Understanding Correlation And Covariance. And What It Means For Your Portfolio.

Jan. 27, 2012 11:53 AM ET
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How to Use Correlation and Covariance

Correlation and covariance are two of those financial terms that can cause the palms to start sweating or call up unpleasant memories of the SAT verbal section. In reality, it isn't that hard to achieve a good working knowledge of these terms and why they are important measures, used in valuing funds and other investments.

Explaining Correlation

Let's start with correlation. In plain English, this is just a mathematical measure of how closely related the price performance of an asset is relative to a market benchmark. Typically, we will use a benchmark that acts as a "universe" from which the holdings in a fund are selected. For example, the S&P 500 for general equity funds, or the Russell 2000 Value index for a small cap value fund. Why do we care about the correlation? There are a couple reasons. First, if we are selecting assets for a specific allocation segment in our portfolio, then it is important to know that the fund we select actually fits in that asset class. For example, if we invest in a small cap value fund, we want that fund to be reasonably correlated with the small cap value universe, as measured by the Russell 2000 value. If the correlation level is low, that could be a sign that the fund manager is not sticking to the fund's advertised discipline - which could be an important warning sign.

On the other hand, sometimes we measure correlation because we want to see a low value. This is particularly true when we are diversifying among different asset classes. We may want to include a frontier markets fund that invests in Gulf States/North African holdings, specifically because it has alow level of correlation with the S&P 500. We diversify in order to reduce the risk that if something causes the S&P 500 to plunge, it will drag all our other assets down with it. Low correlation, in this sense, is a value contributor to multi-asset class portfolios.

How do we measure correlation? You may see this presented in fund literature as "correlation coefficient" or as "R-squared". Don't be put off - these are technically different computations, but for all practical purposes, they serve the same purpose. They will always contain a value between -1 and +1. A correlation coefficient or R-squared of +1 is a predictor of perfect correlation. A value of -1 equals perfectly negative correlation - meaning, if the S&P 500 went up by 5%, your asset would go down by 5%. A value of zero indicates no explanatory relationship - you could not infer anything about your fund's performance from the price movement of the benchmark.

Let's relate those numbers to the examples we provided above. If you are looking to assess the fidelity of a small cap value fund to its asset class, then you would want to see an R-squared or correlation coefficient of 0.7 or more between your fund and the Russell 2000 Value. On the other hand, if you want your Gulf States/North Africa frontier fund to have a low correlation with the S&P 500, then a correlation of less than 0.5 would be desirable.

Explaining Covariance

Having gone through that fairly detailed explanation of correlation, it will be much quicker and easier to get through covariance. The two measures are very closely related - in fact, mathematically, they are really just two different calculations around the same thing - how similar the characteristics are between an asset and its benchmark. The most common measure of covariance we encounter in the market is beta, represented by the Greek symbol β. Beta is a measure of relative volatility. And it is always expressed in relation to 1.0. In other words, we define the beta of the benchmark as 1.0. The asset being measured is either greater than, less than, or equal to 1. If your fund has a beta of 1.5, for every 1% price movement of the benchmark, your fund is expected to move 1.5% in the same direction In other words, your fund is more volatile, or riskier than the benchmark. A beta of 0.5 means that your fund is less risky, as its price variations will only be half those of the benchmark.

Here is an important point to remember: a relative measurement, like beta, is only statistically significant (i.e. valid) when the correlation coefficient is sufficiently strong. What that means is this: if your fund has an R-squared of 0.3 with the S&P 500, you would be advised to ignore whatever value is being given for beta, as it is not meaningful. In this case, an absolute measure, like standard deviation, would be the more appropriate way to evaluate risk. You generally want to see an R-squared of at least 0.65 before you feel comfortable that it is sufficiently valid for purpose of analysis.

Seeking Alpha

There is one more performance measure that is closely related to correlation and covariance - and that is called alpha. Alpha, which is regarded as a measure of outperformance relative to a benchmark, will be the subject of a future post.

Tell us…What risk and correlation measures are you most familiar with?

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Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

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