What Is R-Squared?
In the financial world, R-squared is a statistical measure that represents the percentage of a fund's or a security's movements that can be explained by movements in a benchmark index. Where correlation explains the strength of the relationship between an independent and dependent variable, R-squared explains to what extent the variance of one variable explains the variance of the second variable. The formula for R-squared is simply correlation squared.
Common Mistakes with R-Squared
The first most common mistake is assuming an R-squared approaching +/- 1 is statistically significant. A reading approaching +/- 1 definitely increases the chances of actual statistical significance, but without further testing, it's impossible to know based on the result alone. The statistical testing is not at all straightforward; it can get complicated for a number of reasons. To touch on this briefly, a critical assumption of correlation (and thus R-squared) is that the variables are independent and that the relationship between them is linear. In theory, you would test these claims to determine if a correlation calculation is appropriate.
The second most common mistake is forgetting to normalize the data into a common unit. If you are calculating a correlation (or R-squared) on two betas, then the units are already normalized: The unit is beta. However, if you want to correlate stocks, it's critical you normalize them into percent return, and not share price changes. This happens all too frequently, even among investment professionals.
For stock price correlation (or R-squared), you are essentially asking two questions: What is the return over a certain number of periods, and how does that variance relate to another securities variance over the same period? Two securities might have a high correlation (or R-squared) if the return is daily percent changes over the past 52 weeks, but a low correlation if the return is monthly changes over the past 52 weeks. Which one is "better"? There really is no perfect answer, and it depends on the purpose of the test.
How to Calculate R-Squared in Excel
There are several methods for calculating R-squared in Excel.
The simplest way is to get two data sets and use the built-in R-squared formula. The other alternative is to find a correlation and then square it. Both are shown below: