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There might very well be, but I don't believe you need that to pick your
parameter values. If the peak area of the 3-D graph is flat and broad
enough, 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 well
as any other over time. That is the essence of robustness, and your system
ought to be able to respond to small market changes without having to be
constantly re-optimized. This is not to say that re-optimization is not an
appropriate thing to do occasionally (and I don't know how to define the
word "occasionally").
Al Venosa
Original Message:
-----------------
From: Dave Merrill dmerrill@xxxxxxx
Date: Wed, 22 Oct 2003 07:27:03 -0400
To: amibroker@xxxxxxxxxxxxxxx
Subject: RE: [amibroker] Invitation -- suggest your favorite objective
function
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?
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 -----
From: Dave Merrill
To: amibroker@xxxxxxxxxxxxxxx
Sent: Tuesday, October 21, 2003 8:23 PM
Subject: RE: [amibroker] Invitation -- suggest your favorite objective
function
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.
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.
any other ideas, anyone, on systematically combining them some other way
that captures more of what we do when we eyeball?
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
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