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I
don't know for sure, but I think the point about objective function was missed
completely. If you are looking at a 3-D graph, what is it
graphing? Net profit, CAR, CAR/MDD? Whatever it is
graphing is your objective function. Your objective function could
be a formula with six to eight metrics represented. Most of the ones
I use have more than four. So, using a 3-D graph and looking
for broad, flat areas is a great idea as long as you have decided what it is
that you want to graph.
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<FONT face="Times New Roman"
size=2>-----Original Message-----From: advenosa@xxxxxxxxxxxx
[mailto:advenosa@xxxxxxxxxxxx]Sent: Wednesday, October 22, 2003
8:30 AMTo: amibroker@xxxxxxxxxxxxxxxSubject: RE:
[amibroker] Invitation -- suggest your favorite objective
functionThere might very well be, but I don't believe
you need that to pick yourparameter values. If the peak area of the 3-D
graph is flat and broadenough, and you see no local maxima that could have
been due to chance,then any parameter you select within that broad peak
will do just as wellas any other over time. That is the essence of
robustness, and your systemought to be able to respond to small market
changes without having to beconstantly re-optimized. This is not to say
that re-optimization is not anappropriate thing to do occasionally (and I
don't know how to define theword "occasionally"). Al
VenosaOriginal Message:-----------------From: Dave Merrill
dmerrill@xxxxxxxDate: Wed, 22 Oct 2003 07:27:03 -0400To:
amibroker@xxxxxxxxxxxxxxxSubject: RE: [amibroker] Invitation -- suggest
your favorite objectivefunctionI understand what you're
saying, but doesn't it seem like there might wellbe some useful numerical
measure of the flatness of the 3D graph, forexample?dave
I think there is a human component that has to be included in
systemdevelopment. I am a believer in mechanical systems from the
standpoint oftrade execution. However, when you are trying to develop your
mechanicalsystem and to decide how best to implement it, you have to make
somejudgments that I don't think can easily be automated into a
single,multidimensional matrix out of which comes a simple, black and
white answer.There will always be shades of gray that require human
judgment. That's whyI sent along that figure (just an example). You have
to develop your owndecision rules that are right for your personality, and
those require you toexamine a multitude of objective functions to aid in
your decision. There isa software package called Powerkit, wherein the
developer has included 3canned systems that the user can tweak with any
combination of parametervalues he wants to optimize. When the optimization
is done, a 3-dimensionalgraph automatically appears showing how the
parameters affect profits in3-dimensional space. You pick your parameter
values based on the flatness ofthe 3-D graph, which is a measure of
robustness. TJ once told me that heplans to develop a similar 3-D
graphical capability that will blow Powerkitout of the water. That is
probably on the lower part of his priority listright now, but it will come
eventually. Is that a sufficiently vague answer to your
question? :-)) Al Venosa ----- Original
Message ----- From: Dave Merrill
To: amibroker@xxxxxxxxxxxxxxx Sent: Tuesday, October 21,
2003 8:23 PM Subject: RE: [amibroker] Invitation --
suggest your favorite objectivefunction
that's how I've approached it in general too, eyeballing the variousresult
outputs manually. but if possible, I'd like to systematize it, partlyso it
can be an object comparison measure, and partly so it can become apart of
the trading system itself. do you have any sense of
how that might be done? it doesn't seem thatthe example you gave boils
down to simply weighting and summing the variousindividual
metrics. any other ideas, anyone, on systematically
combining them some other waythat captures more of what we do when we
eyeball? dave I
think there are numerous ways to evaluate your system rather thanrelying
on one objective function. For example, the other day, I was doing
aportfolio optimization to find out the optimum no. of positions I
shouldhave open, given a certain amount of starting equity. I then plotted
theresults of a few of the output parameters TJ now gives us in an
optimizationoutput. See attached png file. If you were simply using one
objectivefunction (CAR) without considering anything else, you would
choose 5 openpositions because that's where CAR max'd out. However, MAR
(=CAR/MDD) wasstill rising as was UPI (you want that to be high), while UI
(you want thatto be low) was still falling and RAR/MDD was still not max'd
out yet. So,when you look at 7 open positions, you see that UI had pretty
much bottomed,UPI, RAR/MDD, and MAR had finally topped. So, in this
particular case, theoptimum no. of open positions would be selected to be
7, in my opinion,rather than 5. So, using this tiny little example, I
think you need to lookat several different objective functions and decide
on the best strategybased on the total story they all tell. I also like to
use expectancy, whichI think is an extremely important and useful
objective function. Sorry forthe multiple answer, but I don't think there
is only one criterion uponwhich to judge a trading
system.
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