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					         Aged and Recent Market Betas in Securities Prices_
                                            Gerard Hoberg
                                         University of Maryland
                                          ghoberg@rhsmith.umd.edu
                                            Ivo Welch
                                     Brown University and NBER
                                            ivo_welch@brown.edu

                                           September 9, 2007

ABSTRACT
Instead of computing only one five-year market-beta, we compute one ―recent‖ beta
from 1 month to 2 years ago, and one ―aged‖ market beta from 2 to 10 years ago, both
using daily stock returns. We find that the aged beta has a positive influence on stock
returns, consistent with standard hedging concerns. The recent beta has a negative
influence on stock returns, whose cause is less clear. The evidence suggests that it
is due to a novel factor, possibly behavioral or attention related. Previous research
had failed to find that market-beta matters, primarily because ordinary market-betas
combine these two opposing forces and because betas based on monthly stock returns
are too weak. The importance of the two separate betas increases if we control for the
                        1
Fama-French factors.

The seminal paper by Fama and French (1992b) documented that market-betas of U.S.
stocks seem to have no influence on future stock returns in cross-sectional Fama and
MacBeth (1973) regressions when book-market and firm-size are controlled for. One does
not have to believe in the CAPM to be astonished by this fact. The rate of return on the
overall stock market seems to be the first principal component in the equity markets, so
stocks that move less with the market should be useful hedges. They should therefore
require lower expected rates of returns. This can be viewed as an unconditional statement
(that betas should be important by themselves) and as a conditional statement (that betas
should be important for investors that have hedged other factors).

Not surprisingly, there have been a number of attempts to resurrect market-beta as
an important component of the pricing of stocks. Many of these attempts derive some
power from the correlation of market-betas with the two Fama-French factors. A loose
interpretation is that these papers suggest good reasons why one should apportion to
market-beta at least some of the explanatory power that is joint. Prominent examples are
Ang and Chen (2005), Avramov and Chordia (2006), and Campbell and Vuolteenaho (2004).
The latter decompose beta into a cash flow related beta that has a positive influence, and a
discount factor related market beta, that has a negative influence. Their betas, too, have
power that is overlapping considerably with that of the other Fama-French factors. Thus,
Fama and French (2006) would probably still argue that the ―CAPM’s general problem is
that variation in beta unrelated to size and value-growth goes unrewarded throughout
1926–2004,‖ and especially after 1962. Another attempt to ―rescue‖ market beta was
proposed by Jagannathan and Wang (1996). They work with conditional market-betas and
control for labor income, and find that there are specifications in which market-beta remains

1
  _We thank Eric Jacquier and Sophocles Mavroeidis for help with the error-in-variables issues. Jonathan
Lewellen, our NBER discussant, also helped us improve our paper considerably. We thank seminar participants
at Purdue, Boston College, the University of Toronto, and York University. Ken French graciously made
some of the data used in our paper available on his website. Our beta factor portfolios are posted at
http://www.rhsmith.umd.edu/faculty/ghoberg/ and http://welch.econ.brown.edu/academics/hoberg-welchbetas.
csv.
significant. This is critiqued by Lewellen and Nagel (2006), who argue that the potential
magnitude of their effect is small.

Our own paper adds to this literature, though with little overlap. We hypothesize that a
beta computed from recent stock returns could play a different role than a beta computed
from earlier stock returns. Our original motivation was behavioral: If investors are slow
to recognize and adjust to changes in beta, a reduction in beta could be associated with a
short-lived increase in the stock price, and therefore a positive average rate of return. A
simple perpetuity model suggests that even a small delay in the full adjustment could have
a large opposing impact—holding future cash flows constant, a change from, say, a 5% to a
5.1% expected rate of return can induce a one-time price adjustment of about 2%—twenty
2 times as high as the 0.1% change in the expected return itself. To uncover such an
opposing effect, this hypothesis suggests that one should find that the recent change in beta
would matter.

Upon reflect, such a ―slow adjustment‖ effect is not the only hypothesis that could
overwhelm the standard hedging motive effect—a negative effect of recent betas on stock
prices that is different from the positive asset-pricing effect that theory would suggest
for (older) betas. For example, investors could pay more attention to stocks that have
recently moved against the stock market, and this could increase their returns temporarily.
Alternatively, stocks that have recently underperformed relative to the market could become
more attractive, while stocks that have recently outperformed even the market in a bull
market could become less desirable. Thus after the market has just gone up, investors might
pour money into those firms that have not yet similarly appreciated. Or, less specifically,
recent betas could simply pick up exposure to some novel factor that investors care about,
for whatever reason.

Again, these hypotheses for a different role for short-term market betas are not based
on standard market-hedging motives, and they are of course just conjectures.1 It is the
empirical evidence that matters. Our paper finds that this evidence suggests that if we
include both recent beta and aged betas, then

• Aged betas (computed from daily stock returns at least two years old) have a solid
positive influence on future stock returns.

