Stocks simply do not appear risky to investors with the preferences in Eq. (6)
and with low γ, and therefore do not warrant a large premium. Of course,
the equity premium predicted by the model can be increased by using
higher values of γ. However, other than making counterintuitive predictions
about individuals’ attitudes to large-scale gambles, this would also predict a
counterfactually high risk-free rate, a problem known as the risk-free rate
puzzle (Weil 1989).
To understand the volatility puzzle, note that in the simple economy de-
scribed above, both discount rates and expected dividend growth are con-
stant over time. A direct application of the present value formula implies
that the price/dividend ratio, P/D henceforth, is constant. Since
(8)it follows that
rt+ 1 =∆dt+ 1 +const.≡dt+ 1 −dt+const., (9)where lower case letters indicate log variables. The standard deviation of
log returns will therefore only be as high as the standard deviation of log
dividend growth, namely 12 percent.
The particular volatility puzzle seen here illustrates a more general point,
first made by Shiller (1981) and LeRoy and Porter (1981), namely that it is
difficult to explain the historical volatility of stock returns with any model
in which investors are rational and discount rates are constant.
To see the intuition, consider the identity in Eq. (8) again. Since the
volatility of log dividend growth is only 12 percent, the only way for a
model to generate an 18 percent volatility of log returns is to introduce
variation in the P/D ratio. But if discount rates are constant, a quick glance
at a present-value formula shows that the only way to do that is to intro-
duce variation in investors’ forecasts of the dividend growth rate: a higher
forecast raises the P/D ratio, a lower forecast brings it down. There is a
catch here, though: if investors are rational, their expectations for dividend
growth must, on average, be confirmed. In other words, times of higher
(lower) P/D ratios should, on average, be followed by higher (lower) cash-
flow growth. Unfortunately, price/dividend ratios are notreliable forecasters
of dividend growth, neither in the United States nor in most international
markets (see Campbell 1999, for recent evidence).
Shiller and LeRoy and Porter’s results shocked the profession when they
first appeared. At the time, most economists felt that discount rates were
close to constant over time, apparently implying that stock market volatil-
ity could only be fully explained by appealing to investor irrationality.
Today, it is well understood that rational variation in discount rates can
RDP
PPD
PDD
t Dtt
ttt
ttt
t+
= +++ = + +++
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/,A SURVEY OF BEHAVIORAL FINANCE 25