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Editor's note: This article is a correction of Richard Shaw's previous article: Correlation Diversification Reduces Portfolio Risk

Sun Tzu wrote in the “Art of War” that every battle is won or lost before it starts.

That declaration is based, in part, on the fact that the strategy set out before the battle critically impacts the outcome. Similarly, the strategy you set out for design of your portfolio will critically impact whether you win or lose in the investment battle. That brings us to the topic of correlation of returns.

Among other things, portfolios need to be diversified as to correlation of the securities they hold in order to obtain the highest available return for the level of risk taken. Here are the correlations of key ETFs that you may be using in constructing your portfolio.

Conventionally, correlations are expressed versus the S&P 500 (large-cap and mega-cap stocks), but we feel that puts tradition ahead of logic. The Russell 3000 represents virtually the entire U.S. stock market which we feel is a better comparator for planning correlation diversification.

36 month corellation chart

Correlation is a statistical measure of how two securities move in relation to each other. Correlation is expressed by numbers ranging from -1 to +1. Perfect negative correlation means the two securities move lockstep in opposite directions. Perfect positive correlation means the two securities move lockstep in the same direction. Zero correlation means the two securities move randomly with respect to each other.

You can see from this chart that the developed non-US countries (NYSEARCA:EFA) offer some correlation diversification as do the emerging markets (NYSEARCA:EEM).

The various Russell indexes of market-cap and growth or value style don’t offer much correlation diversification.

The Dow Jones sector indexes offer varying degrees of correlation diversification, particularly those under +0.7 and even more particularly those under +0.50 [Energy (NYSEARCA:IYE), Healthcare (NYSEARCA:IYH), and Utilities (NYSEARCA:IDU). The REIT sector (NYSEARCA:ICF) also offers decent correlation diversification.

It is important to understand what is being correlated. In portfolio management applications, it is standard to correlate total returns, the percentage change in price (including the effect of splits, dividends and interest), between assets or between assets and indices. The chart above shows correlation of monthly total returns, not just correlation of price changes.

Beware the Black Box:
We made a mistake in our previous article on correlation that this article is meant to correct.

The correlation data we used then came from the State Street Global Advisors Correlation Tracker tool (provided to them by SmartMoney) --- the same correlation tool that is also on the Select SPDRs website.

We assumed that the tool correlated total returns for securities, but it does not. It correlates only prices for securities and that is something else altogether. We should have examined the tool more closely before using it.

Price correlation has other uses in short-term trading systems, but it does not suit our purposes in selecting asset categories for a portfolio. Portfolio and asset allocation theory deals with correlations of total return not just correlations of prices.

We would like to thank Geoff Considine for his Quantext planning tool, Quantext Portfolio Planner, which helped us discover our error. Shortly after publishing our prior article, we purchased Geoff’s tool and the differences between its results and those from the State Street site alerted us that something wasn’t as we thought it was. We contacted Geoff and he was quite patient and helpful in answering our questions.

Some Theoretical Background to Correlation of Returns
Correlating total returns rather than price is fundamental, because we do not experience only price. We also experience income in the form of dividends or interest. Income from a portfolio investment asset is just as much a part of its performance as changes in its price.

Diversification is supposed to help us get to a portfolio in which the total return on one asset is NOT well correlated with the total returns on others, so they all don’t move together in the same direction to the same degree at the same time.

Correlation of price may have some potential application in some short-term trading strategies, but it does not have application in portfolio design and management.

For those of you who wish to dig deeper into the topic, here are two useful articles:

Vanguard Institutional - “Portfolio Rebalancing in Theory and Practice”
P. Peterson PhD, CFA – “Portfolio Risk and Return” (math oriented)

How We Calculated Correlations for This Article
Just to be certain that we got it right this time, we calculated all of the numbers in this report the “old fashioned way”. Here’s how we derived the correlations:

1. Create a master Excel [XLS] file with a separate worksheet for each security we intended to analyze,

2. Download month-end adjusted closing prices for 36 months ending Dec. 31, 2006 (adjusted for splits and income) from Yahoo.com in a CSV format file for each security,

3. Copy the contents of each downloaded CSV file and pasted it in its reserved worksheet in the master Excel file,

4. Calculate the change from month-to-month of the adjusted closing price of each security to get its monthly returns,

5. Use the built in Excel correlation function to calculate the correlations [+CORREL(array1,array2)]. “Array2” refers to our base security ((NYSEARCA:IWV) in this case) and “array1” refers to the security for which the correlation is sought.

The term “array” is a fancy math term, but in this case it simply refers to the list of returns for a security. Excel correlates the returns of one security to the other (array1 to array2).

You Can Do-It-Yourself
We give you this detailed description in case you would like to create some correlations on your own with securities not listed in this article. You can do it for any security with enough months of history. A 36-month history is a good range to select.

Using a pre-built tool is much easier than “hand work” like that described above, but if you are not careful to fully understand how it works, as we were not with the StateStreet/SmartMoney tool, you might not get what you assumed you would be getting.

Our advice is to do it yourself, or fully investigate the Black Box before relying upon it. Make sure that it does what you think it does before you use it. This applies not just in this instance, but in any instance where an opaque Black Box tool cranks out numbers.

Data Table
Here is the table of data that goes with the chart above. All data are for total returns for the 36-month period ending Dec. 31, 2006.



Note About Price Correlation for Short-Term Trading

We aren’t short-term traders and do not use price correlation in our work, but it might be useful to pass along a few notes about the use of price correlation in financial markets. This is no more than something we gleaned from a little web searching. Don’t take any action based on this section, but look into it further for yourself if trading is your interest.

Price correlation is used by some, particularly institutions, to take profits without taking significant market directional risks, sometimes by trading pairs of securities with very high price movement correlation.

The trader finds temporarily “misvalued” securities and takes a position that would produce a profit if the misvaluation is “corrected” by the market.

The techniques involved depend very heavily on market prices returning to historical or predicted normal relationships (which, of course, is not guaranteed to happen). That’s were price movement correlation comes into play.

The time interval for mining opportunities may be short and execution slippage and trading costs may eliminate opportunity or create losses.

Key word terms such as “Correlation Convergence”, “Statistical Arbitrage” and “Relative Value Arbitrage” will help you research price correlation uses on the internet.

Because we are not expert in any aspect of short-term trading or the use of price correlation for trading purposes, we will follow the advice of Will Rogers who said, “Never miss a good chance to shut up.”

Disclosure: Author is long ICF