00Thaler_FM i-xxvi.qxd

framework can be used for portfolio choice and pricing problems, even when
state equations and objective functions are nonlinear.
Maenhout (1999) applies the Anderson et al. framework to the specific
issue of the equity premium. He shows that if investors are concerned that
their model of stock returns is misspecified, they will charge a substantially
higher equity premium as compensation for the perceived ambiguity in the
probability distribution. He notes, however, that to explain the full 3.9 per-
cent equity premium requires an unreasonably high concern about misspec-
ification. At best then, ambiguity aversion is only a partial resolution of the
equity premium puzzle.

4.2. The Volatility Puzzle

Before turning to behavioral work on the volatility puzzle, it is worth
thinking about how rational approaches to this puzzle might proceed.
Since, in the data, the volatility of returns is higher than the volatility of
dividend growth, Eq. (8) makes it clear that we have to make up the gap by
introducing variation in the price/dividend ratio. What are the different
ways we might do this? A useful framework for thinking about this is a ver-
sion of the present value formula originally derived by Campbell and
Shiller (1988). Starting from

(13)

where Ptis the value of the stock market at time t, they use a log-linear ap-
proximation to show that the log price/dividend ratio can be written

(14)

where lower case letters represent log variables—Pt=log Pt, for example—
and where ∆dt+ 1 =dt+ 1 −dt.
If the price/dividend ratio is stationary, so that the third term on the right
is zero, this equation shows clearly that there are just two reasons price/div-
idend ratios can move around: changing expectations of future dividend
growth or changing discount rates. Discount rates, in turn, can change be-
cause of changing expectations of future risk-free rates, changing forecasts
of risk or changing risk aversion.
While there appear to be many ways of introducing variation in the P/D
ratio, it has become clear that most of them cannot form the basis of a
rational explanation of the volatility puzzle. We cannot use changing forecasts

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A SURVEY OF BEHAVIORAL FINANCE 31