Dr. P.V. Viswanath

pviswanath@pace.edu

Why the Math of Correlation Matters: These measurements can aid in the hunt for assets that zig when others zag, thereby reducing portfolio volatility

Many mutual-fund investors strive for diversified portfolios, but few fully grasp a concept that is key to achieving that aim: correlation.

Correlation is the extent to which assets perform in relation to one another. For instance, it's widely considered good practice to reduce volatility in your portfolio by investing in a variety of assets whose values rise and fall independently of one another.

If your investments move in lock step, or are highly correlated, "you'll either be all right or all wrong," says Linda A. Duessel, equity market strategist at Federated Investors Inc.

Financial advisers say they love to analyze correlation but rarely discuss it in depth with clients. At a time when many assets are experiencing unusually high correlation—a trend that has pummeled some portfolios—it's a topic worth grasping.

"It has become more important over the years, because the world is more interconnected, for people to understand on a macro level how things relate to each other," says Cassandra Toroian, president and chief investment officer of Bell Rock Capital LLC, an investment firm based in Rehoboth Beach, Del. "People look to use these kinds of theories because they're trying to smooth out the volatility in their investments."

Here is what you should know about correlation:

How is correlation measured?

Correlation is determined by comparing the returns or general movements of two assets or products. Using what's called a regression analysis, an adviser produces a number, from 1 to negative 1, that displays how likely one asset is to move similarly to another.

A correlation close to zero means the performance of one asset has little or no connection to that of the other. A correlation of 1 is a perfect positive correlation, meaning the two assets always move in sync—in the same direction, and at a scale that doesn't vary. For instance, Asset A will always move at twice the magnitude of Asset B. A correlation of minus 1 is a perfect negative correlation. The assets move in opposite directions at a scale that doesn't vary.

What time periods are used in the calculation?

It's common for analysts to compare the monthly returns of different assets over years, but the figure can also be calculated using daily or weekly returns.

But keep in mind that correlation is a fluid measure. While some assets or securities exhibit general trends of correlation over time, the exact measure often changes depending on the period. For example, a Morningstar Inc. analysis shows the correlation between intermediate U.S. bonds and the Standard & Poor's 500-stock index has historically been low—a mere 0.08 if you look over a period of more than 80 years. But that changes to minus 0.39 if you only look at the past 10 years, showing an increased tendency to move in opposite directions. The change reflects how often investors have sought the safety of bonds when stocks have fallen, and then sold the bonds when stocks looked more favorable again.

Another thing to be wary of: Correlation often surges in a crisis. In the 2008 crash, for instance, many assets across all classes exhibited unusual correlation when they headed down.

Do I want assets that are negatively correlated or uncorrelated?

A key aim of asset allocation is to invest across a range of sectors, countries and asset classes that earn decent returns but are relatively uncorrelated. That way, if one asset in a portfolio suffers, the rest might be unaffected. For example, Treasury inflation-protected securities, or TIPS, usually move unrelated to the performance of the S&P 500.

Sometimes, investors will choose assets that are negatively correlated in order to hedge risk. If you don't want to sell your U.S.-stock funds but want to temporarily cut your stock risk, you might invest in an inverse fund designed to perform well when a stock index does poorly.

Such strategies are only recommended in the short term because they essentially cancel out returns. Holding too many negatively correlated assets can be a little like trying to hit the gas while slamming on the brakes, says Jonathan Satovsky, chief executive officer of Satovsky Asset Management LLC, a wealth-management firm in New York.

So what assets have low correlations?

The core of many portfolios is exposure to large U.S. stocks and intermediate-term bonds. Over the past 10 years, the S&P 500 and the Barclays Capital U.S. Aggregate Bond Index have shown a minus 0.07 correlation. (The correlation is a positive 0.25 if you look back 35 years, but that is still a weak relationship.)

Even weaker is the connection between Treasury bills and the S&P 500, minus 0.05 over the past decade.

Where can I find information on correlation?

Most online correlation calculators are available only for financial advisers. So, one option is to ask your financial planner.

Tools for individuals include assetcorrelation.com, which finds correlations between assets and between asset classes.

R-squared, a measure found on Morningstar.com, shows strength of correlations between funds and benchmark indexes, but not directions of movement. The scale ranges from 0 to 100.

Ms. Marte is a staff reporter for The Wall Street Journal in New York. She can be reached at jonnelle.marte@wsj.com.

Questions (courtesy of The Wall Street Journal Finance Weekly Review):

1. What is correlation?
2. What data would you need to calculate the correlation between the returns on two assets? How would you use this data to calculate the correlation between the returns on the two assets?
3. How is correlation related to diversification?
4. Why do the correlations between the returns on assets change over time?
5. How is correlation related to the expected return on a portfolio?