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Amos Tuck School of Business at Dartmouth College Working Paper No. 03-26 Center for Research in Security Prices (CRSP) University of Chicago Working Paper No. 550

The CAPM: Theory and Evidence
Eugene F. Fama
University of Chicago

Kenneth R. French
Dartmouth College; MIT; NBER

August 2003

This paper can be downloaded without charge from the Social Science Research NetworkElectronic Paper Collection at: http:/ssrn.com/abstract=440920

First draft: August 2003 Not for quotation Comments solicited

The CAPM: Theory and Evidence by Eugene F. Fama and Kenneth R. French* The 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). Before their breakthrough,there were no asset pricing models built from first principles about the nature of tastes and investment opportunities and with clear testable predictions about risk and return. Four decades later, the CAPM is still widely used in applications, such as estimating the cost of equity capital for firms and evaluating the performance of managed portfolios. And it is the centerpiece, indeed often theonly asset pricing model taught in MBA level investment courses. The attraction of the CAPM is its powerfully simple logic and intuitively pleasing predictions about how to measure risk and about the relation between expected return and risk. Unfortunately, perhaps because of its simplicity, the empirical record of the model is poor – poor enough to invalidate the way it is used in applications. Themodel’s empirical problems may reflect true failings. (It is, after all, just a model.) But they may also be due to shortcomings of the empirical tests, most notably, poor proxies for the market portfolio of invested wealth, which plays a central role in the model’s predictions. We argue, however, that if the market proxy problem invalidates tests of the model, it also invalidates mostapplications, which typically borrow the market proxies used in empirical tests. For perspective on the CAPM’s predictions about risk and expected return, we begin with a brief summary of its logic. We then review the history of empirical work on the model and what it says about shortcomings of the CAPM that pose challenges to be explained by more complicated model . s
*

Graduate School of Business,University of Chicago (Fama), and Tuck School of Business, Dartmouth College (French).

I. The CAPM The CAPM builds on Harry Markowitz’ (1952, 1959) mean-variance portfolio model. In Markowitz’ model, an investor selects a portfolio at time t-1 that produces a random return Rpt at t. The model assumes that investors are risk averse and, when choosing among portfolios, they care only about the meanand variance of their one-period investment return. The model’s main result follows from these assumptions. Specifically, the portfolios relevant for choice by investors are mean-variance efficient, which means (i) they minimize portfolio return variance, s 2 (Rpt ), given expected return, E(Rpt ), and (ii) they maximize expected return given variance. The way assets combine to produce efficientportfolios provides the template for the relation between expected return and risk in the CAPM. Suppose there are N risky assets available to investors. It is easy to show that the portfolio e that minimizes return variance, subject to delivering expected return E(Re), allocates proportions of invested wealth, xie (

∑

N i =1

x ie = 1.0) , to portfolio assets so as to produce a

linearrelation between the expected return on any asset i and its beta risk in portfolio e, (1a)

E ( Ri ) = E( Rze ) + [ E( Re ) − E( Rze )]β ie ,
Cov( Ri , Re ) βie = = σ 2 ( Re )

i=1,…,N,

(1b)

∑

x x Cov ( Ri , Rj ) i =1 ie ∑ j =1 je
N N

∑

N j =1

x jeCov ( Ri , Rj )

.

In these equations, Cov denotes a covariance, E(Rze) is the expected return on assets whose returns are...