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Sure, we can think of numerical
descriptions associated with the flatness. For example, establish a center
point where the objective function is highest for the analysis, then perturb
each of the parameters by some amount and remeasure the objective function. Measure
the percentage change to the worst of the surrounding points, or measure the
standard deviation of the surrounding points.
Howard
-----Original Message-----
From: Dave Merrill
[mailto:dmerrill@xxxxxxx]
Sent: Wednesday, October 22, 2003
4:27 AM
To: amibroker@xxxxxxxxxxxxxxx
Subject: RE: [amibroker]
Invitation -- suggest your favorite objective function
<span
>I understand what
you're saying, but doesn't it seem like there might well be some useful
numerical measure of the flatness of the 3D graph, for example?
<span
>dave
I think there is a human component that has to be included in system development.
I am a believer in mechanical systems from the standpoint of trade execution.
However, when you are trying to develop your mechanical system and to decide
how best to implement it, you have to make some judgments 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 why I sent along that figure (just an
example). You have to develop your own decision rules that are right for your
personality, and those require you to examine a multitude of objective
functions to aid in your decision. There is a software package called Powerkit,
wherein the developer has included 3 canned systems that the user can tweak
with any combination of parameter values he wants to optimize. When the
optimization is done, a 3-dimensional graph automatically appears showing how
the parameters affect profits in 3-dimensional space. You pick your parameter
values based on the flatness of the 3-D graph, which is a measure of
robustness. TJ once told me that he plans to develop a similar 3-D
graphical capability that will blow Powerkit out of the water. That is probably
on the lower part of his priority list right now, but it will come eventually.
Is that a sufficiently vague answer to your question? :-))
Al Venosa
----- Original Message -----
<span
>From:<font
size=2 face=Arial> <a
href="" title="dmerrill@xxxxxxx">Dave Merrill
To:<font size=2
face=Arial> <a
href="" title="amibroker@xxxxxxxxxxxxxxx">amibroker@xxxxxxxxxxxxxxx
Sent:<font size=2
face=Arial> Tuesday, October
21, 2003 8:23 PM
Subject:<font size=2
face=Arial> RE: [amibroker]
Invitation -- suggest your favorite objective function
<span
>that's how I've
approached it in general too, eyeballing the various result outputs
manually. but if possible, I'd like to systematize it, partly so it can be an
object comparison measure, and partly so it can become a part of the trading
system itself.
<span
>do you have any
sense of how that might be done? it doesn't seem that the example you gave
boils down to simply weighting and summing the various individual metrics.
<span
>any other ideas,
anyone, on systematically combining them some other way that captures more of
what we do when we eyeball?
<span
>dave
I think there are numerous ways to evaluate your system rather than
relying on one objective function. For example, the other day, I was doing a
portfolio optimization to find out the optimum no. of positions I should have
open, given a certain amount of starting equity. I then plotted the results of
a few of the output parameters TJ now gives us in an optimization output. See
attached png file. If you were simply using one objective function (CAR)
without considering anything else, you would choose 5 open positions because
that's where CAR max'd out. However, MAR (=CAR/MDD) was still rising as was UPI
(you want that to be high), while UI (you want that to 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, the optimum 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 look at several different objective
functions and decide on the best strategy based on the total story they all
tell. I also like to use expectancy, which I think is an extremely important
and useful objective function. Sorry for the multiple answer, but I don't think
there is only one criterion upon which to judge a trading system.
Al
<font size=2
face="Courier New">Send BUG REPORTS to
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