R-Squared vs. Adjusted R-Squared: An Overview
R-squared and adjusted R-squared enable investors to measure the performance of a mutual fund against that of a benchmark. Investors may also use them to calculate the performance of their portfolio against a given benchmark.
In the world of investing, R-squared is expressed as a percentage between 0 and 100, with 100 signaling perfect correlation and zero no correlation at all. The figure does not indicate how well a particular group of securities is performing. It only measures how closely the returns align with those of the measured benchmark. It is also backward-looking—it is not a predictor of future results.
Adjusted R-squared can provide a more precise view of that correlation by also taking into account how many independent variables are added to a particular model against which the stock index is measured. This is done because such additions of independent variables usually increase the reliability of that model—meaning, for investors, the correlation with the index.
- R-squared and the adjusted R-squared both help investors measure the correlation between a mutual fund or portfolio with a stock index.
- Adjusted R-squared, a modified version of R-squared, adds precision and reliability by considering the impact of additional independent variables that tend to skew the results of R-squared measurements.
An R-squared result of 70 to 100 indicates that a given portfolio closely tracks the stock index in question, while a score between 0 and 40 indicates a very low correlation with the index. Higher R-squared values also indicate the reliability of beta readings. Beta measures the volatility of a security or a portfolio.
While R-squared can return a figure that indicates a level of correlation with an index, it has certain limitations when it comes to measuring the impact of independent variables on the correlation. This is where adjusted R-squared is useful in measuring correlation.
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Adding more independent variables or predictors to a regression model tends to increase the R-squared value, which tempts makers of the model to add even more. This is called overfitting and can return an unwarranted high R-squared value. Adjusted R-squared is used to determine how reliable the correlation is and how much is determined by the addition of independent variables.
In a portfolio model that has more independent variables, adjusted R-squared will help determine how much of the correlation with the index is due to the addition of those variables. The adjusted R-squared compensates for the addition of variables and only increases if the new predictor enhances the model above what would be obtained by probability. Conversely, it will decrease when a predictor improves the model less than what is predicted by chance.