Basics Of ETF Risk, Part II: Beta And Alpha



While ETF performance descriptions might bring to mind Mark Twain’s phrase “lies, damn lies, and statistics,” risk metrics are indispensible when evaluating a fund.

When analyzing ETFs, we often evaluate pairs of data. For example, we compare a fund’s market price against its net asset value ( NAV ). Or we might look at a fund’s NAV versus the index it tracks. I described these fundamental relationships in a previous piece looking at what I consider to be crucial terminology.

Basic performance statistics that compare data sets aren’t complicated, but the terms themselves often carry baggage that obscures their meaning.

For example, alpha is often associated with risk takers, and beta with the follow-the-herd crowd. I don’t buy these characterizations. Moreover, I think the mystique around these terms just gets in the way.

Beta and alpha come from regressions. Here’s the basic idea:

Take two sets of numbers, such as daily returns. Plot all the returns on a simple grid, with one set on the horizontal axis and the other on the vertical axis. The regression is the best estimate of a straight line that comes closest to fitting these points. Beta is simply the slope of this line and alpha is the intercept.


Beta is typically used to compare a fund to a broad index. Let’s say you’re looking at an equal-weight fund like the Rydex S'P Equal Weight ETF (NYSEArca:RSP). You want to know how the fund stacks up against a comparable cap-weighted fund like the SPDR S'P 500 ETF (NYSEArca:SPY).

RSP on SPY - Daily Returns (10/20/06 - 10/19/11

Running the regression on 60 months of daily NAV data, we get a beta of 1.10.

Here’s why it matters. Think of beta as a performance multiple. The regression estimates that when SPY is up 1 percent, RSP is up 1.10 percent. When SPY is down 1 percent, the fund is down 1.10 percent. RSP’s 1.1 beta tells us that it’s a bit riskier than SPY, so you should expect more return in compensation.

Bottom line:Beta provides a measure of comparative risk. Beta is not confined to measuring market risk, though that’s often the case. You can use it to compare any two sets of returns. The key is to understand what’s being compared.



Goodness Of Fit

The beta estimate comes from a regression. But how do we know whether to trust the regression itself? R 2 , pronounced “R-squared,” describes the overall “goodness of fit” of the regression to actual data. R 2 ranges from 0 to 1, with 1 as a perfect fit.

Correlation and R 2 are kissing cousins. In fact, R 2 is simply the square of correlation in simple regressions. In the graph above, the data points cling tightly to the regression line. That’s high R 2 (0.976 in this case). A low R 2 regression would have data points farther away from the regression line.

Bottom line:You can only trust the beta number when R 2 is high. When R 2 is low, beta doesn’t tell us much.


Alpha is a measure of outperformance. From a visual standpoint, alpha shows where the regression line crosses the vertical axis, or the Y-intercept. In the example above, alpha is simply the estimate of RSP’s return on days when SPY’s return is zero.

Alpha has its own measure of accuracy. I won’t bore you with too many details, but in short, alpha typically lacks statistical significance. That’s the case for the regression above. Oftentimes, marketing materials claiming a particular investment generates alpha won’t refer to statistical significance at all, in which case you’re probably better off ignoring it.

Bottom line:All regressions spit out an alpha number, but most of the time it’s meaningless. Real alpha is rare. And it’s quite possibly negative to boot. Be skeptical.

It’s All Relative

Beta, R 2 and alpha come in handy when comparing funds side by side. Looking at fund A’s beta to the S'P 500 compared with fund B’s provides insight into the relative market risk between the two funds.

Like all performance measures though, these metrics come with major limitations. They’re backward looking, they change over time and they’re sensitive to the time period used.

Here’s another takeaway:Beta and alpha are relative to whatever baseline is used.

Consider a growth ETF that uses a fancy stock-selection method. You’ll be interested in its beta to a vanilla growth ETF and maybe its beta to the broad market as well.

Some folks have a hard time thinking about the presence of alpha in the context of a passive vehicle like an ETF. But statistically, significant alpha can occasionally be found even comparing a fund’s NAV to its index.

In short, a clear picture of what beta and alpha mean can help you cut through the veiling mists that often cloud the ETF landscape.


Don't forget to check's ETF Data section.

Copyright ® 2011 IndexUniverse LLC . All Rights Reserved.

The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of The NASDAQ OMX Group, Inc.

This article appears in: Investing , ETFs

Referenced Stocks: NAV , RSP , SPY



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