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Wow, you have done your homework, Rudolph. Let's get Walter, Ed and the
others in on this and see if we can quantify some of these risks. I think,
in essence, that is what you are asking -- how can these risks be
quantified.
I am reaching the boundaries of my education in statistics, but I think if
you use historical data to help identify the distribution of the entire
theoretical data set, and then use this distribution to determine risk and
position size, you will have covered (at least for practical purposes) the
risks you identified as single-trade risk and external-events risk. The big
unknown is the size of the tails on your distribution curve, and therefore
the size of a loss out past 3, 4 and 5 standard deviations.
Because I'm not particularly theoretically-inclined, I have been using only
historical results which are a proxy for the real distribution curve. I
realize it is not ideal, but it is the most practical for me. Others will
be more comfortable with the increased precision of parametric methods.
Consider Walter's point, though, that as humans, we are probably going to
find a way to screw up our carefully designed system anyway :)
I think the best we mortals can hope for, is to take a shot at quantifying
the more likely risks and always protect one's position with stop orders
(and maybe personal asset protection strategies if you wish). Ralph Vince
makes the point that if a person was only able to die from a lightning
strike, no matter how improbable or how many years it would take, they would
eventually be struck by lightning and die. Likewise, if one trades in an
unlimited-liability instrument like futures and, to a lesser degree, stocks
for a long enough time, you *will* suffer a catastrophic loss. The only way
to avoid this is to trade in limited liability instruments like long options
or long stocks.
Probability of ruin, in my opinion, is absolutely part of a money management
plan. This will affect the maximum drawdown you are willing to accept, and
therefore your position size. You can certainly optimize the larger losses
out of your system, but two problems arise from this:
1. Your system is less robust and more likely to fail when the character
of your particular market changes over time. I believe you are introducing
a likelihood of a large, unquantifiable loss or a string of losses.
Certainty of overall profitability is more important than minimizing any
single loss.
2. Smaller losses due to (over-)optimization, will mean that to achieve
optimal returns, your position size will increase to the point where you are
maximizing your losses again. You will be so highly levered that when (not
if) you suffer the large, unquantifiable loss, you are more likely to be
ruined.
I'm not advocating an unoptimized trading system, just one that is as robust
as possible and more likely to handle changes in the market. I am also
certainly not saying that you shouldn't try to minimize your losses, but
rather to develop a system that will anticipate and quantify as many of the
possible loss scenarios as it can.
As far as establishing an acceptable probability of ruin, that is your own
call. As it happens, I am going through this process (now that I can
quantify it !) with my wife who is very risk averse. Whatever we decide on,
the results will certainly give me less than the Optimal f. Whatever it
takes so you can sleep nights.
You also asked, "Does the Optimal f method ... use an *analytical* approach
for the probability histogram (instead of the original numerical values)?
And if so: What type of analytical probability distribution is used (e.g.
Weibull?), and does it deal correctly with e.g. unsymmetrical and "tailed"
distributions?"
The Mathematics of Money Management describes several different
distributions, including asymmetrical and fat-tailed distributions and how
to use Optimal f with these. I saw that discussion as more theorectical and
less practical to implement, but I imagine Walter or Ed could put it to
practical use in short order.
OK, I've rambled on again, but I just find this all so fascinating and such
an important component to anyone's trading or investment program.
Regards.
----- Original Message -----
From: rudolf stricker <rst@xxxxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: July 9, 1999 11:42
Subject: Re: Formula for Optimal f needed (long reply)
>
> Thank you, Ed Winter & Glen Wallace, for your very helpful hints on
> the Optimal f method and the necessity of money management in general.
> And because this money management should be "risk-based", it may make
> sense to list my understanding of some kinds of risks in typical
> trading situations. Imo, there is
>
> => some risk (from market & trading strategy), that shows up
> *statistically* in historical trades (statistical risk)
> => some additional risk (from market & trading strategy), that shows
> up for every single emerging trade, at least in my system (single
> trade risk)
> => some additional risk triggered by special external conditions (like
> e.g. political events), that are not modeled by the trading system
> (external risk)
> => (more types of risk; any suggestions?)
>
> The goal of any trading system is, imo, to handle at least the
> "statistical risk". This should include also some general measure for
> this risk. Imo, the probability to loose e.g. more than 90% of the
> investment could be a nice measure, and if I understood the Optimal f
> method, there is something used like this.
>
> But, imo, this should not be seen as a part of money management, but
> should rather be included, e.g. as (part of) the optimization
> criterion for the trading system. And because I'm ready to follow this
> line setting-up my trading system in Excel: What would be an
> appropriate criterion of this kind?
> Is e.g. a max probability of xx=5% for a loss of more than yy=90% of
> the investment a good goal for optimizing a trading system? - Any
> practical hints about realistic values for xx and yy?
>
> (BTW: This "max probability of xx% for a loss of more than yy%" imo
> is a nice basis to compare the profitability of different markets, at
> least for a given trading strategy, because it represents something
> like "trading persistence". - Is there any other measure for such kind
> of "trading persistence" in practical use?)
>
> To come back to Optimal f:
>
> Beyond of the "max probability of xx% for a loss of more than yy%"
> the Optimal f method seemingly uses additionally an "optimal
> investment rate for maximal increase of equity". Both of these
> criterions, imo, can be easily constructed (e.g. in an Excel-based
> system) from a normalized histogram of historical trades, but in the
> Optimal f Excel sheet from Futures Magazine (thanks again to Ed Winter
> for posting it) I see no integration formula for the histogram ...
>
> So my question is:
>
> Does the Optimal f method (for ease of integration) use an
> *analytical* approach for the probability histogram (instead of the
> original numerical values)? And if so: What type of analytical
> probability distribution is used (e.g. Weibull?), and does it deal
> correctly with e.g. unsymmetrical and "tailed" distributions?
>
> Any hints and comments are welcome.
>
> (BTW: All the topics discussed here deal with the "statistical risk"
> only (see definitions above). Maybe, there is also room for how to
> handle the "single trade risk" and the "external risk" later on.)
>
> mfg rudolf stricker
> | Disclaimer: The views of this user are strictly his own.
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