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The CAPM Debate
Federal Reserve Bank of Minneapolis Quarterly Review
Vol. 19, No. 4, Fall 1995, pp. 217
The CAPM Debate
Ravi Jagannathan
Ellen R. McGrattan
Visitor
Senior Economist
Research Department
Research Department
Federal Reserve Bank of Minneapolis
Federal Reserve Bank of Minneapolis
and Piper Jaffray Professor of Finance
Carlson School of Management
University of Minnesota
Abstract
This article describes the academic debate about the usefulness of the capital asset
pricing model (the CAPM) developed by Sharpe and Lintner. First the article
describes the data the model is meant to explainthe historical average returns for
various types of assets over long time periods. Then the article develops a version
of the CAPM and describes how it measures the risk of investing in particular
assets. Finally the article describes the results of competing studies of the models
validity. Included are studies that support the CAPM (Black; Black, Jensen, and
Scholes; Fama and MacBeth), studies that challenge it (Banz; Fama and French),
and studies that challenge those challenges (Amihud, Christensen, and Mendelson;
Black; Breen and Korajczyk; Jagannathan and Wang; Kothari, Shanken, and
Sloan). The article concludes by suggesting that, while the academic debate
continues, the CAPM may still be useful for those interested in the long run.
The views expressed herein are those of the authors and not necessarily those of the Federal
Reserve Bank of Minneapolis or the Federal Reserve System. Most large U.S. companies have built into their capital
budgeting process a theoretical model that economists are
now debating the value of. This is the capital asset pric-
ing model (the CAPM) developed 30 years ago by Sharpe
(1964) and Lintner (1965). This model was the rst appar-
ently successful attempt to show how to assess the risk of
the cash ow from a potential investment project and to es-
timate the projects cost of capital, the expected rate of re-
turn that investors will demand if they are to invest in the
project. Until recently, empirical tests of the CAPM sup-
ported the model. But in 1992, tests by Fama and French
did not; they said, in effect, that the CAPM is useless for
precisely what it was developed to do. Since then, re-
searchers have been scrambling to gure out just whats
going on. Whats wrong with the CAPM? Are the Fama
and French results being interpreted too broadly? Must the
CAPM be abandoned and a new model developed? Or can
the CAPM be modied in some way to make it still a use-
ful tool?
1
In this article, we dont take sides in the CAPM debate;
we merely try to describe the debate accurately. We start
by describing the data the CAPM is meant to explain.
Then we develop a version of the model and describe how
it measures risk. And nally we describe the results of
competing empirical studies of the models validity.
The Facts
Lets start by examining the facts: the historical data on
average returns for various types of assets. We focus on
historical average returns because the averages of returns
over long time horizons are good estimates of expected re-
turns. And estimating expected returns for different types
of assets is a signicant part of what the CAPM is sup-
posed to be able to do well.
Table 1 provides a summary of the average return his-
tory for four types of assets: stocks for large and small
rms, long-term U.S. Treasury bonds, and short-term U.S.
Treasury bills.
2
For each sample period, we report average annual rates
of return. If investors have rational expectations, then the
average returns over a fairly long horizon should be a rea-
sonable measure of expected returns. Notice that the his-
torical returns on different types of assets are substantially
different. The fact that investors did hold these assets im-
plies that investors would demand vastly different rates of
return for investing in different projects.
To the extent that the assets are claims to cash ows
from a variety of real activities, these facts support the
view that the cost of capital is very different for different
projects. During the 66-year period from 1926 to 1991,
for example, Standard & Poors 500-stock price index (the
S&P 500) earned an average annual return of 11.9 percent
whereas U.S. Treasury bills (T-bills) earned only 3.6 per-
cent. Since the average annual ination rate was 3.1 per-
cent during this period, the average real return on T-bills
was hardly different from zero. S&P stocks, therefore,
earned a hefty risk premium of 8.3 percent over the nomi-
nally risk-free return on T-bills. The performance of the
stocks of small rms was even more impressive; they
earned an average annual return of 16.1 percent.
To appreciate the economic importance of these differ-
ences in annual average, consider how the value of a dol-
lar invested in each of these types of assets in 1926 would
have changed over time. As Table 1 shows, by 1991, $1
invested in S&P stocks would be worth about $675,
whereas $1 invested in T-bills would be worth only $11.
Thats not much considering the fact that a market basket
of goods costing $1 in 1926 would cost nearly $8 in 1991.
For another perspective, consider what could have been
purchased in 1991 if $10 had been invested in each of
these assets in 1926. If $10 were invested in small-rm
stocks in 1926, by 1991 it would be worth an impressive
$18,476. Thats enough to cover one year of tuition in
most prestigious universities in the United States. Mean-
while, $10 invested in T-bills would be worth only $110
in 1991, or enough to buy dinner for two in a nice restau-
rant.
3
Notice in Table 1 that the assets with higher average
returns over 192691 also had more variable returns. This
correspondence suggests that the higher average returns
were compensation for some perceived higher risk. For
example, small-rm stocks, which yielded the highest re-
turn in this period, had the highest standard deviation too.
Similarly, in the rst two subperiods, 192675 and 1976
80, small-rm stocks had both the highest return and the
highest standard deviation.
However, something happened in the last subperiod,
198191, according to Table 1. Long-term government
bonds did extremely well. A dollar invested in Treasury
bonds at the end of 1980 would have grown to more than
$4 by the end of 1991, which implies a high annual rate
of return (14.2 percent). The risk premium (over T-bills)
on the S&P 500 for the 198191 subperiod was 7.7 per-
cent, not much different from that for the entire sample
period. However, during this subperiod, the average an-
nual return on T-bills of 8 percent was substantially more
than the average ination rate of 4.3 percent. This unusual
subperiod suggests that the sampling errors for the entire
period computed using conventional time series methods
(which assume that the entire time series is generated from
the same underlying distribution) may overstate the preci-
sion with which the sample averages measure the corre-
sponding population expectations.
Clearly, though, across all subperiods, the time series
of realized returns on these four types of assets are sub-
stantially different in both their average and their volatili-
ty. This can be seen in another way by examining Chart
1. There we display over the sample period 192691 the
logarithm of the values of one dollar invested in each as-
set in January 1926. For example, the values plotted for
December 1991 are logarithms of the numbers in Table 1.
We plotted the logarithms of the values so they could all
be easily displayed together on one chart and compared;
the values themselves are vastly different. The chart is in-
tended to further illustrate the great differences in the
paths of returns across the four assets.
These great differences are unlikely to be entirely acci-
dental. If investors had reasonable expectations in 1926,
they would have guessed that something like this would be
the outcome 66 years later, but still they were content to
invest in portfolios that included all of these different as-
sets. A question that needs to be answered is, In what way
are these assets different that makes investors content to
hold every one of them even though their average returns
are so different? For example, in what way are small-rm
stocks different from S&P 500 stocks that makes investors
satised with an 8.3 p