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ABSTRACT
Kothari, Shanken, and Sloan (1995) contend that the relation between average return and book-tomarket
equity (BE/ME) is seriously exaggerated hy survivor bias. We argue that
survivor bias does not explain the relation between BE/ME and average return. We
also show that annual and monthly j8s produce the same inferences about the /3
premium. Our main point on the /3 premium is, however, more basic. It cannot save
the Capital asset pricing model (CAPM), given the evidence that /3 alone cannot
explain expected return.
FAMA AND FRENCH (FF 1992) PRODUCE two negative conclusions about the empirical
adequacy of the capital asset pricing model (CAPM) of Sharpe (1964)
and Lintner (1965): (i) when one allows for variation in CAPM market /3s that
is unrelated to size, the univariate relation between /3 and average return for
1941-1990 is weak; (ii) /3 does not suffice to explain average return. Size
(market capitalization) captures differences in average stock returns for 19411990
that are missed by j3. For the post-1962 period where we have book equity
data, BE/ME (the ratio of book to market equity) and other variables also help
explain average return.
Kothari, Shanken, and Sloan (KSS 1995) have two main quarrels with these
conclusions. First, they claim that using /3s estimated from annual rather than
monthly returns produces a stronger positive relation between average return
and j3. Second, KSS contend that the relation between average return and
BE/ME observed by FF and others is seriously exaggerated by survivor bias in
the COMPUSTAT sample.
We argue (Section II) that survivor bias does not explain the relation between
BE/ME and average return. We also show (Section III) that annual and
monthly )3s produce the same inferences about the presence of a j3 premium in
expected returns. But our main point on the /3 premium (Section I) is more
basic: It cannot save the CAPM, given the evidence that /3 alone cannot explain
expected return.
I. The Logic of Tests of the CAPM
As emphasized by Fama (1976), Roll (1977), and others, the main implication
of the CAPM is that in a market equilibrium, the value-weight market port
* Graduate School of Business, University of Chicago (Fama), and Yale School of Management
(French). We acknowledge the helpful comments of Josef Lakonishok, Rene Stulz, and a referee.
1947
1948 The Journal ofFinanee
folio, M, is mean-variance-efficient. The mean-variance-efficiency of M in turn
says that:
(i) J3, the slope in the regression of a security's return on the market
return, is the only risk needed to explain expected return;
(ii) There is positive expected premium for j3 risk.
Our main point is that evidence of (ii), a positive relation between j3 and
expected return, is support for the CAPM only if (i) also holds, that is, only if
J3 suffices to explain expected return. Confirming Banz (1981), however, and
like FF (1992), KSS find that size adds to the explanation of average return
provided by j3. Moreover, size is no longer the prime embarrassment of the
CAPM. Variables that (unlike size) do not seem to be correlated with j3 (such
as earnings/price, cashflow/price, BE/ME, and past sales growth) add even
more significantly to the explanation of average return provided by j3 (Basu
(1983), Chan, Hamao, and Lakonishok (1991), FF (1992, 1993, 1996), and
Lakonishok, Shleifer, and Vishny (1994)).
The average-return anomalies of the CAPM suggest that, if asset pricing is
rational, a multifactor version of Merton's (1973) intertemporal CAPM
(ICAPM) or Ross' (1976) arbitrage pricing theory (APT) can provide a better
description of average returns. The excess market return of the CAPM is a
relevant risk in many multifactor alternatives, like the ICAPM and Connor's
(1984) equilibrium version of the APT. Thus, evidence of a positive relation
between /3 and expected return does not favor the CAPM over these alternatives.
