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Unformatted text preview: SUMMER 1993 Are the Reports of Beta’s Death
Premature? Let’s think twice before rushing to discard beta. Louis K.C. Chan andjosef Lakonishok LOUIS K.C. CHAN is assistant
professor of ﬁnance. andJOSEF
LAKONISHOK is the Karnes
professor of ﬁnance, at the Univer— sity of Illinois at UrbanaCham—
paig'n (IL 61820). any would name the concept of beta risk as the single most important contri— bution of academic researchers to the ﬁnancial community. At ﬁrst slow to
accept beta, practitioners have come to use it widely as
a risk measure and for computing expected returns In
European capital markets, the concept of beta is n0w
beginning to gain popularity. Yet, just as beta seems to
be on the verge of widespread use, an article by Fama
and French [1992a] has caused both academics and
practitioners to re—catanuuc the empirical support for
beta’s importance In retrospect. some earlier studies of beta (Fama
and MacBeth [1973]; Black, jeuserr, and Scholes
[1972]) do not provide conclusive evidence in suppor:
of beta. Later studies dating from the 19803 (such as
Reinganum [1982]; Lakonishok and Shapiro [1986];
and Ritter and Chopra [1989]) are not able to detect
any signiﬁcant relation between beta and average
returns The negative ﬁndings of these later studies.
however, have been largely ignored. The recent study
of Fama and French [1992a], which echoes the results
of some of these papers from the 19803, has been
interpreted as the ﬁnal nail in the cofﬁn. Do we really have sufﬁcient evidence to bury
beta? The question assumes added urgency when we
consider how dramatically the practice of portfolio
management has changed in the last ﬁve years. More money managers, for example, are begin— THE JOURNAL OF PORTFOLIO MANAGEMENT 51 s
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:us1s111s pug 0: ssnb1uq39: 1.1011821111111210 ssn 0: Sum for returns. Rather, our point is that. given the limita
tions of the data. it is still an open question whether
beta is dead or alive as a determinant of expected
returns. NOISY STOCK RETURNS Twenty years is a long time in ﬁnancial markets.
Needless to say, the horizon of the money manage—
ment business is very much shorter than twenty years.
There are only a handful of countries where it is possi—
ble to obtain comprehensive data going back twenty
years. Most of the international data bases available to
money managers extend back no farther than ten
years. Widely used commercial data bases. for example,
carry accounting information on SWiss companies
from 1986 onward only. Even the data that are avail—
able are plagued with problems. as they focus only on
surviving companies. It is thus fair to say that many would feel that
having a complete monthly history of twenty years of
data on thousands of stocks should be more than
adequate to answer the simple question whether there
is a significant relation between beta and returns. Yet is
twenty years really enough? One popular procedure to test for the existence
of a relation between betas and returns comes from
Fama and MacBeth [1973]. Monthly cross—sectional
regressions are run relating stock returns to betas. The
slope coefficient from each regression is our estimate
of the compensation per unit of beta in that particular
month. The average of the monthly slopes is thus the
estimate of the compensation per unit of beta risk
received by investors on average. We can then use the
standard deviation of the monthly series on the slope
coefﬁcients to examine whether the average slope is
statistically signiﬁcantly different ﬁom zero. Suppose that each month for the last twenty years in the US. we follow the standard methodology
and run monthly cross—sectional regressions relating returns to betas. Suppose. moreover, that every month
we obtain a slope coefﬁcient exactly equal to rm — If,
the return on the market minus the risk—free rate. This
accords perfectly with the Sharpe—Lintner CAPM.
Indeed. we cannot obtain a more favorable result than
this for the model. Yet would our regressions reveal that beta plays
a Signiﬁcant role in explaining stock returns? From our
regressions, we would obtain an annualized average SUMMER 1993 slope coefficient of 5.05%, and an annualized standard
deviation ofthe slope coeffiCient of 16.58%. The stan~
dard procedure is to test whether the average slope
COCETCICI’IE is significantly different from zero. The t—
statistic for tesring for the significance of the premium
for beta risk is 1.36. signiﬁcant at a level of about 9%.
This signiﬁcance level is not enough to reject the null
hypothesis that the premium is zero, given our typical
insistence on a 5% signiﬁcance level. Given the level of noise in the lasr twenty years
of stock returns, we would need a risk premium of
about 7.4% per year before we could reliably reject the
null hypothesis. What if the compensation per unit of
risk were lower, 4% per year, consistent with the Black
[1972] model but still a non negligible number? How
many years then would we need before we could
declare the premium statistically significant? We would
have to report back to you in sixtyinine years. Because we assume in this exercise that the
premium for beta risk is indeed equal to rm — rf, what
we are doing is the same as testing for the existence of
an equity risk premium (i.e.. whether stocks do better
than T—bills). We thus infer that the annual difference
of5.05% per year does not sufﬁce to reject reliably the
null that stocks do not outperform T—bills. A dollar
invested in T—bills at the beginning of the twenty—year
period in question would have grown to $4.41, while
an equivalent investment in stocks would have yielded
$9.211 Yet this huge difference is still not statistically
signiﬁcant at the §% level. Noise poses a problem in cases beyond testing
whether high—beta stocks outperform low—beta stocks.
