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Timothy,
I've done much work in this area. The foundation of my work has been from Vince, The Mathematics of Money Management.
Generate normalized daily equity curves for each market system.
Calculate the mean (arithmetic) daily return for each market system. Calculate the covariance of all market system combinations.
Use the principles of Modern Portfolio Theory to construct an portfolio that yields the best portfolio return for a given level of portfolio variance. Or, if you really want your money to grow fast, choose a portfolio that is geometrically optimal.
*** Using MPT for portfolio construction is only valid to the extent that the constituent asset's mean-variances are stable in the future!***
Hence, the bulk of system design effort and the measurement of the quality thereof should be focused on characterizing the stability of the return distributions in the future, not principally on optimizing the mean return of the past data which I suspect is what most people do.
Scott Hoffman
Issaquah, WA
-----Original Message-----
From: Timothy Morge [SMTP:tmorge@xxxxxxxxxxxxxxx]
Sent: Thursday, August 06, 1998 2:19 PM
To: omega-list@xxxxxxxxxx
Subject: Portfolio Trading and trade allocations
Hi folks!
I am playing with a spread sheet exercise and thought I'd ask for input from
people on this list. In my current longer-term trading, I use what I term
'equivalent trading units' that allow me to risk similar amounts on a given
trade, relative to my capital and the average true range of X for each of the
commodities I trade. Now, In my normal trading, I never even approach a level of
margin use where I'd ever get a margin call. And when looking at several papers
and a few books, I see that most people use something similar when determining
how many contracts to trade of a given commodity. I also take this information
into consideration when looking at my maximum stops, which means I won't take a
trade that has a percieved risk that is larger than one I am comfortable [and
those maximum risks per trade are all equal].
But this exercise is slightly different [I think]. And my guess is that some of
you out there, systems traders perhaps, may already have elegant solutions. So
here goes:
You have a methodology that you are able to code and back test. It works well
across a broad spectrum of commodities, financials and indexes. If, for the
basis of this discussion, it helps you to be able to envision a technique,
assume it is th trend trading technique of your choice. Assume it will be traded
on ten seperate commodities and that for each of these commodites, it's equity
curve is positive in slope. To make it easier to visualize, let's say that all
ten commodities win an average that hovers around 50 percent, and the average
wins hover around 2-3 times the average losses. I don't think these matter for
the sake of the exercise--I am simply adding them in here to make it easier to
visualize.
Now, also assume you will always take a trade in each of the commodities and
that the system is such that 95 percent of the time, you are in the market in
each of the commodities--the only time you will not have a position is when you
have hit a disaster stop, and then you will be flat in that market until a new
signal is generated.
The question is: If you have already determined how to relate each commodity, so
that the risk asociated with each trade is set to an equal amount, how do you
decide how trade size? For example, suppose that when you do your equivalent
units, you find:
Commodity Equivalent Unit
Corn 15
CRB 3
Cotton 5
DM 3
Dollar Index 6
Euros 12
Five Year 6
Copper 10
Heat Oil 3
Unleaded Gas 3
JPY 3
Coffee 3
Lumber 3
Live Cattle 7
German Bunds 5
Muni Bunds 5
Natural Gas 10
Swiss Francs 2
Silver 6
SP 2
TYAM 5
Bonds 4
Wheat 5
NYFE 3
Now, if you traded just these amounts, you'd use much less [something less than
$250K] in margin. IF you were trading a $1 million dollar account, how would you
determine the multiple of equivalent units to trade? What if it were 20
commodities?
I hope this makes some sense.
Best,
Tim Morge
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