The three-factor model in Fama and French (1993, 1994, 1995, 1996) illustrates
our point. The model provides a better description of average returns
than the CAPM, and it captures most of the average-return anomalies missed
by the CAPM. Because of its strong theoretical standing, the excess market
return is one of the three risk-factors in the model, and our tests confirm that
it is important. It captures strong common times-series variation in returns,
and the market premium is needed to explain the large differences between the
average returns on stocks and bills. Moreover, as in the CAPM, the market
premium in our multifactor model is just the average return on M in excess of
the risk-free rate. Tests on long sample periods say that this premium is
reliably positive. In short, our tests of the CAPM against a multifactor alternative
illustrate that a positive j3 premium does not in itself resuscitate the
CAPM, or justify using it in applications.
KSS are not misled on this basic point. But their focus on the univariate ^
premium may confuse some of their readers. Indeed, because the CAPM is
such a simple and attractive tool, we think that many of our colleagues want
to be confused on this point. Otherwise, we can't explain the strong interest in
the KSS /3 tests, given that, like many others (including Amihud, Christensen,
and Mendelson (1992) and Jagannathan and Wang (1996)), KSS consistently
find that /3 does not suffice to explain expected return.
The CAPM is Wanted, Dead or Alive
II. Survivor Bias and BE/ME
KSS argue that survivor bias in COMPUSTAT data is important in the strong
positive relation between average return and book-to-market-equity (BE/ME)
observed by EF (1992) and others. COMPUSTAT is more likely to add distressed
(high-BE/ME) firms that ultimately survive and to miss distressed
firms that die. The survivors are likely to have unexpectedly high returns in
the turnaround years immediately preceding their inclusion on COMPUSTAT.
Since COMPUSTAT typically includes some historical data when it adds firms,
there can be positive survivor bias in the returns of high-BE/ME firms on
COMPUSTAT.
There are counter arguments. In the most detailed study of the issue, Chan,
Jegadeesh, and Lakonishok (1995) conclude that survivor bias cannot explain
the strong relations between average return and BE/ME observed by Lakonishok,
Shleifer, and Vishny (1994) and EF (1992) in tests on the post-1968 and
post-1976 periods. After 1968, and certainly after 1976, almost all the traded
securities on Center for Research in Security Prices (CRSP) that are not on
COMPUSTAT are missing for reasons that have nothing to do with survivor
bias. Many of the missing firms are closed-end investment companies, REITs,
ADRs, primes, and scores that produce no accounting information or produce
information that is not comparable to that of other firms. Many financial
companies are also missing because, judging that their accounting data are
different from that of other firms, COMPUSTAT limited its coverage of financials
for many years. These omissions, which are the result of COMPUSTAT's
ex ante policy decisions, are not a source of survivor bias. Finally, some of the
securities that seem to be on CRSP but not COMPUSTAT in fact appear on
both, but with different identifiers.
There is other evidence that survivor bias cannot explain the relation between
average return and BE/ME. Lakonishok, Shleifer, and Vishny (1994)
find a strong positive relation between average return and BE/ME for the
largest 20 percent of NYSE-AMEX stocks on COMPUSTAT, where survivor
bias is not an issue. FF (1993) find that the relation between BE/ME and
average return is strong for value-weight portfolios of COMPUSTAT stocks
formed on BE/ME. Since value-weight portfolios give most weight to larger
stocks, any survivor bias in these portfolios is probably trivial. In three different
sets of comparisons (Table VII), KSS themselves find that the relation
between average return and BE/ME is strong and strikingly similar for value-
weight and equal-weight portfolios of COMPUSTAT stocks formed on BE/ME.
KSS concede that survivor bias cannot explain the results for value-weight
portfolios.
To support their survivor-bias story, KSS make much of the fact that stocks
on CRSP but not COMPUSTAT have lower average returns than stocks on
COMPUSTAT. When they risk-adjust returns using a three-factor model like
that in FF (1993), however, only the smallest two size deciles of the NYSEAMEX
stocks missing from COMPUSTAT have strong negative abnormal
http://www.ukassignment.org/kjessay/2011/0920/11898.html
The Journal of Finance
returns (Table IV). This suggests that survivor bias is Umited to tiny stocks;
the average market cap of the stocks in the second decile is $13 million, while
the average for the first decile is between $3 million and $7 million. The
remaining 80 percent of the stocks missing on COMPUSTAT, which account
for almost all the combined value of the missing stocks, have three-factor
abnormal returns that are close to zero and random in sign. In other words,#p#分页标题#e#
these missing stocks behave like stocks that are on COMPUSTAT. Similarly,
Chan, Jegadeesh, and Lakonishok (1995) fill in missing COMPUSTAT book
equity (BE) data for the largest 20 percent of the NYSE-AMEX firms on CRSP.
