Finance: Correlation Coefficient
The correlation coefficient quickly becomes your best friend when it comes to comparative quantitative analysis. This number gives you a numerical relationship between two variables. While the application of correlation coefficients is essentially infinite, I like to apply this tool to the financial markets.
To get started, you will want to compile a data set in a spreadsheet. For this example, this data we will be using is quarter-over-quarter percent change in GDP and the Unemployment Rate divided by 100 – both ranging from the second quarter of 2000 (00Q2 through 09Q1).
Why do I use different forms of the data? Because the percent change in unemployment is too high relative to the percent change in GDP and I am trying to create a visual that is easily interpreted. By keeping unemployment positive, and letting GDP fluctuate both positive and negative, we can better see the inverse relationship between the two. Unfortunately, our current situation has unemployment close to 10%, which is still high to view against GDP. Such are the times. Manipulating the data this way does not affect the result correlation coefficient by much (.01).
Now you want to select the cell you wish to view your result in, then type “correl(select the first data set, select the second data set)” and hit the return key. Great! You’ve just done your first correlation coefficient formula in Excel. Thank god for computers! The real formula looks something like this:
What do your results mean? The result will range from -1 to 1. A coefficient of -1 means there is a perfect negative correlation, 0 means there is no correlation, and +1 means there is a perfect positive correlation. If you used the same data as I did, you should get a correlation coefficient of -.51, meaning that there is a fairly significant negative correlation between GDP and Unemployment. If you want, you can also create a scatter plot graph for a visual representation of the data sets. Here is what the graph looks like:
A more advanced way to interpret the correlation coefficient is to square it. Statisticians will call this number the coefficient of determination and scientists will call it r squared. Either way, it’s the same thing. To get r squared, you simply multiply the correlation coefficient by itself. In this example, r^2=0.34, meaning 34% of the variance in GDP can be explained by variation in Unemployment. Conversely, 34% of the variance in Unemployment can be explained by the variation in GDP.
If you wanted to apply this to stocks, you would first need to get a table of historical stock prices for, let’s say, the past 90 days. The further back you can go, the more reliable your results will be. There are also websites that offer this service, with much less effort. However, you will need to do this on your own if you are comparing data sets that other people haven’t thought of or won’t freely give you the results of. If you find a strong correlation between disparate variables in the stock market (either negative or positive), you may be well on your way to riches.
A good stock movie, that also has a scene about correlation is Trader: The Documentary. Trader is about Paul Tudor’s hedge fund in the 1980′s, it’s almost comical with the advances we have in technology now. Definitely a solid watch if you are interested in seeing the stock markets from the view point of a pro, and you can see it online for free here.
There are many more applications for the correlation coefficient, especially as it pertains to finance, but for now you should practice using it in easy examples such as the one outlined above. This will give you a different viewpoint to see how different variables in the economy affect one another.
For much more detailed information about correlation coefficients click here.
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