law of small numbers, whereby people expect even short samples to reflect
the properties of the parent population. If the investor sees many periods of
good earnings, the law of small numbers leads him to believe that earnings
growth has gone up, and hence that earnings will continue to be high in the
future. After all, the earnings growth rate cannot be “average.” If it were,
then according to the law of small numbers, earnings should appearaver-
age, even in short samples: some good earnings news, some bad earnings
news, but not several good pieces of news in a row.
Another belief-based story relies more on private, rather than public in-
formation, and in particular, on overconfidence about private information.
Suppose that an investor has seen public information about the economy,
and has formed a prior opinion about future cash-flow growth. He then
does some research on his own and becomes overconfident about the infor-
mation he gathers: he overestimates its accuracy and puts too much weight
on it relative to his prior. If the private information is positive, he will push
prices up too high relative to current dividends, again adding to return
volatility.^21
Price/dividend ratios and returns might also be excessively volatile be-
cause investors extrapolate past returnstoo far into the future when form-
ing expectations of future returns. Such a story might again be based on
representativeness and the law of small numbers. The same argument for
why investors might extrapolate past cash flows too far into the future can
be applied here to explain why they might do the same thing with past
returns.
The reader will have noticed that we do not cite any specific papers in
connection with these behavioral stories. This is because these ideas were
originally put forward in papers whose primary focus is explaining cross-
sectionalanomalies such as the value premium, even though they also apply
here in a natural way. In brief, many of those papers—which we discuss in
detail in section 5—generate certain cross-sectional anomalies by building
excessive time series variation into the price/earnings ratios of individual
stocks. It is therefore not surprising that the mechanisms proposed there
might also explain the substantial time series variation in aggregate-level
price/earnings ratios. In fact, it is perhaps satisfying that these behavioral
theories simultaneously address both aggregate and firm-level evidence.
A SURVEY OF BEHAVIORAL FINANCE 33(^21) Campbell (2000), among others, notes that behavioral models based on cash-flow fore-
casts often ignore potentially important interest rate effects. If investors are forecasting exces-
sively high cash-flow growth, pushing up prices, interest rates should also rise, thereby dampening
the price rise. One response is that interest rates are governed by expectations about consump-
tiongrowth, and in the short run, consumption and dividends can be somewhat delinked:
even if dividend growth is expected to be high, this need not necessarily trigger an immediate
interest rate response. Alternatively, one can try to specify investors’ expectations in such a
way that interest rate effects become less important. Cecchetti, Lam, and Mark (2000) take a
step in this direction.