Basically, there are two ways to get a better feel for the maximum drawdown.
One is to calculate the average drawdown and the standard deviations of all draw-
downs, and then see where the maximum drawdown fits within this spectrum. The
further away from the average drawdown the standard deviation boundaries are
located, the more dispersed the drawdowns and the less sure you can be about what
to expect in the future. Remember also that all drawdowns will be represented by
either a negative or a positive number (depending on how you measure them), with
zero drawdown being a definitive boundary in either case. Thus, the distribution
of the drawdowns won’t take the familiar bell-shaped curve associated with a nor-
mal distribution. (What you really should do in this case is measure the value of
all runs, both positive and negative, from equity lows to equity peaks, and vice
versa.)
Another way to get a feel for the maximum drawdown is to compare it to
both the average value and the median value of all drawdowns. For example, in the
number series 2, 1, 14, 6, 12, the mean is equal to 7 [(2, 1, 14, 6, 12) / 5], where-
as the median is represented by the number 6: 2, 1, 14, 6, 12 (sorted: 1, 2, 6, 12,
14). The higher the maximum drawdown is in relation to the median drawdown,
the more of a freak occurrence the maximum drawdown has been, especially if the
average drawdown is closer to the maximum drawdown than to the median draw-
down. For the example above, the maximum value being 14, the average value is
much closer to the median value, which indicates that a drawdown of 14 isn’t as
much of a freak occurrence as we would like it to be.
A bad situation occurs when the median drawdown is larger than the average
drawdown. Then the smaller drawdowns are in minority, representing the freak
occurrences, all the more so, the closer the average drawdown is to the smallest
drawdown. To express this mathematically, divide the average drawdown, by the
median drawdown. The higher this value is above one, the more freakish the large
drawdowns behind the large average drawdown. Similarly, dividing the maximum
drawdown by the average drawdown, gives an indication of how large the maxi-
mum drawdown is in relation to the average drawdown, with a value of two indi-
cating that the maximum drawdown is twice as large as the average drawdown. An
alternative is to divide half the maximum drawdown by the average drawdown, so
that the 2:1 relationship will be represented by the value one.
Multiplying these formulas with each other gives us a combined value for
how freakish the average drawdown is in relation to the median drawdown, and
how freakish the maximum drawdown is in relation to the average drawdown:DFI (AD / MeD) * [(MaD / 2) / AD] (MaD / 2) / MeD
Where:
DFI Drawdown freak index
AD Average drawdownCHAPTER 5 Drawdown and Losses 61