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What is R Squared?
R-Squared measures the extent of variation in the dependent variable due to the independent variable. In other words, it tells how much a variable’s performance can be due to the behaviour of another variable.
The value varies between zero to one and, as a percentage, ranges from zero to 100%. If the value is close to one or 100%, then the dependent variable’s performance is highly affected by the independent variable. In contrast, if the value is low (close to 0), then the behaviour of the dependent variable is not explained by the independent variable.
It is also known as the coefficient of determination. It is a popular metric for proving a hypothesis or predicting outcomes. Technical analysts and investors use this to predict the share price of a stock based on several factors, such as benchmark performance or the company’s financial performance.
For example, the R-Squared of a share and the market index Nifty 50 tells by what proportion the variation in share price is based on the movement in the index.
Mutual fund investors use this to determine the extent to which the benchmark index is responsible for the change in the fund’s returns.
How to Calculate R Squared?
One can calculate by subtracting the ratio of unexplained variation and total variation from one. In other words, the unexplained variation is the sum of squared regression, and the total variation is the total sum of squares.
Formula
R2 = 1 – (Sum of Squared Regressions) / (Total Sum of Squares)
The calculation is a time taking process. Hence analysts usually use Microsoft Excel to estimate the R-Squared for two data sets. The function for R-Squared in Excel is RSQ.
The formula in Excel
RSQ ([Data set 1],[Data set 2])
How to Interpret R Squared?
It varies between 0-1 or 0%-100%. A 0 or 0%. R-Square indicates that one variable’s performance is not caused by the other variable. In contrast, a 1 or 100% R-Squared indicates that one variable’s performance is completely due to the performance of the other variable.
Let’s understand this with an example if the R-Squared of a mutual fund and benchmark is 60%. Here the fund is the dependent variable, and the index or benchmark is the independent variable. The investor is using this metric to measure the variation in the fund’s return due to changes in the benchmark. A 60% value indicates the benchmark is responsible only for 60% of changes in the fund’s net asset value or NAV. A 100% value would mean the benchmark is fully responsible for the change in the fund’s return.
Use of R-Squared in Mutual Fund Investments
It tells what proportion of a mutual fund’s movements is explained by the changes in the benchmark. A high value indicates the fund and benchmark are closely related. On the other hand, a low value would mean the fund’s performance is very different from its benchmark.
Index funds and Exchange Traded Funds (ETF) track the index and mimic the portfolio. Hence, they tend to have a value closer to 1 or 100%. Whereas actively managed funds may or may not have a 100% value.
Explore Exchange Traded Funds (ETF).
Limitations of R Squared
It has a few drawbacks. The calculations are on the basis of historical data, and the predictions may not be accurate. Moreover, the R-Square of one investment doesn’t tell how it will behave against other similar investments.
It will also not tell whether the data and predictions are biased. Hence a high or a low value doesn’t necessarily mean it’s good or bad. This is because it doesn’t convey whether the model is reliable or whether the chosen variables are right or wrong.
Therefore, one should never use this value in isolation. It is better to use other statistical measures to test a hypothesis or to predict outcomes.
R-Squared vs Adjusted R-Squared
R-Squared measures the extent to which the performance of a dependent variable is due to the independent variables. However, it doesn’t tell the impact of each independent variable on the correlation of variables. It can increase and change by adding more independent variables. This is where adjusted R-Squared comes into the picture. Adjusted R-Squared tells how reliable the correlation of dependent and independent variables is and the impact of the correlation due to adding a variable.
The primary difference between the two is that the adjusted R-Squared considers the effect of each of the independent variables against the dependent variable, and R-Squared doesn’t. If the new variable’s effect is more, the value of the adjusted R-Squared will increase, and vice versa. However, the R-Squared value will increase if the model adds new independent variables.
While investing the R-square value helps to measure the extent to which the change in the benchmark affects the fund’s returns. However, beta measures how large the change in the fund returns with respect to its benchmark.
R-Squared helps in testing the trustworthiness of the beta of financial securities such as shares and mutual funds. If the R-Square is high and the beta is also high, then the fund has a high chance of giving better returns than the benchmark in a bull market. Alternatively, the data can be deceptive if the R-Squared is low and the beta is high. In such cases, a high beta might not give high returns in a bull market.
Learn Beta in Mutual Funds.
Frequently Asked Questions
R-Squared values are not considered good or bad. This is because it doesn’t convey whether the model is reliable or not or whether the variables under consideration are right or wrong. It simply tells to what extent the changes in the dependent variable are due to the changes in the independent variable.
R-Square values are different for different fields of study. For investing, a high value would mean a greater correlation between the security price and the benchmark. But it doesn’t necessarily mean a high value is better. Biased data can also give a high value, which is not accurate. This value is simply used to make an investing decision.
An R-Squared value of 0.5 would mean that the independent variable explains only 50% of the variability in the data. The model cannot explain the rest 50% of the variability.
If the R2 of an investing model is low, then it would mean there is a very low correlation between the price of the security and the benchmark.
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