The capital asset pricing model (CAPM) provides an appealing explanation of the
relationship between risk and asset returns. The authors summarize the theory
and review empirical tests of the CAPM. The CAPM fails to fully explain the
relationship between risk and returns. They conclude that the empirical failures
of the CAPM invalidate most of its applications.
The capital asset pricing model (CAPM) builds on the Markowitz
mean–variance-efficiency model in which risk-averse investors with a one-period
horizon care only about expected returns and the variance of returns (risk). These
investors choose only efficient portfolios with minimum variance, given expected return,
and maximum expected return, given variance. Expected returns and variance plot a
parabola, and points above its global minimum identify a mean–variance-efficient
frontier of risky assets.
Sharpe–Lintner CAPM theory converts the mean–variance model into a
market-clearing asset-pricing model. All investors agree on the distributions of returns
and may borrow or lend without limit at a risk-free rate. The risk-free rate clears the
market for borrowing and lending. Combining the risk-free asset and risky assets results
in a linear mean–variance-efficient frontier that is tangent to the efficient
frontier/risky asset frontier. All who hold risky assets hold this tangent portfolio,
the value-weighted portfolio of all risky assets. The CAPM implies that the market
portfolio is efficient.
The Sharpe–Lintner version assumes a risk-free rate, whereas the Black version of
the CAPM allows unlimited short selling. Both imply that beta, the covariance of asset
returns with the market relative to variance of the market, is sufficient to explain
differences in asset or portfolio expected returns and that the relationship between
beta and expected returns is positive. The risk-free rate is the intercept in the
Sharpe–Lintner version, but the Black version requires only that the expected
market return be greater than the expected return on assets that are uncorrelated with
the market.
Early cross-sectional and time-series regression tests on the linear relationship between
asset returns and beta show that although the relationship is approximately linear, the
observed slope is flatter than the slope predicted by the Sharpe–Linter CAPM.
Other early tests find no improvement from additional explanatory variables, indicating
that the market proxy portfolio is efficient. This finding is consistent with the Black
version.
More recent tests, both cross-sectional and time series, find that variables such as
size, earnings to price, debt to equity, and the book-to-market ratio (B/M) provide
explanatory power not captured by beta. These studies confirm the now-recognized
empirical flaws in both the Sharpe–Lintner and the Black versions of the CAPM.
Behavioralists interpret the results as evidence of irrational pricing caused by
investor overreaction. The rational pricing interpretation is that a more sophisticated
asset-pricing model is needed.
The intertemporal CAPM expands investor behavior to include values of future state
variables, such as labor income, consumer goods prices, and investment alternatives,
after the initial period. Additional betas capture the effects of these variables in
multifactor models. The most common is the three-factor model that relates expected
excess return to excess market return, measures the difference in returns between small-
and big-company portfolios, and measures the difference between returns on portfolios
with high and low B/Ms.
The three-factor model captures variations in asset returns that the CAPM misses.
Behavioralists argue that violations of the CAPM reflect irrational pricing that the
three-factor model catches with the B/M factor. In fact, it is impossible to tell
whether the problem in explaining returns is because of irrational pricing or rational
pricing in an incomplete model. Testing the CAPM is difficult because of lack of
theoretical or empirical clarity on what constitutes the market portfolio. Some argue
that it is impossible to test the CAPM because empirical results test whether the market
portfolio proxy is efficient but tell nothing about the CAPM. Efforts to find a
reasonably efficient proxy have extended the market portfolio to include assets other
than stocks and international assets. Still, the market proxy is ineffective because
adding the B/M and other variables in regressions effectively annuls the CAPM-predicted
beta–expected return relationship.
The authors conclude that the power of variables other than beta to explain average
returns invalidates most CAPM applications. They specifically reject using the CAPM to
estimate the cost of equity capital and to evaluate performance of mutual fund managers.