Correlation has to be the most over-hyped and least understood word in investing. How often have you been told by so-called “investment experts” to buy a product because it has low correlation with stocks? I’ve heard it at least 10,000 times in my career. Most people who say this have no real knowledge of correlation or know to use it to select asset classes. I hope this article sheds some light on the subject.

In Part 1 of the Basics of Asset Allocation, I recommended four gates an asset class must pass to be included in a well-diversified portfolio. Gate 1 determines if an asset class is fundamentally different from other asset classes in a portfolio. Part of this analysis requires a correlation study to test if the asset class has unique risk.

Technically speaking, correlation is a measure of dependency between two variables. It measures the change in one variable relative to the change in another, and it’s doesn’t matter whether the changes are in different amounts or in different directions.

(*Sorry for the jargon. I have to slug through these technical details before getting to the core of the discussion.*)

The correlation range runs from positive 1.0 to negative 1.0. Positive correlation occurs when one variable moves above its moving average while the second also moves above its moving average. When “Investment A” zigs, “Investment B” also zigs. Negative correlation occurs when one variable moves above its moving average while the second moves below its moving average. When “Investment A” zigs, “Investment B” zags. Non-correlation (0.0) is when there is no dependency. Investment A and Investment B go their separate ways.

Figure 2 illustrates that the theoretical risk reduction benefit from holding two asset classes, A and B, assuming four different correlation tendencies between A and B (-0.5, 0.0, +0.5 and +1.0). The vertical axis (Y axis) is the compounded portfolio return and the horizontal axis (X axis) is portfolio risk as measured by the annual standard deviation of return.

Each marker on the correlation lines in Figure 1 signifies a 10 percent change in asset allocation from Asset Class A to Asset Class B. For example, one up from the bottom is 90 percent A and 10 percent B, two up is 80 percent A and 20 percent B, and so on.

**Figure 1: The Efficient Frontier of Two Asset Classes with Different Correlations **

*Source: All About Asset Allocation, 2 ^{nd} Edition, Richard Ferri, McGraw-Hill, 2012*

The portfolio where A and B have negative correlation (0.5) on the far left benefited by having substantially lower annual standard deviation (risk) than the other three portfolios having higher correlations. All things being equal, portfolio risk is lower when A and B have lower correlation. The risk reduction benefit diminishes as correlation becomes more positive, and risk reduction goes away entirely when the correlation reaches +1.0.

The theoretical talk is over. Now we can get back to the real world.

The 62-year correlation between the S&P 500 and 5-year Treasury notes has been +0.08. That’s pretty close to non-correlation.

If you invested in the S&P 500 and 5-year Treasury notes using a fixed asset allocation for 62 years and kept this mix constant by rebalancing diligently each year, your portfolio risk and return line would have been close to the non-correlated model in Figure 1 (the second line from the left). Where your portfolio was on that line depended on your fixed allocation between stocks and bonds, i.e. 40/60, 50/50, 60/40, etc.

Unfortunately, good theory in the long-term doesn’t always work out in the short-term. What happens in the short-term may be opposite what you’re expecting because correlation in the short-term is not a static number.

Correlations are dynamic, not static. They change and change often, and sometimes by large and unpredictable amounts. Consequently, the benefits of low long-term correlation may take decades to materialize.

Figure 2 illustrates how wildly correlations fluctuate in the short-term. It shows the rolling 3-year correlation between the S&P 500 and 5-year Treasury notes from 1950 to 2012. A rolling average is calculated using 36 months of asset class returns that roll data forward over a long period of time.

**Figure 2: Rolling 3-year Correlation between the S&P 500 and 5-Year T-Notes**

*Source: Standard and Poor’s, Federal Reserve interest rate data*

The horizontal line in the center of Figure 2 is a 0.00 correlation, also called non-correlation. This line is close to the average 0.08 long-term correlation that existed between the S&P 500 and 5-year T-Notes from 1950 to 2012.

You can see that over a 3-year period the correlation has rarely been 0.08. It was there only a few times as correlation passed through that number on the way up or down. The range of 3-year correlation has been very wide between -0.6 and +0.6.

Many asset allocation programs require that investors plug in a single correlation number for two asset classes to find the “optimal asset allocation”. If an investor used 0.08 as the correlation between S&P 500 and 5-year T-Notes, the program would generate the wrong solution 99.5 percent of the time.

This brings us to **Lesson 1** concerning correlation:

*The past correlation between two asset classes is period dependent and not a reliable indication of future correlation. Any portfolio decision that relies on a single correlation number that is generated from past data is subject to gross error. *

When someone says that you should buy a specific investment because it has a low correlation with another investment, you should question the wisdom of their recommendation and their knowledge of correlation. Correlations are dynamic, not static. Any investment decision that relies solely on past correlation as a reason for inclusion is prone to fail. * *

Even if by chance the correlations between two asset classes are the same in the future as they were in the past, it doesn’t mean the outcome will be the same. Figure 3 vividly illustrates this point. The 10-year correlation between the S&P 500 and 5-year Treasury notes was +0.24 in the 1970s and +0.24 in the 1980s, but the outcomes were quite different.

**Figure 3: Risk and Return of Two Asset Classes with the Same Correlation over Independent Decades **

*Source: All About Asset Allocation, 2 ^{nd} Edition, Richard Ferri, McGraw-Hill, 2012*

Low correlation between the S&P 500 and 5-year T-notes was little help to a portfolio during the 1970s. A 50 percent stock and 50 percent bond portfolio rebalanced annually returned close to the middle of the asset classes with only a small reduction in portfolio risk from rebalancing. The result was far from the outcome interpolated from Figure 1 for a +0.25 correlation portfolio.

The 1980s were quite different. There were large benefits to diversification. A 50 percent stock and 50 percent bond portfolio rebalance annually returned about 3 percent higher than an all-bond portfolio with practically no increase in risk. The result was much better than the outcome interpolated in Figure 1.

This brings us to **Lesson 2** about correlation:

*Low correlation between two asset classes does not guarantee risk reduction in the short-term. It may take decades for any benefit to become apparent. *

I believe Lessons 1 and 2 created a lot of issues with investors during the financial crisis. They expected their low correlation asset classes to provide protection. It didn’t happen. The reason is two-fold. First, correlations are not static, and second, low correlation itself does not guarantee a portfolio benefit in the short-term.

Now that I’ve shattered these correlation myths, I’ll explain how I use correlation to make asset class decisions.

If an asset class has unique risk, it will exhibit variability in a rolling 3-year correlation analysis similar to Figure 2. This variability in correlation confirms the presence of unique risk. The analysis doesn’t have to show periods when it’s negative. The outcome may always be positive as long as long as it varies by a meaningful amount. It’s the amount of variation the measures the amount of unique risk.

If there is no unique risk between two asset classes, then the rolling 3-year correlation will always be very high, hovering around +0.9 to +1.0 all of the time. For example, an analysis between large-cap U.S. stocks and mid-cap U.S. stocks shows the rolling 3-year correlation is always very high. Consequently, the risks inherent in the two size segments are the same for all practical purposes. You would not get much diversification benefit from dividing large-cap and mid-cap stocks, and it’s the reason I don’t divide them in a portfolio.

One final note − don’t be misled by any sales pitch where a claim is made that an investment has negative correlation with stocks. They don’t exist, and even if they did, you wouldn’t want it in your portfolio because the return would negate any gain from stocks. The best you’re going to find is an asset class similar to Treasury bonds in Figure 2, where correlations vary from positive to negative and are non-correlated in the long-term.

More information is available in All About Asset Allocation.