How This Simple Math Can Improve Your Trading Results

We all don’t have Donald Trump money, which
brings most of us to a serious issue: unless you are fortunate to have an
infinite supply of capital, you must choose a grouping of markets to track and
trade. You can’t trade everything, but sure as heck don’t want to only be stuck
trading one market. What should you do?

Even more importantly, once you are to the point
of honestly dealing with the idea of selecting a portfolio, are you dealing with
the number-one issue in portfolio construction: correlation.

Don’t let your eyes glaze over. Correlation might
sound like the college class you long since purged from your memory banks, but
for portfolio purposes, it’s easy.

“Just what is correlation, and how do we
derive the correlation coefficient? Correlation is a statistical term giving the
strength of linear relationship between two random variables. More simply
defined, it is the historical tendency of one thing to move in tandem with
another. The correlation coefficient can be a number from -1 to +1, with -1
being the perfectly opposite behavior of two investments (e.g., up 5% every time
the other is down 5%), and +1 reflecting identical investment results (up or
down the same amount each period). The further away from +1 you get (and thus
closer to -1), the better a diversifier one investment is for the other. The
most simplistic description of correlation is the tendency for one investment to
zig while others are zagging.”

If you don’t wrap your arms around the concept of
correlation in your portfolio, you are in trouble. Why? Simple example. You have
Dell and Apple in your portfolio and for the sake of argument let’s assume they
both go up and down together like clockwork. Now let’s say your trading strategy
dictates that you only trade 2% of your portfolio in Apple. If you are also
trading 2% of your portfolio in Dell, and these 2 stocks have very high
correlation, you are essentially trading double the amount of Apple than you
were supposed to be. That’s taking twice the risk that you wanted to take.

What’s the optimal number of markets in a
portfolio for diversification?

Adequate diversification can be found typically
in 10-30 markets. Amazingly, only 10% of investors have that level of

But keep in mind, that diversification needs to
take into account correlation. A so-called diversified portfolio filled with
stocks or futures where all markets are nearly 100% correlated does not pass the
smell test of proper diversification.

Let’s take an example. Assume your portfolio is
comprised of:

Five Year Notes (CBOT)

Corn (CBOT)

Wheat (CBOT)

EuroDollars (CME)

Japanese Yen (CME)

Australian Dollar (CME)

To some, this would seem like a well-diversified
portfolio. The grains, financials and currencies are all represented. However,
closer inspection shows that the portfolio consists of a double exposure in each
of the sectors. A drawdown in any one sector will, in effect, be felt twice as
hard. You can easily see that portfolio exposure will be increased – not a good

Positive Correlation

A positive correlation means that two markets
will move in tandem with each other. An up-move in one market will occur with an
up-move in another market. For instance, a move higher in the S&P 500 Index
would most likely correspond to an upward movement in the Dow Jones Industrial
Index. We all know this intuitively, but correlation takes hunches and reduces
it to objective numbers, easily analyzed.

Negative Correlation

On the other hand, a negative correlation means
that two markets will move in opposite directions. A move higher in one market
would occur when another market moves lower. For instance, a move up in the Euro
Currency (CME) would correspond with a move lower in the Dollar Index (NYBOT).
Remembering the sample portfolio, we can assume that the Five Year Notes and
Eurodollars will move in a very similar fashion. If Five Year Notes are up, then
you would expect the Euro dollars to be up as well. Why would you have a
portfolio of six markets consist of both issues? You should not. The risk
dollars in your account would be better suited in another complex or market.
Perhaps the risk would be better utilized in the energies or softs.

Stock Symbol Guide:

BAC – Bank of America

BA – Boeing

KO – Coca Cola

DELL – Dell Computers

F – Ford

GM – General Motors

HAL – Halliburton

HLT – Hilton Hotels

IP – International Paper

$SPX – S&P 500 Cash

WMT – Wal Mart

Futures Symbol Guide:

AD – Australian Dollar (Chicago Mercantile Exchange)

C – Corn (Chicago Board of Trade)

ED – Eurodollar (Chicago Mercantile Exchange)

FV – Five Year Notes (Chicago Board of Trade)

GC – Gold (New York Board of Trade)

LH – Lean Hogs (Chicago Mercantile Exchange)

JY – Japanese Yen (Chicago Mercantile Exchange)

O – Oats (Chicago Board of Trade)

SP – S&P 500 (Chicago Mercantile Exchange)

US – Thirty Year Treasury Bongs (Chicago Board of Trade)

W – Wheat (Chicago Board of Trade)

When selecting a portfolio using correlation as a
‘test’ it is best to find the issues with correlations closest to zero. For
instance you might avoid a portfolio combination of Dell and the S&P 500 because
they correlate at 0.82. A portfolio of Halliburton and International Paper would
be the least correlated because their correlation coefficient is 0.01. See the


Ed Seykota, the famed trend follower, was
recently asked this question at his site:

“When you select what looks like a “promising”
stock, do you keep pulling the trigger after being stopped out or do you move on
to other markets if the first attempt fails? The reason I am asking is because I
noticed many stocks will break out with strength only to fall back, hit my stop,
linger a couple months or so and then really take off.”

Ed responded:

“A promise is a statement that you will do
something in the (non-existing) future. As such, all promises have an inherent
design flaw. I don’t know of any stocks that make promises. I merely know stocks
that meet various mathematical criteria in the now. You might consider having a
look at what you mean by a “promising” stock.”

Many miss that message. They don’t reduce their
hunches to numbers. One reader argued:

“Recently it appears that all markets in all
countries are well correlated. Thus in the current environment, position sizing
doesn’t manage risk very much. For example, if all your appreciating positions
decline as simultaneously and deeply as they appreciated. Look at metals, for
example. Why bother diversifying among the commodities and producers with
position sizing? The same result would have been obtained by simply exclusively
buying any one of gold, copper, or zinc alone. In the end they all sold off more
or less at the same time and by roughly as they appreciated.”

Selecting a portfolio to track and trade is not
just guessing. Correlation must be considered in precise mathematical terms and
even then it is not a perfect diversity measurement 100% of the time. Sometimes,
in the short-term, everything can quickly move together. That said, considering
correlation is the best we have. We can’t ignore it. The great traders certainly
don’t. A great example of that? In June, I was in Chicago for the Managed Funds
Association’s Forum 2006. The lunch keynote was delivered by Elizabeth Cheval,
Chairman, EMC Capital Management, Inc. (she
was a Turtle
). Her whole presentation centered on correlation. If the
traders with twenty-year track records fixate on correlation like there is no
tomorrow, why are the rest of us not following their lead? The next time you get
that twinge right above your belt line, when your so-called diversified
portfolio seems to be acting as “one”, ask yourself one question, “Have I
considered the correlations?”



Michael W. Covel
is the founder and
President of Trend
. A researcher of the most successful Trend Following investment
managers, he has been in the alternative investments industry consulting on
Trend Following to individual traders, hedge funds and banks for ten years. His
best selling book,

Trend Following: How Great Traders Make Millions in Up or Down Markets, New
Expanded Edition
(Prentice Hall, November 2005) is a complete and concise
guide to trend following.

Mr. Covel is also Managing Editor at, the
leading Trend Following news and commentary resource since 1996. Thousands of
visitors from more than 70 countries as well as hundreds of trading
professionals engaged in years of debate and interchange making the site the
rich archive of trading information, data and opinion that it continues to be
today. TurtleTrader, one of the largest & strongest trading community on the web
with over 7.5 million unique visitors since its inception, also functions as a
resource center for the Trend Following Educational Course.

Justin Vandergrift is with Chadwick
Investments. He can be reached at