Strategies based on B/M (the book—EO—market ratio)
have recently gained popularity (Chan, Hamao. and
Lakonishok [1991], Fama and French [1992a]).
Following this rack. for each year ﬁom 1968 to 1990.
we form ten portfolios from the universe of NYSE
and AMEX stocks. ranked by B/M. we compare the
returns of the two extreme portfolios: the portfolio
comprising those stocks with the highest B/M ratio,
and the portfolio made up of those stocks with the
lowest B/M portfolio, The standard error of the difference is 3.6%.
implying that unless the high B/M portfolio outper—
forms the low B/M portfolio by at least 7.2% a year.
the difference will not be significant. Luckily for the
partisans of B/M, the difference over the sample peri—
od is 8.7%, passing the test of signiﬁcance. Strategies developed in hindsight do not ensure THE _lOURNA_L OF PORTFOLIO MANAGEMENT 53 successful future performance for a money manager,
however. How conﬁdent can one be that high B/M
stocks will continue to outperform low B/M stocks at
such a pace? On the one hand, the publicity that we have
collecrively given to B/ M may make'high B/M stocks
less attractive in the future. On the other hand, if B/M
is simply proxying for risk, then we might expect simi
lar returns in the future for high B/M SEOCkS. Many of
us, however, have serious doubts whether the extraor—
dinary performance of high B/M stocks can be
explained by their riskiness (see Lakonishok, Shleifer,
and Vishny [1992a]). Another popular trading strategy is based on
market capitalization. We compare the returns over the
period 1979—1991 on the Russell 2000 index to the
returns on the S&P 500. The standard error for the
difference in returns is 3.63% per year. Llnless the
return on small stocks is at least twice this much
(7.26%) over the return on the S&P 500, we cannot
judge the difference to be signiﬁcant. As it turns out, the mean returns over the lasr
thirteen years differ by 0.28% per year. This difference
does not amount to much — should we conclude that
the size effect is dead? In a different context. take a money manager
who outperforms a benchmark by 2% a year, repre
senting an extraordinary feat. Assume that tracking
error is 5% a year, which is below the median for
active money managers (based on the SE1 universe of
equity managers). we would still need to accumulate twenty—ﬁve
years of data on returns earned by this manager before
we can reject the null hypothesis that performance of
this magnitude is no better than the benchmark. This
example highlights how dangerous our assumption of
stability can be. Are we getting twenty years later the
same money manager as the one responsible for the
extraordinary early performance? These examples illustrate how difficult it is to
make unambiguous inferences from the very noisy and
ever—changing environment generating stock returns.
While our research is often posed as clear—cut black—
and—white statements, we often do not have the luxury
of drawing such unqualiﬁed conclusions ﬁom the data
at hand. If a hypothesis is based on a sound theory
(some might say “story”) and is relatively free of data—
snooping biases, it may not be the most productive
way to proceed if we insist unthinkingly on a signiﬁ— 54 ARE THE REPORTS OF BETA'S DEATH PREMATURE cance level of 5% before we can reject the null
hypothesis. TESTS OF THE CAPM W'c use all the available data on the monthly
Center for Research on Security Prices (CRSP) tape
from 1926 to 1991 to examine the relation between
beta and returns, following the Fama~MacBeth proce—
dure. The ﬁrst three years of monthly observations are
used in a market model regression to estimate each
stock’s beta relative to the CRSP value—weighted
market index. Our universe is restricted to NYSE and
AMEX stocks. The stocks are then ranked on the basis of the
estimated betas and assigned to one of ten portfolios.
Portfolio 1 contains steels with the lowest betas, while
Portfolio 10 contains stocks With the highest betas. The assignment of stocks to portfolios in part
reﬂeCts measurement errors in the betas Such errors
would result in a “regression to the mean.” To avoid such bias. an intermediate step 18
necessary: the beta of each stock in a portfolio is re—
estimated using the next three years of returns; a port~
folio’s beta is then a simple average of the betas of the
individual stocks assigned to that portfolio. Thus the
ﬁrst three—year period is used to classify stoela to port—
folios. and the next three—year period is used to esti
mate betas for the portfolios. In each month of the subsequent year, we
regress the returns on the ten portfolios on their esti—
mated betas. Nore that this is a predictive test in the
sense that the explanatory variable (beta) is estimated
over a period disjoint from the period over which
returns are measured. At the end of the year, we repeat
the process of forming portfolios from three years of
data, estimating betas over three years, and adding
twelve more cross—sectional regressions. Ultimately we
obtain 720 cross—sectional regressions. Exhibit 1 provides summary statistics on the
betas for the ten portfolios and their average returns.