The survivor-bias story says that the relation between BE/ME and average
return should be weak for the firms missing on COMPUSTAT. They find that
it is as strong for the missing firms as for the included firms.
KSS also speculate that the positive relation between book-to-market-equity
and average return is the result of data dredging and so is special to the
post-1962 COMPUSTAT period. Using a hand-collected sample of large firms
that is not subject to survivor bias, however, Davis (1994) finds a strong
relation between BE/ME and average return in the 1941-1962 period.
In the end, the KSS survivor-bias story rests on their evidence that there is
little relation between average return and BE/ME for the rather limited
industry portfolios in the S&P Analyst's Handbook. Their results for the S&P
industries are strange since FF (1994) document a strong positive relation
between average return and BE/ME for value-weight industry portfolios that
include all NYSE, AMEX, and Nasdaq stocks on CRSP. (We use COMPUSTAT
firms only to estimate industry BE/ME.)
KSS do not say that the relation between average return and BE/ME is
entirely the result of survivor bias. They push so hard on the survivor-bias
story, however, that serious readers are led to strong conclusions. For example,
in the lead article to volume 38 of the Journal of Financial Economics,
MacKinlay (1995, p. 5) concludes,
"Their analysis suggests that deviations from the CAPM such as those
documented by Fama and French (1993) can be explained by sample
selection biases."
III. Minor Points
KSS claim that using j3s estimated from annual rather than monthly returns
explains why they measure somewhat stronger relations between /3 and average
return than FF (1992). They also claim that although the explanatory
power of size is statistically reliable, for practical purposes, size adds little to
the explanation of average return provided by j3. The tests that follow explore
these issues.
A. Portfolios Formed on /3
Table I summarizes returns for 1928-1993 on /3 deciles of NYSE stocks. Like
KSS, we weight the stocks equally. We form the portfolios in June of each year.
The CAPM is Wanted, Dead or Alive 1951
Table I
Summary Statistics and Cross-Section Regressions for
Postformation Equal-Weight Returns on NYSE j3 Deciles: 1928-1993
Starting in 1927, ten portfolios of NYSE stocks on CRSP are formed in June of each year based on
VW-S ps, the sum of the slopes from regressions of monthly returns on the current and one lag of
the value-weight NYSE market return. The formation period /3s use 24 to 60 months of past returns
(as available), except for 1927, where 18 months are used. Equal-weight monthly postformation
returns on the /3 deciles are calculated from July to June of the following year, yielding time-series
of postformation returns for July 1927 to December 1993. The equal-weight monthly decile returns
are compounded to get annual returns. The |3s shown in Panel A are estimated using all postformation
monthly (VW, VW-S, EW, EW-S) or annual (VWA, EWA) returns for 1928-1993 and the
value-weight (VW, VW-S, VWA) or equal-weight (EW, EW-S, EWA) NYSE market portfolio. VW-S
and EW-S βs are the sums of the slopes from the regressions of the monthly postformation decile
returns on the current and one lag of the market return. VW, VWA, EW, and EWA J3s use only the
contemporaneous market returns. Average Ln (Size) is the average across postformation months of
the average monthly value of the natural log of size (price times shares) of the stocks in a ^ decile.
Panel B shows the average slopes (Means) and the ^-statistics for the average slopes from univariate
cross-section regressions of postformation monthly or annual returns on the ten j3 portfolio on each
of the six different estimates of their postformation ps.
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