What Does R-Squared Reveal?

Question: Last week you noted that the beta statistic may be irrelevant if a fund has a limited correlation with an index. How would I know how well my fund is correlated with an index?

Answer: In last week's 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,  T. Rowe Price High-Yield Bond (PRHYX) has an R-squared of just 8.5 with the Barclays Capital Aggregate Bond Index, indicating a very low correlation with that index. (Like most high-yield funds, the T. Rowe offering's performance is actually more correlated with the stock market than the bond market.) That means that investors shouldn't place too much weight on the fund's MPT statistics, including alpha and beta, relative to that benchmark.

Choose the Most Closely Correlated Index
Because a fund's correlation with a given index is so important when viewing MPT statistics, Morningstar allows users to see a fund's modern portfolio statistics, including R-squared, alongside two benchmarks. We show MPT statistics relative to a standard, widely recognized benchmark for the fund's broad asset class, such as the S&P 500 for all stock funds and the Barclays Aggregate Bond Index for bond funds.

In addition, we show MPT statistics relative to a benchmark that we call the best-fit index, which is calculated in-house at Morningstar by comparing the fund's performance with that of a number of different indexes to find the one that has the highest performance correlation with the fund during the last 36 months. In the case of T. Rowe Price HighYield, for example, its best-fit index is Credit Suisse High Yield; the fund has an R-squared of 98 with that index.

If a fund has a high correlation with its best-fit index, then investors can put a fair amount of weight on the corresponding MPT statistics.

For a more detailed explanation of the difference between the best-fit and standard index, read this article.

But 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.