What does R-Squared reveal?

May 29, 2012
In Part 3 of our series on modern portfolio theory, we discuss how R-squared can determine the usefulness of other MPT statistics.

In a recent article, we went over how beta and other modern portfolio theory statistics can be a helpful way to assess an investment's risk/return characteristics.

 A fund's beta gauges an investment's sensitivity to movements in a market index. When a market index is up on a given day, for example, the beta looks at whether the fund has a tendency to gain more or less than that benchmark.

But MPT statistics like beta also have limitations, particularly that they're relative measures. That means their validity depends on whatever benchmark an investment is being measured against and the degree of correlation between that investment.

If a fund has a very high beta but a limited correlation with the index on which that beta statistic depends, investors should discount that data point accordingly.

To help demonstrate the extent to which a fund's performance tracks that of a benchmark, Morningstar provides a statistic called R-squared.

How it works

The R-squared figure demonstrates how much of a fund's movements can be explained by the movements in its benchmark index.

The higher the R-squared figure, the more closely the fund's performance can be explained by its index, whereas a fund with a lower R-squared doesn't behave much like its index. And the higher the R-squared, the more relevant the beta figure.

R-squareds can range from zero, meaning there's no degree of performance correlation between a market benchmark and a given investment, to 100, meaning that an investment is highly correlated with an index.

Not surprisingly, index-tracking funds will have an R-squared figure of exactly 100 or very close to it, while a fund whose movements diverge widely from its index will have a very low R-squared figure.

For example, Religare Agile has a three-year R-squared of just 61.97 with its index, indicating a very low correlation with that index. That means that investors shouldn't place too much weight on the fund's MPT statistics, including alpha and beta, relative to that benchmark.

How to (and not to) use the R-squared

Investors should note R-squared has its limitations. As with beta, R-squared is based on historical returns, so its predictive ability is far from guaranteed. In addition, the R-squared of a single fund won't tell you how the fund behaves relative to other funds in your portfolio.

With that said, an appropriate R-squared validates more than just the beta statistic. Next week, we'll discuss the importance of both R-squared and beta in determining the usefulness of a fund's alpha, which measures how successful a fund has been at generating outperformance relative to the risks it has taken. We'll also delve into how investors can use that piece of the MPT puzzle to paint a more complete picture of a fund's risk/reward profile.

Other articles in this series

Investment Ratios

Modern Portfolio Theory

The article first appeared on Morningstar.com, our sister US site and has been formatted for India.

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AshaKanta Sharma
Jun 17 2018 06:42 AM
Very Well Explained.....
Jun 4 2012 10:15 AM
Sir, Excellent . We are really thankful for such a nice article. Please keep sharing.
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