Journal of Economic Perspectives—Volume18,Number3—Summer2004—Pages25–46 The Capital Ast Pricing Model: Theory and Evidence
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Eugene F.Fama and Kenneth R.French
中国有几大战区T he capital ast pricing model(CAPM)of William Sharpe(1964)and John Lintner(1965)marks the birth of ast pricing theory(resulting in a
Nobel Prize for Sharpe in1990).Four decades later,the CAPM is still widely ud in applications,such as estimating the cost of capital forfirms and evaluating the performance of managed portfolios.It is the centerpiece of MBA investment cours.Indeed,it is often the only ast pricing model taught in the cours.1
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 ud in applications.The CAPM’s empirical problems may reflect theoretical failings,the result of many simplifying assumptions.But they may also be caud 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 in
热心的clude not just tradedfinancial asts,but also consumer durables,real estate and human capital.Even if we take a narrow view of the model and limit its purview to tradedfinancial asts,is it
1Although every ast pricing model is a capital ast pricing model,thefinance profession rerves the acronym CAPM for the specific model of Sharpe(1964),Lintner(1965)and Black(1972)discusd here.Thus,throughout the paper we refer to the Sharpe-Lintner-Black model as the CAPM.
y 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 address are͗eugene.fama@gsb.uchicago. edu͘and͗kfrench@dartmouth.edu͘,respectively.
26Journal of Economic Perspectives
legitimate to limit further the market portfolio to stocks(a typical choice),or should the market be expanded to include bonds,and otherfinancial asts,perhaps around the world?In the end,we argue that whether the model’s problems reflect weakness 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 po 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 lects a portfolio at time tϪ1that produces a stochastic return at t.The model assumes investors are risk aver and,when choosing among portfolios,they care only about the mean and variance of their one-period investment return.As a result,investors choo“mean-variance-efficient”portfolios,in the n that the portfolios1)minimize the variance of portfolio return,given expected return,and2)maximize expected return,given variance.Thus,the Markowitz approach is often called a“mean-variance model.”
The portfolio model provides an algebraic condition on ast 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 ast prices are to
clear the market of all asts.
Sharpe(1964)and Lintner(1965)add two key assumptions to the Markowitz model to identify a portfolio that must be mean-variance-efficient.Thefirst assump-tion is complete agreement:given market clearing ast prices at tϪ1,investors agree on the joint distribution of ast returns from tϪ1to t.And this distribution is the true one—that is,it is the distribution from which the returns we u to test the model are drawn.The cond 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.
Figure1describes 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 asts that minimize return variance at different levels of ex-pected return.(The 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 a,must accept high volatility.At point T,the investor can have an interme-
diate expected return with lower volatility.If there is no risk-free borrowing or lending,only portfolios above b along abc are mean-variance-ef ficient,since the portfolios also maximize expected return,given their return variances.
Adding risk-free borrowing and lending turns the ef ficient t into a straight line.Consider a portfolio that invests the proportion x of portfolio funds in a risk-free curity and 1Ϫx in some portfolio g .If all funds are invested in the risk-free curity —that is,they are loaned at the risk-free rate of interest —the result is the point R f in Figure 1,a portfolio with zero variance and a risk-free rate of return.Combinations of risk-free lending and positive investment in g plot on the straight line between R f and g .Points to the right of g on the line reprent borrowing at the risk-free rate,with the proceeds from the borrowing ud to increa investment in portfolio g .In short,portfolios that combine risk-free lending or borrowing with some risky portfolio g plot along a straight line from R f through g in Figure 1.2
2
Formally,the return,expected return and standard deviation of return on portfolios of the risk-free ast f and a risky portfolio g vary with x ,the proportion of portfolio funds invested in f ,as
微波炉为什么不能用金属器皿
R p ϭxR f ϩ͑1Ϫx ͒R g ,
E ͑R p ͒ϭxR f ϩ͑1Ϫx ͒E ͑R g ͒,͑R p ͒ϭ͑1Ϫx ͒͑R g ͒,x Յ1.0,
which together imply that the portfolios plot along the line from R f through g in Figure 1.
