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." (1)

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 diversification.

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 thing.

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 logic?

Conclusion

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?"

Footnotes:
(1) JWH.com.

Michael W. Covel is the founder and President of Trend Following. 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 TurtleTrader.com, 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 www.chdwk.com