### Proper Asset Allocation Requires Understanding Correlation Coefficients

Correlation coefficients? What on Earth does this have to do with creating a diversified portfolio? If this sounds foreign or complex to you, don’t be alarmed. It isn’t nearly as scary as it sounds. You’re probably picturing high school or college math classes, but correlation coefficient is just a fancy way of saying how close two different types of investments react to each other. And if you want to truly create a diversified portfolio, it helps if you understand how different assets move relative to the performance of others.

Think of it this way. You could create a portfolio that consisted of a few index funds that spanned 2,000 different companies, yet have virtually no diversification. I know that doesn’t make sense to a lot of people since it seems as if you were invested in that many companies, you’re very diversified. But the true goal of asset allocation is to create a portfolio that has investments that are not correlated so that you can minimize risk while maximizing returns. So, let’s see how it works.

## Defining Correlation

Proper asset allocation requires knowing the degree in which different asset classes correlate with one another. The possible correlation values range from -1.00 to 1.00. A value of 1 is perfect correlation, and a value of -1 is negative correlation. For example, if you were comparing two investments, A and B, and they had a correlation of 1, if investment A saw a return of 1%, investment B would realize a 1% return as well. If A and B had a -1 correlation, if investment A had a 1% return, investment B would have a 1% loss.

Of course, in the real world, 1 and -1 correlations almost never exist. But for the sake of comparing asset classes, most people view a correlation value between 0 and 0.5 as a very weak correlation, which is a good starting point for finding diversification. The farther from a +1 correlation two investments are, the more diversification you’ll realize by holding those two investments. A correlation of -0.5 provides more diversification than 0.1, and 0.1 provides more diversification than 0.5.

### Correlation of Returns Among Asset Classes Between 1970-2006

*Source: Jack Wilson and Charles Jones, North Carolina State University*

Looking at this chart, you can get a rough idea of the correlation across different asset classes. Looking at large-cap stocks, you’ll see that it is most closely correlated with mid-cap stocks, and they become less correlated as you work your way down the list. So, by looking at the list, if you had a portfolio consisting of mostly mid-cap stocks, adding some small-cap holdings would provide little diversification since their correlation is nearly 0.9. Even large-cap and mid-cap are fairly correlated with a 0.76, so if you want to really add diversification, you should be looking for asset classes with 0.5 or less. In this case, adding some foreign stock or bonds would provide the greatest diversification.

The same goes for bonds if you’re looking to add some diversification. If you look at the chart, the correlation between government bonds and corporate bonds are nearly 1. So, if you already have a corporate bond position in your portfolio, adding, or changing to a government bond would provide little difference since history shows they move almost exactly the same.

## Why Even Worry About Correlation?

This probably seems like overkill. Who has the time to worry about these silly numbers? Well, I only bring it up because I meet with a lot of people who have spent time constructing what they think is a **good diversified portfolio**, only to find that even though they may have five or six good funds, their overall allocation is hardly as diversified as they thought.

Most of the time, this happens when people build a portfolio centered around large-cap stocks and then add just a little bit of small and mid-cap stocks, and some international to round out the mix. Sure, you may be diversified across every sector in the market and across various market caps, but if your average correlation between everything is generally around 0.8, you’re creating a more complicated portfolio than you need to. There is no need to worry about a handful of funds that are more or less highly correlated if you could achieve the same thing with one or two index funds.

So, this is just another tool at your disposal to help you build the right portfolio. Don’t get too caught up in it. But just because you own a bunch of funds doesn’t automatically make it diversified. You can spot opportunities for true diversification by adding investments that are less correlated, or even reverse correlated to minimize volatility.

### Remember, These Are Long Term Averages

The correlation between asset classes does change depending on recent economic events or global market performance. So, when diversifying based on correlation, make sure you’re applying it to a long-term portfolio since the numbers can fluctuate in the short-term.

#### Author: Jeremy Vohwinkle

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