Figure 1
Investment
Opportunities
Eugene F.Fama and Kenneth R.French 27
To obtain the mean-variance-efficient portfolios available with risk-free bor-rowing and lending,one swings a line from R f in Figure1up and to the left as far as possible,to the tangency portfolio T.We can then e that all efficient portfolios are combinations of the risk-free ast(either risk-free borrowing or lending)and a single risky tangency portfolio,T.This key result is Tobin’s(1958)“paration theorem.”
The punch line of the CAPM is now straightforward.With complete agreement about distributions of returns,all investors e the same opportunity t(Figure1), and they combine the same risky tangency portfolio T with risk-free lending or borrowing.Since all investors hold the same portfolio T of risky asts,it must be the value-weight market portfolio of risky asts.Specifically,each risky ast’s weight in the tangency portfolio,which we now call M(for the“market”),must be the total market value of all outstanding units of the ast divided by the total market value of all risky asts.In addition,the risk-free rate must be t(along with the prices of risky asts)to clear the market for risk-free borrowing and lending.
In short,the CAPM assumptions imply that the market portfolio M must be on the minimum variance frontier if the ast 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 N risky asts,
͑Minimum Variance Condition for M͒E͑R i͒ϭE͑R ZM͒
ϩ͓E͑R M͒ϪE͑R ZM͔͒iM,iϭ1,...,N. In this equation,E(R i)is the expected return on ast i,andiM,the market beta of ast i,is the covariance of its return with the market return divided by the variance of the market return,
͑Market Beta͒iMϭcov͑R i,R M͒2͑R M͒.
Thefirst term on the right-hand side of the minimum variance condition, E(R ZM),is the expected return on asts that have market betas equal to zero, which means their returns are uncorrelated with the market return.The cond term is a risk premium—the market beta of ast i,iM,times the premium per unit of beta,which is the expected market return,E(R M),minus E(R ZM).
Since the market beta of ast i 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 nsitivity of the ast’s return to v饭粒邪恶网
ariation 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 ofiM),is a weighted average of the covariance risks of the asts in M(the numerators ofiM for different asts). 28Journal of Economic Perspectives
The Capital Ast Pricing Model:Theory and Evidence29 Thus,iM is the covariance risk of ast i in M measured relative to the average covariance risk of asts,which is just the variance of the market return.3In economic terms,iM is proportional to the risk each dollar invested in ast i contributes to the market portfolio.
The last step in the development of the Sharpe-Lintner model is to u the assumption of risk-free borrowing and lending to nail down E(R ZM),the expected return on zero-beta asts.A risky ast’s return is uncorrelated with the market return—its beta is zero—when the average of the ast’s covariances with the returns on other asts just offts the variance of the ast’s return.Such a risky ast is riskless in the market portfolio in the n that it contributes nothing to the variance of the market return.
When there is risk-free borrowing and lending,the expected return on asts that are uncorrelated wi
th the market return,E(R ZM),must equal the risk-free rate, R f.The relation between expected return and beta then becomes the familiar Sharpe-Lintner CAPM equation,
͑Sharpe-Lintner CAPM͒E͑R i͒ϭR fϩ͓E͑R M͒ϪR f͒]iM,iϭ1,...,N.
In words,the expected return on any ast i is the risk-free interest rate,R f,plus a risk premium,which is the ast’s market beta,iM,times the premium per unit of beta risk,E(R M)ϪR f.
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 asts.In brief,back in Figure1,if there is no risk-free ast,investors lect portfolios from along the mean-variance-efficient frontier from a to b.Market clearing prices imply that when one weights the efficient portfolios chon 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 chon by investors.With unrestricted short lling of risky asts,portfolios made up of efficient portfolios are themlves efficient.Thus,the market portfolio is efficient,which means that the minimum variance condition for M 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 ZM),the expected return on asts uncorrelated with the market.The Black version says only that E(R ZM)must be less than the expected market return,so the 3Formally,if x
is the weight of ast i in the market portfolio,then the variance of the portfolio’s iM
宁波旅游return is
实训报告
2͑R M͒ϭCov͑R M,R M͒ϭCovͩiϭ1N x iM R i,R Mͪϭiϭ1N x iM Cov͑R i,R M͒.
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