# R-Squared

R-Squared (R²) is one of the statistical tools to measure the risk of a mutual fund. R-squared compares the performance of a mutual fund scheme to a given benchmark index. There are tools like alpha, beta as well, which measure the risk of a mutual fund in other ways.

Read on to learn more about how R-squared works and what it does it tell about a mutual fund.

## What is R-Squared?

R-Squared is an analytical tool for mutual funds. It helps to determine how identical a mutual fund’s performance is to a given benchmark index. Do take note that R-squared does not measure the performance of the fund. R-squared does not tell us if a particular mutual fund is good to invest in or not. It simply compares the performance to a given benchmark’s returns.

## How to Read an R-squared for a Fund?

A higher R-squared value means that the fund has a higher correlation with the benchmark. It means that a more significant part of the mutual fund portfolio is affected by the benchmark. A lower r-squared value means the reverse. It does not mean that a lower R-squared value is bad for a mutual fund. There are different types of mutual funds available. There are some, like index funds, where the objective is to map the benchmark index accurately. Here, R-Squared will be naturally high. R-Squared might be lower for other equity funds where the aim is to beat the benchmark, and the portfolio does not precisely imitate an index’s portfolio.

Therefore, an R-squared number of 100% would mean that the benchmark’s movement entirely explains the performance of the portfolio.

## How does it work

R-squared value ranges from 0 to 100. It reflects how much of a fund’s movements can be explained by changes in its benchmark index.

An R-squared of 100 means that shifts in the index thoroughly explain all actions of a fund. Thus, index funds that invest only in Nifty 50 stocks will have a very high R-squared, maybe even close to 100.

Conversely, if a mutual fund has a low R-squared value, it indicates that changes in its benchmark index do not explain much about the fund’s movements. An R-squared measure of 18, for example, means that changes in its benchmark index can explain only 18% of the fund’s movements.

## How to calculate R squared

R-squared is expressed as a percentage within the 0-100 range.

The value of R-squared is divided into three tiers:

• 1-40%: low correlation to the benchmark
• 40%-70%: average correlation to the benchmark
• 70%-100%: high correlation to the benchmark

## R-squared Formula:

R-squared is a technical tool and the formula for R-squared requires us to consider a few statistical metrics like correlation and standard deviation.

R-squared= Square of correlation

Correlation = Covariance between Benchmark(Index) and Portfolio/ (SD of Portfolio*SD of the benchmark)

SD stands for standard deviation.

## How are R Squared and Beta Related

Before understanding their relation, let’s first understand what is meant by beta. Beta is also a statistical tool that measures risk for a mutual fund scheme. Beta is used to measure a fund’s volatility, the degree to which a fund’s value will go up and down. This volatility or movement in price is compared to the benchmark.

In mutual funds, the starting value for beta is 1. Value 1 means that a particular fund is responding almost similar to the benchmark index’s volatility. This means that the shift in the prices of the fund is sort of equivalent to the benchmark index’s movements. A value above 1 means that the fund’s volatility is higher than the chosen benchmark index, and a value below 1 indicates that the fund is less volatile.

Why is it important to read both of them in unison? Suppose a fund’s beta is extremely high but the R-Squared is low, in some cases, it may not be correct to just read the beta and compare the volatility with the benchmark because the fund has very little correlation with the benchmark.

Used together, R-squared and beta give investors a thorough picture of the performance of asset managers.

## R-Squared and Adjusted R-Squared

Adjusted R-squared is a modified version of R-squared. Therefore both help investors to measure the performance of a mutual fund against a benchmark.

R-squared is a statistical tool so it is used in many other contexts. However, in the investment scenario, R-squared is used to compare a fund or portfolio to a benchmark. It is expressed as a percentage anywhere between 0 to 100. While we have discussed other aspects of Rs-squared, let’s jump straight into adjusted r-squared.

Adjusted r-squared gives a precise view of the above correlation by adding more independent variables to the statistical model. Independent variables help enhance the model. Enhancement of the reliability of the r-squared model in the context of investing means something else. The correlation with the index that has been established by R-squared becomes lightly more reliable with adjusted r-squared.

## To Sum Up: How can an investor use R2

R-Squared of a single fund will not tell investors much about their portfolio. Also, it is a technical and statistical tool so to calculate R-Squared requires some expertise in the domain. For a true comparative analysis, R-Squared will have to be calculated for every fund to see how the entire portfolio is doing. R-squared is beneficial when it is analysed along with beta or alpha. Metrics like R-squared are good enablers and catalysts to an investor’s research but not the sole reference point.

Related Mutual Fund Pages

 SIP Lumpsum AUM Systematic Transfer Plan Exit Load Mutual Fund Units Expense Ratio Childrens Fund NAV Interval Funds Systematic Withdrawal Plan (SWP) Emerging Market Funds Hedge Funds Benchmark

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