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Replying to your message of Monday, August 5, 2002, 10:14:48 PM,
> Paul Zislis wrote:
>>While it is true that you can use the same formula in drawdown as in
>>equity runup, Jones' book goes into several other variations of
>>how to manage drawdowns. They are worth looking into.
> Admittedly I have not looked into them in any depth. For good
> reason. Allow me to editorialize for a few paragraphs.
> The problem I have with Jones' variations is that they seem to be
> band-aids to compensate for the failings of his fixed-ratio position
> sizing model. He has a stake in promoting it, so he's going to come
> up with all sorts of ways to fix its failings.
While he certainly has a stake in Fixed Ratio, the need to consider
position sizing variations during drawdown is still important. The
key problem of any position sizing method is that you need a larger
percentage increase in equity to counteract a specific percentage
decrease in equity. E.g., If you suffer a 33 1/3% loss of equity you
need a 50% increase in equity to get back to where you were. That is
true regardless of the position sizing method you use. Jones suggests
alternative strategies for reducing position sizes during drawdown
and reincreasing position sizes as equity starts to build again.
Users are free to choose whatever method best fits with their
objectives.
Handling position sizing during drawdown may be more important with
Fixed Ratio because FR starts out more aggressively. If you risk a
higher percentage of capital in order to build equity faster in the
beginning with a smaller account size, then a series of losses will
also have a more negative effect. If you reduce position size faster
during drawdown (using one of the variations) then a series of losses
will not have as large an effect. And the time to recover will
improve.
> 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 regard fixed ratio as one of the most
> dangerous things you can do with your account, almost as bad as
> trading with no plan at all.
Fixed Ratio expects the user to determine the level of aggressiveness
in the choice of delta. Historical tests allow the user to determine
what kinds of drawdowns have occurred and delta can be chosen as a
smaller (more aggressive, higher risk) or higher (more conservative,
lower risk) percentage of maximum expected drawdown. A Monte Carlo
test may help the user get a better handle on what kind of max
drawdowns may occur and they may adjust their choice of delta and
initial account size accordingly. Neither a vanilla historical test
nor a Monte Carlo test will tell you for sure what the largest
drawdown will be in the future. They can only provide a guide.
However, there is a similar problem with fixed fractional. What
fraction of account equity do you use to have your risk of ruin be
acceptable?
Fixed Ratio ceratinly considers more than account capital in its
calculations. A major factor is current drawdown. Even the basic
Fixed Ratio automatically reduces position sizes as account equity
goes down during a drawdown. It is true that you could trade yourself
into oblivion with FR. It is also true that you could trade your way
into oblivion with fixed fractional.
There are other variations of Fixed Ratio that I would like to study,
but for someone (like me) with a limited account size, the ability to
grow my account more rapidly using FR with one of the variants for use
during drawdowns has already been helpful. The "other" variations I
have in mind I would characterize as additional risk management.
These variations would be useful in conjunction with fixed fractional
as well. Both methods basically depend on selecting a key parameter
(Delta for FR, f for fixed fractional). Suggested variations:
1. sector diversification. I'd rather have trades in multiple market
sectors than have all my trades in one sector. I'd like to identify
what the largest percentage of capital may be risked in a single
sector at one time.
2. market diversification. I'd rather have trades in multiple
markets, even within the same sector, than have all my trades in a
single market. I'd like to identify what the largest percentage of
capital may be risked in a single market at one time.
3. total portfolio risk. I'd like to stop taking trades when my
current trades exceed some threshhold.
All of these issues can be dealt with manually in either FR or FF.
I'd like to have a way to specify these things so I can test their
effectiveness through historical testing at the portfolio level. I use
a testing platform that supports portfolio level testing of money
management strategies as well as custom development of money
management strategies, and this is an area of work I expect to get
into.
> 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.
I haven't done Monte Carlo tests myself, yet. What you say may or may
not apply to the drawdown variations since you haven't tested those.
I've also heard this story about Ryan Jones. I don't know if it is
true or not. Even if it is true, I don't know whether he was using
Fixed Ratio, how aggressively he chose Delta, whether he used
discretion or purely mechanical systems, etc.
> 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.
It would be interesting to see the results including more of the Fixed
Ratio methods than just the basic formula. It would also be
interesting to see what mean returns and mean drawdowns you would see
given a fixed risk of ruin. Clearly you can go bust using fixed
fractional or Fixed Ratio. But for a given level of risk of ruin, how
do the strategies compare? While your tests show P(ruin)>0 only with
FR for the starting conditions you described, it may be that FR
delivers superior risk adjusted return for P(ruin)= 1%, 2% or
whatever. I don't know whether that would be true or not, I'm just
suggesting that your tests, while very interesting, only look at some
of the issues of interest, not all of them.
> I'm saying all this because I think that inventing variations to
> manage the drawdowns associated with fixed ratio seems like trying
> to fix something that was broken to begin with. Why not instead
> just use something that works?
For me, the variations represent enhancements that improve on a method
that is already useful for building up small accounts rapidly. I can
choose the level of aggressiveness I'm willing to take on via Delta.
I can choose from a few different methods for preserving capital
during drawdowns.
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