|
PureBytes Links
Trading Reference Links
|
A while back I posted the idea of not reducing your trade
size during a drawdown. This approach had been suggested by
a couple of people in Chuck Le Beau's Systems Traders club
(and is intuitively attractive as fixed fractional does have
a negative expectancy). I compared it with the traditional
approach (setting trade size as a proportion of equity so
that trades size reduces during a drawdown) such as used
when calculating optimal F or Secure F.
Earlier tests on simple sequences suggested that for high
win ratio (discretionary) trading it might be better not to
decrease bet size until a predetermined uncle point was
reached. Those tests suggested that for low win ratio
trading (as experienced with trend following systems) you
would always be better to decrease absolute bet size
(keeping it at 2%-6% of equity, say).
I wondered if it was just the sequence of trades that
favoured holding the absolute bet size constant or if I had
found a real advantage. To test that I needed to scramble
the trade order. Monte Carlo testing allows you to scramble
the sequence of trades 1000s of times and look at what
happens statistically.
I finally got my Monte Carlo analyser and was able to test
the ideas myself. My goal was to determine if it was better
to reduce absolute bet size (keeping the percentage of
equity the same) as equity is reduced or hold it constant
while equity was reduced until an uncle point (say 30%
drawdown) is reached at which point the absolute bet is
reduced.
I used an excel monte carlo simulator released by Alex
Matulich on the Tradestation group. This allows you to test
a different money management techniques on a sequence of
trades and scramble them to look at the statistical effect
of different sequences to the one you recorded. Other Monte
Carlo tools are typically hundreds of dollars plus but
Alex's is $32 from
http://unicorn.us.com/trading/prosizer.html
making it very affordable.
I tested 4 sequences of wins and losses (the simplest was
win 1, win 1, lose 1; the most complex won 3, lost 0.5
twice, won 1 and again lost 0.5 twice).
In each case 106 trades were taken with 1000 monte carlo
iterations. The bet size (around 6%-7%) was adjusted to
give a mean drawdown of 30%.
The results below give the mean gain, the mean drawdown and
the gain/drawdown on the first line and the second standard
deviation the simulations on the second line. What it shows
is that you are always better to reduce absolute bet size as
equity is reduced (hold % constant). The reason for this is
that you have a higher initial bet size for a given mean
drawdown. This give a better return for the mean of every
sequence. Perhaps even more important, the 2 standard
deviation drawdown is also lower if you reduce bet size so
your risk of ruin for a given mean drawdown is lower.
Reducing (Vince) Non-reducing
(Alternative)
66% win ratio systems
Bet Percentage >> 7.6 6.9
1 1 -1 . 960% 29.8% 32.9 918% 30.0%
31.8
expectancy .32 991% 45.9% 47.1 950% 51.7%
49.3
Bet Percentage >> 8.78 8
1 .5 .5 -1 665% 30.0% 22.7 649% 30.0%
22.5
expectancy .24 682% 46.9% 32.9 684% 51.9%
34.8
Bet Percentage >> 13.4 11.7
2 2 .5 -1 60150% 30.0% 2095.4 57729% 30.0%
2035.6
expectancy .85 61638% 55.0% 3553.2 59005% 59.2%
3500.9
33% win ratio systems
Bet Percentage >> 7.1 6.3
1.5 .5 -1 790% 30.0% 27.0 732% 29.9%
25.4
expectancy .31 818% 46.2% 38.6 767% 51.4%
39.1
Bet Percentage >> 7 6.1
2 -.5 -.5 710% 30.0% 24.2 663% 30.0%
22.9
expectancy .6 738% 46.3% 34.7 701% 50.2%
34.6
Bet Percentage >> 6.5 5.6
3 -.5 -.5 1 -.5 -.5 613% 30.0% 20.9 573% 30.0%
19.8
expectancy .6 642% 46.3% 30.0 612% 51.1%
30.5
More complex sequences of real trades also support the same
view.
For Craig: In my view you are best to use an optimal f
style calculation but set the maximum drawdown to a level
where you could stand experiencing twice as bad a future
drawdown!
John
|