00Thaler_FM i-xxvi.qxd

between our approach and the consumption-based framework then be-
comes much clearer.
In both economies, we construct a one-factor Markov equilibrium in
which the risk-free rate is constant and the Markov state variable ztdeter-
mines the distribution of future stock returns. Specifically, we assume that
the price/dividend ratio of the stock is a function of the state variable zt:

(19)

and then show for each economy in turn that there is indeed an equilibrium
satisfying this assumption. Given the one-factor assumption, the distribu-
tion of stock returns Rt+ 1 is determined by ztand the function f(⋅) using

(20)

A. Stock Prices in Economy I

In the first economy we consider, consumption and dividends are modeled as
identical processes. We write the process for aggregate consumption as

(21)

where
t∼i.i.d. N(0,1). Note from equation (1) that the mean gDand
volatility σDof dividend growth are constrained to equal gCand σC, re-
spectively. Together with the one-factor Markov assumption, this means
that the stock return is given by

(22)

Intuitively, the value of the risky asset can change because of news about
consumption
t+ 1 or because the price/dividend ratio fchanges. Changes in
fare driven by changes in zt, which measures past gains and losses: past
gains make the investor less risk averse, raising f, while past losses make
him more risk averse, lowering f.
In equilibrium, and under rational expectations about stock returns and
aggregate consumption levels, the agents in our economy must find it opti-
mal to consume the dividend stream and to hold the market supply of zero
units of the risk-free asset and one unit of stock at all times.^17 Proposition 1
characterizes the equilibrium.^18

R

fz

fz

t t e

t

gCCt

+

= + + + +

1

1 () (^11)
()
σ
.
log(CCtt++ 11 / )==+log(DD gt t C Ct/ ) σ
+ 1 ,
Ct
R
PD
P
PD
PD
D
D
fz
fz
D
t D
tt
t
tt
tt
t
t
t
t
t
t

• = +++ = + +++= + ++
  1
  1111111 / 11
  /
  ()
  ()
  .
  fPDfzttt≡=/(),t
  PROSPECT THEORY AND ASSET PRICES 241
  (^17) We need to impose rational expectations about aggregate consumption because the
  agent’s utility includes aggregate consumption as a scaling term.
  (^18) We assume that log ρ+(1−γ)gC+0.5(1−γ) (^2) σC (^2) <0 so that the equilibrium is well be-
  haved at t=∞.