Another well-known difficulty with consumption-based models is that
attempts to make them match features of the stock market often lead to
counterfactual predictions for the risk-free rate. For example, these models
typically explain the equity premium with a high curvature γof utility over
consumption. However, this high γalso leads to a strong desire to smooth
consumption intertemporally, generating high interest rates. Furthermore,
the habit formation feature that many consumption-based models use to
explain stock market volatility can also make interest rates counterfactually
volatile.^23
In our framework we use loss aversion over financial wealth fluctuations
rather than a high curvature of utility over consumption to explain the eq-
uity premium. We do not therefore generate a counterfactually high interest
rate. Moreover, since changes in risk aversion are driven by past stock mar-
ket performance rather than by consumption, we can maintain a stable, in-
deed constant interest rate.
One feature that our model does share with consumption-based models
like that of Campbell and Cochrane (1999) is contrarian expectations on
the part of investors. Since stock prices in these models are high when in-
vestors are less risk averse, these are also times when investor require—and
expect—lower returns than on average.
Durell (1999) has examined investor expectations about future stock
market behavior and found evidence of extrapolative, rather than contrar-
ian expectations. In other words, some investors appear to expect higher
than average returns precisely at market peaks. Shiller (1999) presents re-
sults of a survey of investor expectations over the course of the U.S. bull
market of the late 1990s. He finds no evidence of extrapolative expecta-
tions; but neither does he find evidence of contrarian expectations. It is not
clear whether the samples used by Durell and Shiller are representative of
the investing population, but they do suggest that the story in this chapter—
or indeed the consumption-based story—may not be a complete description
of the facts.
D. A Note on AggregationThe equilibrium pricing equations in subsections 4.A and 4.B are derived
under the assumption that the investors in our economy are completely ho-
mogeneous. This is certainly a strong assumption. Investors may be hetero-
geneous along numerous dimensions, which raises the question of whether
the intuition of our model still goes through once investor heterogeneity is
recognized. For any particular form of heterogeneity, we need to check that
246 BARBERIS, HUANG, SANTOS
(^23) Campbell and Cochrane’s paper (1999) is perhaps the only consumption-based model
that avoids problems with the risk-free rate. A clever choice of functional form for the habit
level over consumption enables them to use precautionary saving to counterbalance the strong
desire to smooth consumption intertemporally.