TheCapitalAssetPricingModel-TheoryAndEvidence(FamaFrenchJEP2004).pdf

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Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004 —Pages 25– 46

The Capital Asset Pricing Model:

Theory and Evidence

Eugene F. Fama and Kenneth R. French

he capital asset pricing model (CAPM) of William Sharpe (1964) and John

Lintner (1965) marks the birth of asset pricing theory (resulting in a

Nobel Prize for Sharpe in 1990). Four decades later, the CAPM is still

widely used in applications, such as estimating the cost of capital for ﬁrms and

evaluating the performance of managed portfolios. It is the centerpiece of MBA

investment courses. Indeed, it is often the only asset pricing model taught in these

courses.

The attraction of the CAPM is that it offers powerful and intuitively pleasing

predictions about how to measure risk and the relation between expected return

and risk. Unfortunately, the empirical record of the model is poor—poor enough

to invalidate the way it is used in applications. The CAPM’s empirical problems may

reﬂect theoretical failings, the result of many simplifying assumptions. But they may

also be caused by difﬁculties in implementing valid tests of the model. For example,

the CAPM says that the risk of a stock should be measured relative to a compre-

hensive “market portfolio” that in principle can include not just traded ﬁnancial

assets, but also consumer durables, real estate and human capital. Even if we take

a narrow view of the model and limit its purview to traded ﬁnancial assets, is it

Although every asset pricing model is a capital asset pricing model, the ﬁnance profession reserves the

acronym CAPM for the speciﬁc model of Sharpe (1964), Lintner (1965) and Black (1972) discussed

here. Thus, throughout the paper we refer to the Sharpe-Lintner-Black model as the CAPM.

Eugene F. Fama is Robert R. McCormick Distinguished Service Professor of Finance,

Graduate School of Business, University of Chicago, Chicago, Illinois. Kenneth R. French is

Carl E. and Catherine M. Heidt Professor of Finance, Tuck School of Business, Dartmouth

College, Hanover, New Hampshire. Their e-mail addresses are eugene.fama@gsb.uchicago.

edu and kfrench@dartmouth.edu , respectively.

Journal of Economic Perspectives

legitimate to limit further the market portfolio to U.S. common stocks (a typical

choice), or should the market be expanded to include bonds, and other ﬁnancial

assets, perhaps around the world? In the end, we argue that whether the model’s

problems reﬂect weaknesses in the theory or in its empirical implementation, the

failure of the CAPM in empirical tests implies that most applications of the model

are invalid.

We begin by outlining the logic of the CAPM, focusing on its predictions about

risk and expected return. We then review the history of empirical work and what it

says about shortcomings of the CAPM that pose challenges to be explained by

alternative models.

The Logic of the CAPM

The CAPM builds on the model of portfolio choice developed by Harry

Markowitz (1959). In Markowitz’s model, an investor selects a portfolio at time

1 that produces a stochastic return at

The model assumes investors are risk

averse and, when choosing among portfolios, they care only about the mean and

variance of their one-period investment return. As a result, investors choose “mean-

variance-efﬁcient” portfolios, in the sense that the portfolios 1) minimize the

variance of portfolio return, given expected return, and 2) maximize expected

return, given variance. Thus, the Markowitz approach is often called a “mean-

variance model.”

The portfolio model provides an algebraic condition on asset weights in mean-

variance-efﬁcient portfolios. The CAPM turns this algebraic statement into a testable

prediction about the relation between risk and expected return by identifying a

portfolio that must be efﬁcient if asset prices are to clear the market of all assets.

Sharpe (1964) and Lintner (1965) add two key assumptions to the Markowitz

model to identify a portfolio that must be mean-variance-efﬁcient. The ﬁrst assump-

tion is

complete agreement:

given market clearing asset prices at

1, investors agree

on the joint distribution of asset returns from

1 to

And this distribution is the

true one—that is, it is the distribution from which the returns we use to test the

model are drawn. The second assumption is that there is

borrowing and lending at a

risk-free rate,

which is the same for all investors and does not depend on the amount

borrowed or lent.

Figure 1 describes portfolio opportunities and tells the CAPM story. The

horizontal axis shows portfolio risk, measured by the standard deviation of portfolio

return; the vertical axis shows expected return. The curve

abc,

which is called the

minimum variance frontier, traces combinations of expected return and risk for

portfolios of risky assets that minimize return variance at different levels of ex-

pected return. (These portfolios do not include risk-free borrowing and lending.)

The tradeoff between risk and expected return for minimum variance portfolios is

apparent. For example, an investor who wants a high expected return, perhaps at

point

must accept high volatility. At point

the investor can have an interme-

Eugene F. Fama and Kenneth R. French

Figure 1

Investment Opportunities

E(R

)

Mean-variance-

efﬁcient frontier

with a riskless asset

Minimum variance

frontier for risky assets

s(R

)

diate expected return with lower volatility. If there is no risk-free borrowing or

lending, only portfolios above

along

abc

are mean-variance-efﬁcient, since these

portfolios also maximize expected return, given their return variances.

