|
PureBytes Links
Trading Reference Links
|
Mark,
You raise some very interesting points and have given me some great
ideas to research.
With respect to correlation, as long as the coefficient is less than
one, then there are diversification benefits from adding additional markets.
As you pointed out, the more 'uncorrelated' the greater the benefit.
If I recall, the number of stocks suggested for 'full'
diversification is in the neighborhood of 30. Beyond that, there is very
little gained by adding additional stocks.(This might be in the CAPM model,
I can't remember.) You mention that diversification can be achieved more so
in futures than in stocks. If this is the case, then why is the optimal
number of futures markets to trade infinity? Is this a function of the
markets or the system itself? It seems to me that it should require less not
more, at least in theory.
If you were to plot variance versus number of markets, I would
expect to see diminishing marginal returns to variance reduction from an
additional market at some point. I guess this assumes that there is a risk
factor common among all futures markets, something along the lines of a
commodity beta. Is it possible to estimate or identify the source of the
risk that is being diversified/not diversified away?
Trey
-----Original Message-----
From: Mark Johnson [mailto:janitor@xxxxxxxxxxxx]
Sent: Wednesday, April 16, 2008 11:24 AM
To: omega-list@xxxxxxxxxx
Subject: Position trading 100+ futures markets times 8 systems
DANGER! THERE IS RISK OF LOSS IN FUTURES TRADING!!
In email, Gary Fritz suggested that I begin a thread here,
talking about the philosophy behind position-trading a
mechanical system on more than 100 futures markets, using
the same parameters in each market. Here goes.
Trading lots of markets simultaneously out of the same
account means you'll have lots of simultaneous positions.
You hope to get some benefits of "diversification", such
as: when one position zigs, another position zags, and
the net result is a smoother ride. If you want to think
of it this way, by trading 100 markets simultaneously,
you are summing together 100 different equity curves
from 100 "market-systems" as Ralph Vince calls them.
Your net result is the AVERAGE of the 100 different
equity curves (times 100). And the average of the
individual equity curves is, we hope!, much smoother
than the individual curves themselves.
They gave a Nobel Prize to Harry Markowitz who worked
out a theory of diversification benefits in the 1950's.
His book "Portfolio Selection" talks about it, in very
down-to-earth terms, and I *strongly* recommend reading
the book if you're going to make smooth-equity-curve-by-
means-of-diversification one of your goals.
The math boils down to this: you can increase returns
and decrease "non-smoothness" (variance) by adding more
traded markets to your system, as long as the correlation
coefficient between (the new market-system's equity curve)
and (the equity curves of the other systems) is small.
Which, hallelujah and praise Buddah, happens to be the
case in futures. Much more so than in stocks!
The math becomes especially simple if you make a
numerically convenient but wildly unrealistic assumption:
that all the correlation coefficients are equal to zero.
Occasionally you'll see an article in which someone
blithely assumes the individual market-systems are
"uncorrelated" (correlation equals zero). It ain't
true in real life, amigo. It ain't true at all.
But what does appear to be true, at least in my own
research, is that the correlation coefficients between
the equity curves of different markets traded with the
same mechanical system, are Quite Low. They are
Sufficiently Low. Low enough so you get SOME positive
benefit by adding yet another market. Sure, you get
less benefit than if the correlation had been Zero,
but SOME benefit nevertheless. In fact, my research
suggests to me a rather startling result:
The optimum number of commodity markets to
trade simultaneously with a mechanical system,
is Infinity.
I see that the more markets I add, the better and
better the final results become. In fact, I chuckle
with Bob Fulks that this approach could be called
"Wildly Excessive Diversification."
Applying the first principle of underwater demolition,
>> "If some is good then more is better" <<
I have chosen to increase the amount of diversification
yet further, by trading several different mechanical
systems simultaneously, each one of them on the enormous
100+ market portfolio. Again I find that the marginal
utility of adding that last system and that last
market, is positive.
There are a couple of drawbacks however. First of all,
it means the trader must manage several hundred
simultaneous positions. Which requires software that
can deal with multiple simultaneous systems trading
large baskets of instruments. I don't know whether
the current Tradestation can or can't do this; I'm
using non-TS software at present. Generating orders
for the next bar (I use daily bars myself) is a big
production, since there are times when system B
buys Crude Oil on the same day that system F sells
Crude Oil. Perhaps at the same price (in which case
you can net-out the orders), or perhaps at different
prices. Getting the stops positioned and re-positioned
is a bigger task than some software products can handle.
Another drawback is: it requires a large account. The
average risk I have on any one position in one market
for one system, is around 0.05% of the account. Five
one-hundredths of one percent. If stops were $1500
from entry, (which they're actually not, but it makes
a simple example) then I'd be trading one contract
per 3 million dollars of account equity. (Math:
$1500 / 0.0005 = 3E6)
A third drawback: This approach has always got a lot
of simultaneous (small) positions, so it's always
exposed to price shock risk, "Black Swans" as the
press likes to say, in a lot more ways than other
traders. If there's huge price shock in Crude Palm
Oil, I'll get injured when most other traders won't.
On the other hand, if there's a huge price move in
an obscure market, and I happen to be on the RIGHT
side of it (like the bull move in LME Aluminum Alloy
in February 08), then I catch a windfall that few
other traders do.
I'll wrap up by offering a few points to ponder.
As they say in academic papers, Suggestions For
Further Research.
1. What is an appropriate measure of goodness,
a quantification of desirability, for evaluating
the trading results of a multi-system, multi-market
approach?
2. How would YOU go about testing the hypothesis
that adding more market-systems improves the trading
results? (Or, equivalently, testing the NULL hypothesis
that adding more market-systems makes no difference
at all?)
3. If you absolutely HAD NO CHOICE and knew that
you MUST build a software and hardware and infrastructure
trading room so you could simultaneously trade 8
different systems, each one of them on 100 markets, what
products would you buy and why?
4. Does it give you any additional comfort that
the parameters of your mechanical system are not
"over fitted", when you apply those parameters to
100+ different markets? Does this increase the
ratio of (#trades / (#degrees of freedom consumed))
by a factor of 100, and if so, does it matter?
5. Since this approach trades all markets, it guarantees
you will be trading next year's hottest market, the one
everybody agrees was "best". It also guarantees you
will be trading next year's absolutely worst market.
Is this desirable? Undesirable? Neither?
6. What five-letter word, often used in discussions
of trading methodology, is completely absent from this
posting?
Best wishes to all,
Mark Johnson
(who gets the O-List Digest, the next day)
DANGER! THERE IS RISK OF LOSS IN FUTURES TRADING!!
|