaking, it shouldn’t happen any-
time within, say, the next 1,000 years or so. But even so, and no matter the
precautions, for some it can and will happen tomorrow, simply because of bad luck.CHAPTER 6 Quality Data 77