age trade. If that is the case, the kurtosis should increase with the number of trades
from which we can draw any statistical conclusions, while the dispersion of these
trades stays the same. That is, the standard deviation should stay the same between
alterations of the system. If both the standard deviation and the kurtosis increase,
it could be because the new system is producing more outlier trades. (An outlier
trade is an abnormally large winner or loser that we didn’t expect to encounter,
given the characteristics of the system.)
What probably cannot be seen from Figure 2.6 is that the distribution also is
slightly skewed to the left (a negative skew), with the tail to the left of the body
stretching out further than the tail to the right. Normally, a negative skew results
in a mean smaller than the median. When building a trading system, we prefer the
returns to be positively skewed, with the tail to the right stretching out further from
the body than the tail to the left, so that we make sure that we’re cutting our loss-
es short and letting our profits run. In that case, the value of the average trade also
will be larger than the median trade, which means that for most trades, we can
expect to make a profit similar to the median value. Every so often, however, we
will encounter a really profitable trade that increases the value of the average trade
as well. This, too, is a double-edged sword in that the final outcome now is more
dependent on a few large winners, which might or might not repeat themselves in
the future. To calculate the skewness of the distribution, you can use the skewfunc-
tion in Excel. In this case, the skew equals 2.01, with the average return per day
equal to 0.0296 percent and the median equal to 0.0311 percent, respectively.STANDARD ERRORS AND TESTS
Many times, when testing a system on several markets, it is easier to work with the
averages from each system/market combination (symac) and then calculate an
average and standard deviation interval around this newly computed average of all
other averages. This presents a small statistics problem, because when we work
with averages from several samples to calculate an average of those averages and
a standard deviation interval around the new average of averages (now called the
standard error), we really should use the following formula:sM∑s^2 ̇
2 /N
Where:
sMStandard error of average from all markets tested
∑s Standard deviation of all trades from all markets
N Number of markets tested
As you can see from the formula, sMwill be smaller than s (how much
depends on N). Because both a single sample observation and a sample average
are estimates of the same true average for the entire population, and because there28 PART 1 How to Evaluate a System