00Thaler_FM i-xxvi.qxd

S&P 500 index is 3.9 percent higher than the average log return on short-
term commercial paper.

Volatility. Stock returns and price–dividend ratios are both highly vari-
able. In the same data set, the annual standard deviation of excess log re-
turns on the S&P 500 is 18 percent, while the annual standard deviation of
the log price/dividend ratio is 0.27.

Predictability. Stock returns are forecastable. Using monthly, real, equal-
weighted NYSE returns from 1941 to 1986, Fama and French (1988) show
that the dividend/price ratio is able to explain 27 percent of the variation of
cumulative stock returns over the subsequent four years.^15

All three of these facts can be labelled puzzles. The first fact has been
known as the equity premium puzzle since the work of Mehra and Prescott
(1985) (see also Hansen and Singleton 1983). Campbell (1999) calls the
second fact the volatility puzzle and we refer to the third fact as the pre-
dictability puzzle. The reason they are called puzzles is that they are hard to
rationalize in a simple consumption-based model.
To see this, consider the following endowment economy, which we come
back to a number of times in this section. There are an infinite number of iden-
tical investors, and two assets: a risk-free asset in zero net supply, with gross
returnRf,tbetween time tand t+1, and a risky asset—the stock market—in
fixed positive supply, with gross return Rt+ 1 between time tand t+1. The
stock market is a claim to a perishable stream of dividends {Dt}, where

(3)

and where each period’s dividend can be thought of as one component of a
consumption endowment Ct, where

(4)

and

(5)

ε

η

ω

ω

t

t

N







































0

0

1

1

,,i.i.d.over time.

C

C

t g

t

CCt

+

=++

1

exp[ ση 1 ],

D

D

t g

t

DDt

+

=++

1

exp[ σε 1 ],

A SURVEY OF BEHAVIORAL FINANCE 23

(^15) These three facts are widely agreed on, but they are not completely uncontroversial. A
large literature had debated the statistical significance of the time series predictability, while
others have argued that the equity premium is overstated due to survivorship bias (Brown,
Goetzmann and Ross 1995).