While ETF performance descriptions might bring to mind Mark
Twainâs phrase âlies, 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 fundâs market price against its net asset
). Or we might look at a fundâs 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 arenât
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 donât buy these
characterizations. Moreover, I think the mystique around these
terms just gets in the way.
Beta and alpha come from regressions. Hereâs the basic
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.
Letâs say youâre 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.
Hereâs 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. RSPâs 1.1 beta tells us that itâs a bit
riskier than SPY, so you should expect more return in
Bottom line:Beta provides a measure of comparative risk. Beta is
not confined to measuring market risk, though thatâs often the
case. You can use it to compare any two sets of returns. The key is
to understand whatâs being compared.
Goodness Of Fit
The beta estimate comes from a regression. But how do we know
whether to trust the regression itself? R
, pronounced âR-squared,â describes the overall âgoodness of
fitâ of the regression to actual data. R
ranges from 0 to 1, with 1 as a perfect fit.
Correlation and R
are kissing cousins. In fact, R
is simply the square of correlation in simple regressions. In the
graph above, the data points cling tightly to the regression line.
Thatâs high R
(0.976 in this case). A low R
regression would have data points farther away from the regression
Bottom line:You can only trust the beta number when R
is high. When R
is low, beta doesnât 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 RSPâs return on days when SPYâs return is zero.
Alpha has its own measure of accuracy. I wonât bore you with
too many details, but in short, alpha typically lacks statistical
significance. Thatâs the case for the regression above.
Oftentimes, marketing materials claiming a particular investment
generates alpha wonât refer to statistical significance at all,
in which case youâre probably better off ignoring it.
Bottom line:All regressions spit out an alpha number, but most
of the time itâs meaningless. Real alpha is rare. And itâs
quite possibly negative to boot. Be skeptical.
Itâs All Relative
and alpha come in handy when comparing funds side by side. Looking
at fund Aâs beta to the S'P 500 compared with fund Bâs provides
insight into the relative market risk between the two funds.
Like all performance measures though, these metrics come with
major limitations. Theyâre backward looking, they change over
time and theyâre sensitive to the time period used.
Hereâs another takeaway:Beta and alpha are relative to
whatever baseline is used.
Consider a growth ETF that uses a fancy stock-selection method.
Youâll 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
fundâs 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
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