# A Lesson in Modern Portfolio Theory

How do investors use r-squared data when picking mutual funds?

QUESTION: How do investors use r-squared data when picking mutual funds? A couple of the funds I'm considering have r-squared figures in the 50s. What does this mean?

-- Anonymous

ANSWER: R-squared is one of the cornerstones of modern portfolio theory, or MPT. It gauges how closely a mutual fund tracks a particular index. Investors can use r-squared to figure out how much diversity various funds would add to their portfolio. R-squared is also essential in studying a fund's alpha and beta. (Don't worry -- we'll explain all three terms.)

R-squared is used to see how large a percentage of a portfolio's returns can be attributed to the movement of a particular benchmark, explains John Markese, president of the American Association of Individual Investors. A fund's r-squared figure can range from zero to 100, with 100 indicating complete overlap with the index with which it's being compared. For instance, if you look under the "risk" tab on our fund snapshot for the Vanguard 500 Index fund (VFINX), you'll see that this fund's r-squared is 100 when compared with the Standard & Poor's 500. In other words, the fund has a 100% correlation with the index. (On our fund snapshots, the r-squared figure is based on three-year historical data.)

Reviewing a fund's r-squared figure can be helpful in assessing the amount of diversification a fund might bring to your portfolio. For example, if you already own an S&P 500 index fund, and you're considering a fund that has a very high r-squared when measured against this benchmark, then this fund probably isn't going to add much diversity to your portfolio. You can also keep an eye on r-squared to see if you own a closet index fund. "If you have an r-squared in the high 90s and it's an actively managed fund, you should buy the index and forget about it," says Markese. After all, why pay more in annual fees for active management, when you could just buy a cheap index fund instead?

A fund's r-squared figure is also a stepping stone to the two other main components of MPT: alpha and beta. Beta is a measure of a fund's volatility in relation to a specific benchmark. A beta of 1.0 indicates that the fund has experienced roughly the same magnitude of movements as the benchmark itself. If the figure is greater than 1.0, the fund has performed better than the index in up markets, and worse in down markets. "It's useful to gauge what the range of motion is relative to a given benchmark," says Shannon Zimmerman, a mutual-fund analyst at investment-research firm Morningstar. "It's a way of assessing how much risk is being taken on for the sake of excess returns."

Consider, for example, the Fidelity Growth and Income fund (FGRIX), which has an r-squared of 92 and a beta of 0.70. Translation? This large-cap blend fund tracks the S&P 500 pretty closely, but at lower risk. Based on the beta, this fund has performed 30% better than the S&P 500 during down markets, and 30% worse during up markets. Given this fund's emphasis on income, that's not surprising.

Alpha compares how a fund has actually performed with its expected returns, based on the beta figure. A positive alpha figure indicates that the fund has performed better than expected. Some investors use alpha as an indicator of manager talent: The theory goes that if the fund is performing better than expected, it's probably the person at the helm who's driving that outperformance. Just be sure it's the current manager who racked up those returns, notes Zimmerman.

To see what we mean, take a look at the Chesapeake Core Growth fund (CHCGX). This large-cap growth fund has an r-squared of 87 vs. the S&P 500, a beta of 1.21 and an alpha of 5.37. The alpha figure indicates that the fund has performed 5.37% better than expected, given its beta. Pretty impressive.

So how helpful are these stats? Much depends on the r-squared figure. If it's below 75, then it's not terribly helpful -- in fact, it makes the alpha and beta figures pretty much worthless. (In that case, there's probably a better index for the fund to be compared with; Morningstar lists a "best fit" index on its snapshots.) But if the r-squared figure is sufficiently high, then "taking those data points as a constellation can be useful because they are all interrelated," says Zimmerman.

Bottom line? When evaluating a fund, these measures can provide some useful information. But there's a whole lot of other data you need to process as well, such as the fund's returns, expenses, manager philosophy, investment strategy and so on.