Adding risk-free borrowing and lending turns the efﬁcient set into a straight

line. Consider a portfolio that invests the proportion

of portfolio funds in a

risk-free security and 1

in some portfolio

If all funds are invested in the

risk-free security—that is, they are loaned at the risk-free rate of interest—the result

is the point

in Figure 1, a portfolio with zero variance and a risk-free rate of

return. Combinations of risk-free lending and positive investment in

plot on the

straight line between

and

Points to the right of

on the line represent

borrowing at the risk-free rate, with the proceeds from the borrowing used to

increase investment in portfolio

In short, portfolios that combine risk-free

lending or borrowing with some risky portfolio

plot along a straight line from

through

in Figure 1.

Formally, the return, expected return and standard deviation of return on portfolios of the risk-free

asset

and a risky portfolio

vary with

the proportion of portfolio funds invested in

E R

x R

x E R

1.0,

which together imply that the portfolios plot along the line from

through

in Figure 1.

Journal of Economic Perspectives

To obtain the mean-variance-efﬁcient portfolios available with risk-free bor-

rowing and lending, one swings a line from

in Figure 1 up and to the left as far

as possible, to the tangency portfolio

We can then see that all efﬁcient portfolios

are combinations of the risk-free asset (either risk-free borrowing or lending) and

a single risky tangency portfolio,

This key result is Tobin’s (1958) “separation

theorem.”

The punch line of the CAPM is now straightforward. With complete agreement

about distributions of returns, all investors see the same opportunity set (Figure 1),

and they combine the same risky tangency portfolio

with risk-free lending or

borrowing. Since all investors hold the same portfolio

of risky assets, it must be

the value-weight market portfolio of risky assets. Speciﬁcally, each risky asset’s

weight in the tangency portfolio, which we now call

(for the “market”), must be

the total market value of all outstanding units of the asset divided by the total

market value of all risky assets. In addition, the risk-free rate must be set (along with

the prices of risky assets) to clear the market for risk-free borrowing and lending.

In short, the CAPM assumptions imply that the market portfolio

must be on

the minimum variance frontier if the asset market is to clear. This means that the

algebraic relation that holds for any minimum variance portfolio must hold for the

market portfolio. Speciﬁcally, if there are

risky assets,

Minimum Variance Condition for

E R

1, . . . ,

In this equation,

E(R

) is the expected return on asset

and

, the market beta

of asset

is the covariance of its return with the market return divided by the

variance of the market return,

cov

Market Beta

The ﬁrst term on the right-hand side of the minimum variance condition,

E(R

), is the expected return on assets that have market betas equal to zero,

which means their returns are uncorrelated with the market return. The second

term is a risk premium—the market beta of asset

, times the premium per

unit of beta, which is the expected market return,

E(R

), minus

E(R

Since the market beta of asset

is also the slope in the regression of its return

on the market return, a common (and correct) interpretation of beta is that it

measures the sensitivity of the asset’s return to variation in the market return. But

there is another interpretation of beta more in line with the spirit of the portfolio

model that underlies the CAPM. The risk of the market portfolio, as measured by

the variance of its return (the denominator of

), is a weighted average of the

covariance risks of the assets in

(the numerators of

for different assets).

The Capital Asset Pricing Model: Theory and Evidence

Thus,

is the covariance risk of asset

measured relative to the average

covariance risk of assets, which is just the variance of the market return.

economic terms,

is proportional to the risk each dollar invested in asset

contributes to the market portfolio.

The last step in the development of the Sharpe-Lintner model is to use the

assumption of risk-free borrowing and lending to nail down

E(R

), the expected

return on zero-beta assets. A risky asset’s return is uncorrelated with the market

return—its beta is zero—when the average of the asset’s covariances with the

returns on other assets just offsets the variance of the asset’s return. Such a risky

asset is riskless in the market portfolio in the sense that it contributes nothing to the

variance of the market return.

When there is risk-free borrowing and lending, the expected return on assets

that are uncorrelated with the market return,

E(R

), must equal the risk-free rate,

. The relation between expected return and beta then becomes the familiar

Sharpe-Lintner CAPM equation,

Sharpe-Lintner CAPM

E R

]

1, . . . ,

In words, the expected return on any asset

is the risk-free interest rate,

, plus a

risk premium, which is the asset’s market beta,

, times the premium per unit of

beta risk,

E(R

)

Unrestricted risk-free borrowing and lending is an unrealistic assumption.

Fischer Black (1972) develops a version of the CAPM without risk-free borrowing or

lending. He shows that the CAPM’s key result—that the market portfolio is mean-

variance-efﬁcient— can be obtained by instead allowing unrestricted short sales of

risky assets. In brief, back in Figure 1, if there is no risk-free asset, investors select

portfolios from along the mean-variance-efﬁcient frontier from

Market

clearing prices imply that when one weights the efﬁcient portfolios chosen by

investors by their (positive) shares of aggregate invested wealth, the resulting

portfolio is the market portfolio. The market portfolio is thus a portfolio of the

efﬁcient portfolios chosen by investors. With unrestricted short selling of risky

assets, portfolios made up of efﬁcient portfolios are themselves efﬁcient. Thus, the

market portfolio is efﬁcient, which means that the minimum variance condition for

given above holds, and it is the expected return-risk relation of the Black CAPM.

The relations between expected return and market beta of the Black and

Sharpe-Lintner versions of the CAPM differ only in terms of what each says about

E(R

), the expected return on assets uncorrelated with the market. The Black

version says only that

E(R

) must be less than the expected market return, so the

Formally, if

is the weight of asset

in the market portfolio, then the variance of the portfolio’s

return is

Cov R

Cov

Cov R

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