# Basics Of ETF Risk, Part II: Beta And Alpha

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While ETF performance descriptions might bring to mind Mark Twainâs phrase âlies, damn lies, and statistics,â risk metrics are indispensible when evaluating a fund.

When analyzing ETFs, we often evaluate pairs of data. For example, we compare a fundâs market price against its net asset value ( NAV ). Or we might look at a fundâ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 arenâ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 donât buy these characterizations. Moreover, I think the mystique around these terms just gets in the way.

Beta and alpha come from regressions. Hereâ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

Beta is typically used to compare a fund to a broad index. Letâs say youâ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).

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

Hereâ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. RSPâs 1.1 beta tells us that itâ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 thatâs often the case. You can use it to compare any two sets of returns. The key is to understand whatâs being compared.

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Goodness Of Fit

The beta estimate comes from a regression. But how do we know whether to trust the regression itself? R 2 , pronounced âR-squared,â describes the overall âgoodness of fitâ 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. Thatâ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 doesnât tell us much.

Alpha

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 RSPâs return on days when SPYâs return is zero.

Alpha has its own measure of accuracy. I wonât bore you with too many details, but in short, alpha typically lacks statistical significance. Thatâs the case for the regression above. Oftentimes, marketing materials claiming a particular investment generates alpha wonât refer to statistical significance at all, in which case youâre probably better off ignoring it.

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

Itâs All Relative

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

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

Hereâs another takeaway:Beta and alpha are relative to whatever baseline is used.

Consider a growth ETF that uses a fancy stock-selection method. Youâ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 fundâ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.

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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.

Referenced Stocks: NAV , RSP ,

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