Here, ztis a state variable that tracks past gains and losses on the stock
market. For any fixed zt, the function υ ̃is a piecewise linear function similar
in form to υˆ, defined in Eq. (12). However, the investors’ sensitivity to
losses is no longer constant at 2.25, but is determined by zt, in a way that
reflects the experimental evidence described above.
A model of this kind can help explain the volatility puzzle. Suppose that
there is some good cash-flow news. This pushes the stock market up, gener-
ating prior gains for investors, who are now less scared of stocks: any losses
will be cushioned by the accumulated gains. They therefore discount future
cash flows at a lower rate, pushing prices up still further relative to current
dividends and adding to return volatility.
5.Application: The Cross-section of Average ReturnsWhile the behavior of the aggregate stock market is not easy to understand
from the rational point of view, promising rational models have nonethe-
less been developed and can be tested against behavioral alternatives. Em-
pirical studies of the behavior of individualstocks have unearthed a set of
facts which is altogether more frustrating for the rational paradigm. Many
of these facts are about the cross-sectionof average returns: they document
that one group of stocks earns higher average returns than another. These
facts have come to be known as “anomalies” because they cannot be ex-
plained by the simplest and most intuitive model of risk and return in the fi-
nancial economist’s toolkit, the Capital Asset Pricing Model (CAPM).
We now outline some of the more salient findings in this literature and
then consider some of the rational and behavioral approaches in more detail.
The Size Premium. This anomaly was first documented by Banz (1981).
We report the more recent findings of Fama and French (1992). Every year
from 1963 to 1990, Fama and French group all stocks traded on the NYSE,
AMEX, and NASDAQ into deciles based on their market capitalization,
and then measure the average return of each decile over the next year. They
find that for this sample period, the average return of the smallest stock
decile is 0.74 percent per month higher than the average return of the
largest stock decile. This is certainly an anomaly relative to the CAPM:
while stocks in the smallest decile do have higher betas, the difference in
risk is not enough to explain the difference in average returns.^23
A SURVEY OF BEHAVIORAL FINANCE 35that people are willing to take risks in order to avoid a loss; Thaler and Johnson’s (1990) evi-
dence suggests that if these efforts are unsuccessful and the investor suffers an unpleasant loss,
he will subsequentlyact in a more risk-averse manner.
(^23) The last decade of data has served to reduce the size premium considerably. Gompers and
Metrick (2001) argue that this is due to demand pressure for large stocks resulting from the
growth of institutional investors, who prefer such stocks.