• Recent betas (computed from daily stock returns no more than two years old) have a
solid negative influence on future stock returns.

As noted, the positive influence of aged betas is easy to explain as the standard hedging
motive. Indeed, we see it as the primary contribution of our paper that it is able to uncover
such a reliable positive influence of this aged beta in the cross-section of future stock
returns.

The negative part is more mysterious. Although our paper does offer some explanations
(those mentioned above) and some related evidence, these do not have the same theoretical
grounding as the hedging motive and are thus more speculative. Moreover, some of our
evidence suggests that we document a ―change in beta‖ effect, although other evidence
points to two separate and opposite beta effects.2

2
  A combination of these hypotheses has also been proposed by Jacquier, Titman, and Yalcin (2001). They
omit the most recent 12 months in computing beta, include a contemporaneous beta, and then explore the
differences in portfolios across momentum losers and momentum winners. Nor have changes in beta gone
unnoticed, either. For example, Cohen, Polk, and Vuolteenaho (2003) noticed that betas of growth firms
tended to fall, while betas of value firms tended to rise.
Unlike earlier attempts to rescue beta, the role of our two betas does not overlap with
those of the two Fama-French factors or momentum. Indeed, the two market betas become
stronger if we control for these factors. Moreover, the influence of the two market betas
seems economically significant: An extreme corner quintile portfolio of stocks with high
aged betas and low recent betas outperforms its mirror image by an annualized 5% to 7%
per year. If anything, the effect seems to have become stronger in recent years, unlike that
of the other factors (e.g., the book-market effect) that we are controlling for.

VI Conclusion

Our paper’s most important contribution is a diagnosis of why market-betas have performed
so poorly in detecting the positive hedging role of low-beta stocks in cross-sectional
predictive return regressions. Stocks that have a high aged beta also tend to have a high
subsequent recent beta. (If they did not, historical betas would have no use in designing
hedges.) However, aged beta and recent beta have opposite roles in predicting future stock
returns. Using only either the aged or the recent beta in a regression without including
the other therefore inevitably picks up the opposite effect of the other beta. Thus, it is no
wonder that earlier work has not found that market-betas by themselves are not important.
Successful prediction in which aged beta can help explain the cross-section of future stock
returns requires holding the recent beta constant—or at least including a set of alternative
variables that can assume the role of recent beta (as in we did in Table X).

To compute good market-betas, we recommend using daily stock returns, about two
years of history, and Vasicek shrinkage. We find that the hedging role of recent market betas
seems to be overwhelmed by a non-hedging related effect—possibly a delayed response,
an attention-related effect, or a novel factor exposure. In contrast, aged market betas do
have the theoretically predicted positive hedging correlation with the stock market. These
two effects are robust among firms of difference sizes, types, and momentum. The effect is
stronger in Januaries, and after 1990. It is also fairly persistent. Aged betas are significantly
positively related to stock returns for up to two years, recent market betas for about 6-12
months. Including other variables does not change the importance of aged beta, but can
affect the importance of recent betas. Indeed, the influence of aged and recent betas does
not arise because these variables ―steal‖ explanatory power from the Fama-French variables
or from the momentum variables. On the contrary, the two betas are stronger when the
Fama-French factors are controlled for. However, it is not yet fully clear whether we are
observing primarily a ―change in beta‖ effect or two separate beta effects.

We also proposed a test to determine whether aged and recent betas pick up covariation
with the stock market, or covariation with a novel unspecified factor. This test suggests
that aged beta matters primarily because it is a covariation with the stock market per sé,
not because it is an exposure to a novel factor. In contrast, recent beta primarily picks up a
covariation to some novel factor—a contaminant. Although we would prefer knowing why
this novel factor is so important to investors, we could only speculate about its ultimate
source (slow response, attention changes, etc.). We would argue that this puts our novel
factor in the same category as many other familiar non-hedging related pricing factors. In
fact, although there are good suggestions after 20 years of empirical research, there is still
some disagreement why the Fama-French factors and momentum work so well.

Although there may be other more or equally important factors determining stock
market pricing, the effect of our betas is not economically small. We find an observed
spread of 5% to 7% per annum between a portfolio with high aged market beta and low
recent market beta and its reverse. When recent market beta is replaced by our proposed
novel factor exposure, this increases to 8% to 10% per annum. Again, in our opinion, it is the
relation of this spread to the predictions of hedging theory that renders this cross-sectional
return spread more interesting than return spreads that factors without much theoretical
background would produce.

Finally, as expected, we found that only recent market beta constituted a novel factor
detectable by the Fama-French time-series techniques. The hedging motive has of course
always been a part of the Fama-French factors (captured by their XMKT factor), and it is thus
not a surprise that aged market beta could not pick up a novel factor above and beyond the
Fama-French factors.

				
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