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# Correlation Definition and Tutorial

People use the term correlation loosely without fully grasping its context and limitations. For portfolio managers, properly demonstrating this understanding is a path to success.
1. Define - Define the Correlation Coefficient.
2. Context - Use Correlation in a sentence.
3. Video - See the video for visuals.
4. Script - Follow along with the transcript below.
5. Quiz - Test yourself. by Paul Alan Davis, CFA
Updated: February 17, 2021
In investments, negative correlation can be as meaningful as positive correlation. Keep reading to learn why.

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## Understanding Correlation for Investment Modeling

Intermediate

Correlation is a measure of the co-movements between data points. It is used in risk measurement of securities or factors. There is one correlation per pair of assets, not one per asset. It is more interpretable than the related covariance measure because the scale ranges from -1 to +1. To calculate, take the covariance between each pair of assets and divide by the product of the standard deviations.

Synonym: correlation coefficient

For context, recall that in any statistical study involving Finance we're using backward-looking data to make an assertion about what we think will happen in the future. Calculations of correlation come with some level of error, so while it is convenient to latch on to correlations from the past and assume they will occur in the future it is wise to monitor changes in correlation over time and build in some estimation error in the investment decision-making process.

### In a Sentence

Ali:  Doc, why doesn't the Excel function =CORREL() care about variable order?
Doc:  Remember, correlation is not causation, so order doesn't matter.

### Video

This video can be accessed in a new window or App , at our YouTube Channel or from below.

Correlation definition for investment modeling (4:41)

### Video Script

The script includes two sections where we visualize and demonstrate the calculation of correlation.

#### Visualize

We're sitting in Excel, and this is a snippet from our boot camp course.

This is one depiction of correlation, from a scatterplot of returns for one stock, Merck, versus a basket of stocks, the Market, for 60 periods. Think about each dot here as return for the Market on the x-axis and Merck on the y-axis, for each month.

So if stocks exhibit co-movements, as they appear to here, then a pattern will look linear. A random shotgun pattern would have low correlation.

This is an example of positive correlation because a rise in the Market, corresponded with positive movements for Merck. A line sloping to the left demonstrates negative correlation. The calculation helps us understand correlation, so let's head there now.

#### Demonstrate

Let's walk through a calculation for two stocks, Microsoft and eBay.

We have six monthly returns for each stock from April to September 2003. Column F is the return on Microsoft. eBay is in column G. Next we compute the average of each, here 2.38% and 3.98%. Then move those over to columns H and I.

In column J, take the return minus the average which gives us 3.24%. That's 5.62% minus 2.38%. For eBay it is 8.91% minus 3.98% or 4.93%. Carry that formula down, and let's call these demeaned returns.

Next, in column L, multiply these together. As you notice, when the stocks moved together, like in April, the product is positive. And when they moved in opposite directions, the product is negative.

Next, using the `=SUM()` function, add up the products to get -0.0037 for the pair of stocks. Next, divide by 6 observations for a covariance of -0.0006. This isn't interpretable as the units are in returns-squared, so we translate it to correlation by dividing by the product of the two standard deviations.

So to interpret, these two stocks had negative correlation, meaning as one moved up, the other moved down. These would be examples of diversifying stocks. And the reading of 0.45 means that the points are fairly tight around the line of best fit.

### Quiz

In the social sciences, like economics, correlations above 0.70, and below -0.70, are considered high. | True or False?

True

On an XY Scatterplot, decreases in the X-variable which correspond to increases in the Y-variable will have a negative correlation. | True or False?

True

Still unclear on correlation? Leave a question in the comments section on YouTube or check out the Quant 101 Series, specifically Four Essential Stock Risk Measures and How to Interpret Correlation and R-squared.

### Related Terms

Our trained humans found other terms in the category statistics basics.

## What's Next?

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• To see all terms in the Glossary, click Outline.
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• Fight big greedy and creepy tech companies, click Tip.
• To see how the correlation for many stocks is interpreted using a Correlation Matrix, click Next.

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