There is a positive relation between betas and average
returns: a finding consistent with a recent paper by
Black [1992]. Exhibit 2 provides results from the monthly
cross—sectional regressions. The mean estimated slope
coefficient is 0.47% per month. with a marginally
significant t—statistic of 1.84.2 Given our standard
errors, it is as likely that the compensation per unit Of SUMMER 1993 l
l EXHIBIT 1 Mean. Standard Deviation (in Percent), and Beta ofRetums on Portfolios Formed on Beta january 1932December 1991 (Low) (High)
1 2 3 4 6 7 8 9 10
Mean 1.30 1.33 1.32 1.46 1.56 1.59 1.52 1.65 1.54 1.60
Standard
Deviation 5.51 6.07 6.55 7.36 7.50 7.87 8.58 9.12 9.08 10.37
Beta 0.90 1.03 1.12 1.25 1.26 1.32 1,44 1.49 1.51 1.70 beta is 0% per year as it is 12% per year. The realized
market premium (rm — rf) over this period averages
0.76% per month Thus our estimated premium is
62% of the market excess return, in line with the
results of earlier work. The Sharpe—Unmet CAPM implies that the
risk premium is equal to the mean of (rm — If) — the
absolute difference between the average slope and the
average market excess return is only 29 basis points, so
we cannot reject the null hypothesis that the mean
slope coefﬁcient is equal to the average market excess
return (the t—statistic is —1.15). In contrast, over the period 1963—1990. Fama
and French [1992a] obtain a much lower point esti—
mate for the slope coefficient (0.15% per month), with
a t—statistic of 0.46. The case against beta is thus much
stronger in Fama and French’s sample period. Upon reflection. however. their finding may
not be as striking as it ﬁrst seems. In order for them to undoubtedly on the high side relative to the experi» ence of the last thirty years, or relative to any projec—
tion of future returns. 30 the failure to find a statistically signiﬁcant role for beta should not come as
a total surprise. Exhibit 3 plots the average cumulative monthly
difference between the estimated premium for beta
risk and rm  rf, the value predicted by the Sharpe—
Lintner CAPM. We start cumulating the difference
from January 1932, although the exhibit focuses on
the post—1942 experience. It is clear from the figure that the relation
between betas and returns varies considerably over time. If we were to stop our test in 1982, we would
conclude that there is a lot (if support For the CAPM. Up until 1982. the estimated compensation for beta EXHIBIT 3 obtain a t—statistic of 2, the compensation per unit of CUMULATIVE AVERAGE DIFFERENCE BETWEEN beta risk would have to be 7.83% per year — EXHIBIT 2
Monthly Fama—MacBeth Cross—Sectional Regressions T‘Test
for
Slope =
Sample Period Intercept Slope R2 rm — If
Jan 1932 — Dec. 1991 0.0059 0.0047 0.48 —1.15
(rm — r5: 0.0076) (3.50) (1.84)
Jan. 1932 — Dec. 1961 0.0075 0.0074 0.48 —1.01
(rm — q: 0.0115) (2.80) (1.82)
Jan. 1962  Dec. 1991 0.0042 0.0020 0.47 40.57
(rm — rf = 0.0038) (2.10) (0.64) SUMMER 1993 ESTIMATED SLOPE AND EXCESS MARKET
RETURN —JANUARY 1942—DECEMBER 1991 0.0080
0.0060 "
0.0010 — 0 0070 ‘ 0.0000
.0070 " 'DO‘D ‘ ) . . i . i . . , I i . . . . . .
1512 1947 15S2 I957 1952 1967 1972 1577 1982 “387 THE jOURNAL OF PORTFOLIO MANAGEMENT 55 EXHIBIT 4 FIVEYEAR MOVING AVERAGES OF ESTLMATED
SLOPE AND EXCESS MARKET RETURN
jANUARY 1937DECEMBER 1991 0.030 0.020 0.000 ‘UID' e°’'C‘ Hint. , "1, trﬁyiuwit irm,mimmunrrttumyt' 1337 1942 1947 [552 1557 1552 1557 1572 1977 1532 1937 1I1AIt risk is strik...
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