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What's the most reliable way to calculate expected drawdown, given a
series of trade numbers generated by a system?
I am not very mathematically inclined, and I may understand only
enough to be dangerous about the standard measures of determining risk
such as Sterling, Sharpe, and K-Ratio. The problem that I see with them
is that they include in their calculations the winning trades or the
upswings in equity. This seems to create misleading assessments.
For example, I started trading a system in late August. At that time
its K-Ratio (by Lars Kestner; its a measure of the relationship of the
points of an equity curve to a regression line of the curve) was 4.7
(the higher, the better). The system over the next several weeks went
into a steep ascent, the best of its history, and had few losers. This,
of course, is what we want a sytem to do, so one would think that a
formula to measure the risk of such an event would say the risk is less,
since the equity curve has an increased upward bias. However, the
K-Ratio has steadily decreased, now standing at 3.1, and implying that
the system has gotten riskier. Had the system not made so much money,
the K-Ratio (and I assume Sterling and Sharpe) would have been greater,
implying the system risk was less.
This doesn't make sense to me. These measures of risk penalize a
system for unusual jumps in equity. Don't we need a measure of the
downside risk alone? From what I understand, the standard measures look
at the "swinginess" of the equity curve, without isolating the swings we
are most concerned about, downswings. Perhaps the theory is that what
goes up is as likely to go down, so if a system produces sudden and
sharp moves up, it is just as likely to produce sudden and sharp moves
down? But with a trading system, aren't the numbers supposed to be
biased to the upside? We've created it to make money, and if it's one of
those rare creatures that works, the trade results should not be a
random series of numbers, but one tending up. Yes, it's prettier if the
equity curve is smooth, without big jumps either way, but what trader
would not be glad to have a few big jumps up added to his/her month-end
statements, so long as these were in addition to more incremental
increases and didn't constitute the majority of the gain?
A trader/statistician with whom I had contact last year suggested
the following way to assess risk (specifically, I was asking him how to
determine the drawdown norms for a system). As I've never seen it
anyplace else, I'd be interested in feedback on whether it's valid. In a
spreadsheet, enter all the trades of a system. In column two add each
trade to the previous total, to get the equity curve. In column 3
subtract each value of the column 2 from the previous value (this will
be the same as col. 1, giving the gain/loss of each trade). Delete all
the positive values of col. 3, leaving you with only the losing trades
(this is the key: we are looking only at the losers). For column 3,
determine the average of the losing trades and the standard deviation;
then multiply the standard deviation by 3, and subtract the average
loser form this number. This will give a number which should contain
99.5% of the future losers, because it's 3 standard deviations from the
average (I hope I'm saying this correctly). However, we've only looked
at single losers, not runs of losers (which is what we get in real
trading), so it's necessary to perform the same operations we did on
column 3 upon a new series of numbers derived from looking back two
trades (rather than one) in the equity curve. To do this, in column 4 we
list the results of looking two trades back in column 2 (the equity
curve). Then we again delete any positive numbers, figure the average
2-trade loser, the standard deviation, and the 3 std minus avg loser. We
keep doing this, looking back an additional trade (in effect looking for
longer and longer strings of losers, or drawdowns), until the resulting
3 standard deviation minus average loser number stops getting larger.
The largest of these 3 std minus loser numbers should be the largest
drawdown for a string of losing trades that this system should expect to
see, with a 99.5% assurance level. An example may make this clearer.
trade cumu. 1 back 2 back 3 back 4 back 5 back 6 back 7
back 8 back
-175 -175 -175
225 50 225
-1050 -1000 -1050 -825
25 -975 -1025 -800
1175 200
125 325
-975 -650 -975 -850 -700 -475
-125 -775 -125 -1100 -975 -825 -600
-485 -1260 -485 -1910 -1585 -1460 -285 -260
-1310 -1085
-525 -1785 -525 -1010 -1135 -2110 -1985 -810
-785 -1835
-250 -2035 -250 -775 -1260 -1385 -2360 -2235
-1060 -1035
-250 -2285 -250 -500 -1025 -1510 -1635 -2610
-2485 -1310
425 -1860 -75 -600 -1085 -1210 -2185 -2060
50 -1810 -25 -550 -1035 -1160 -2135
550 -1260 -485 -610
1000 -260
avg -401.11 -999.4 -979.3 -1182 -1229 -1183
-1259 -1439
std 385.55 386.1 434.5 678.8 723.9
773.4 677 537.1
three STD+avg 1557 2157 2283 3218 3400 3502
3290 3049
If there were sufficient trades to make a judgment, these numbers
would indicate an expected max drawdown of 3502. With such a method,
subsequent runups do not alter the expected drawdown. Instead, it looks
only at runs of losers. For those of you who are
mathematically/statistically versed, does this method make sense? Does
it give a valid expectation of drawdown? If not, what is it measuring?
Thanks for your time in reading this long post,
Lincoln
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