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At 8/5/2002 09:14 PM, Alex Matulich wrote:
>Fixed ratio fails to account for capitalization, it fails to
>account for trade risk or market volatility, it fails to manage
>risk and drawdown, it fails to preserve capital. It reacts purely
>to net profit without regard to anything else. A small account
>can trade itself into nearly 100% drawdown with this technique;
>an impossibility for other position sizing methods that yield far
>more profit for less risk.
I have to disagree with the statement that 100% drawdown is an
impossibility with some position sizing methods. No money management can
eliminate risk of ruin.
>In my Monte Carlo experiments, I couldn't help but notice that
>the distribution of returns using fixed ratio always had a long
>tail on the left (low) side of the mean return. This implies a
>higher probability of doing worse than the mean, than better. And
>invariably a tiny percent of trials achieved the dubious status of
>"ruin" -- and this was using trades from a *positive expectancy*
>system! In view of this observation I was not surprised to learn
>recently that Ryan Jones has traded his own account into a 95%
>drawdown level.
>
>For similar mean returns and mean drawdowns, using the same trade
>history, all other sizing models I implemented in ProSizer exhibited
>symmetrical return distributions with zero chance of ruin.
The same comment as above. Maybe I am misreading what you are saying, but
no money management can yield zero chance of ruin.
With fixed fractional as you go into a drawdown position sizes reduce.
Eventually position sizes will hit 1 contract. At that point a trader would
need to decide whether to exceed their predetermined risk percentages by
trading 1 contract, or follow the predetermined risk percentages by trading
zero contracts.
If you continue to trade 1 contract, you can hit ruin. On the other hand,
trading zero contracts is essentially the same as ruin, except you still
have a little left in your account when you are forced to stop trading.
Either way, you are forced to stop trading, which is what ruin really means.
Another comment about the above discussion goes back to my fixed ratio
spreadsheet:
http://www.powertesting.com/FixedRatioExample.html
My main interest in creating that spreadsheet was to relate fixed ratio
position sizes to fixed fractional style percents. The spreadsheet allows
experimentation with different delta values and account sizes, and from
that it calculates percent risk per trade at progressive account levels.
The essential difference between fixed fractional and fixed ratio is that
with fixed fractional the risk per trade percent is the same at all account
levels, where with fixed ratio the risk per trade percent varies at
different account levels.
I believe that if you choose a delta which yields X% maximum percent risk
(which can be determined using the spreadsheet), that the risk of ruin for
fixed ratio with that delta will be identical to the risk of ruin for X%
fixed fractional. In other words, I don't think there is anything
inherently different about fixed ratio that makes it more prone to risk of
ruin than fixed fractional.
However, it is also clear that fixed ratio is often used as a way to be
more aggressive in the beginning then progressively less aggressive as
account size grows. This is a major theme Jones discusses.
Of course, higher aggression will always yield higher risk of ruin. This is
a decision a trader needs to make, whether to increase risk of ruin to grow
the account more rapidly in the early stages. What I am saying is that I
think your cautions are good, but they do not point out a flaw in fixed
ratio. For example, a trader can decide not to be more aggressive in the
early stages to keep risk of ruin the same as fixed fractional. In other
words, the trader can decide to, for example, limited maximum per trade
risk to 5%, or any other percent, and only use fixed ratio as a way of
decreasing position sizes as account equity grows. In that case, I believe
that the risk of ruin would be identical to 5% risk per trade fixed fractional.
Certainly your caution that higher aggression in the early stages will
increase risk of ruin is an important caution any trader considering fixed
ratio should be aware of. But to my perspective, it is not pointing out a
flaw in fixed ratio. Rather, it only means the trader needs to make a
judgement about this. It depends on the goals and risk tolerance of the
trader. I think some traders will be willing to accept the increased risk
in exchange for the potential of the faster initial account growth. But,
yes this is a decision a trader needs to make with his eyes wide open. I
think my spreadsheet very clearly shows the risks. Monte Carlo experiments
can lend additional data.
Bob Bolotin
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