is a higher likelihood for a sample average to come close to the true population
average, the standard error for a set of sample averages will be smaller than the
standard deviation for a set of individual observations.
The problem with this formula is that, if we first calculate an average profit
per trade and market, we won’t be able to find the standard deviation of all trades
from all markets, and if we did, we wouldn’t have a need for this formula in the
first place. So, what to do, and why?
Let’s start with the why. We’re doing this because testing a system over sev-
eral markets (I usually use 30 to 60 markets, tested over the last 10 years of mar-
ket action) produces lot of trades, which makes things very cumbersome and
results in very large Excel spreadsheets needed for the calculations. It is also valu-
able to know the standard error of the average for future reference, if and when we
start to trade the system for real and would like to compare the averages it pro-
duces in real-life trading with those estimated from the testing.
Nonetheless, somehow we need to come up with a value for the standard
deviation of all trades from all markets. To do this, assume that the variable we’re
investigating isn’t the profit per trade, as in the original standard deviation formu-
la, but the average profit per trade from several markets. Use the same formula to
compute s. In that case, Nin the original formula will represent number of mar-
kets tested, and Xithe average profit from a specific market, as indicated by i. (A
more correct way would be to calculate all the averages and standard deviations
for all the markets tested and then calculate a standard error of the averages as a
function of the mean square error, which simply is the average of all standard
deviations. But what the hell—this is not a book about statistics.)
It is important to remember that whatever variable we’re investigating—such
as the average profit per trade—will always be an estimate of the true average
profit per trade. This is because no matter how many markets we’re using and how
far back in time we do the testing, the test will only contain a small sample of mar-
kets producing the price pattern the system is trying to catch. Think about it: There
are various types of markets all over the place, and some of them are already sev-
eral hundred years old. It would be impossible to collect all the data to test them
to compute the true average profit per trade for a specific system, as of today. And
even if we could do that, the true value, as of today, would be nothing but an esti-
mate for what the true value will be at some point in the future, when all markets
cease to exist.
Therefore, it would be interesting if we could calculate an estimate, or at
least some sort of a confidence interval, for what the true average profit per trade
might be. For example, what if we, using our 30 to 60 markets and 10 years of
data, calculate the average profit per trade for a system to be $300, when in fact
the true value is $100, and the system slowly but surely starts to move closer to
that value over the next several years, when we’re trading it live. In that case, the
system has not broken down and the market conditions have not changed.CHAPTER 2 Calculating Profit 29