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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.
Ali: Doc, why doesn't the Excel function
=CORREL() care about variable order?
Doc: Remember, correlation is not
causation, so order doesn't matter.
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Correlation definition for investment modeling (4:41)
The script includes two sections where we visualize and demonstrate the calculation of correlation.
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.
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.
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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.
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