are separated out. We show that there is an equilibrium in which the risk-
free rate and the stock’s price/dividend ratio are both constant and stock re-
turns are i.i.d.
Proposition 3.For the preferences given by (39)–(41), there exists an
equilibrium in which the gross risk-free interest rate is constant at(42)
and the stock’s price/dividend ratio, ft, is constant at fand given by(43)where(44)That returns are i.i.d. is a direct consequence of the fact that the
price/dividend ratio is constant. To see this, note that the stock return is re-
lated to the stock’s price/dividend ratio, denoted by ft≡Pt/Dt, as follows:
(45)Given the assumption that the dividend growth is i.i.d. (see [1]), a constant
price/dividend ratio ft=fimplies that stock returns are i.i.d.
Table 7.12 summarizes our choices of parameter values. Many of the pa-
rameters of the earlier model now no longer play a role. The parameters
that remain are gC, gD, σC, σD, γ, ρ, γ, and b 0 , and we assign them exactly
the same values as those chosen earlier. For comparison, we list the earlier
parameters alongside.
Figure 7.7 presents the implied values of the price/dividend ratio and eq-
uity premium for different values of b 0 and table 7.13 reports uncondi-
tional moments of returns. By comparing the results in table 7.13 with
those in the bottom panel of table 7.4, we can isolate the impact of prior
outcomes.
Our results suggest that a model which relies on loss aversion alone can-
not provide a complete description of aggregate stock market behavior.
RPD
PPD
PDD
Df
fD
t Dtt
ttt
ttt
tt
tt
t+++ +++ ++
=+
=+
=+
11111111 / 11
/.ˆ()
()for
.,
,,
,vRRR
RRRR
t RRtft
tfttft
tft
++
++
+=−
−
≥(^1) <
1
1
1
λ 1
1
1
1
(^2221)
1
12
0
+
−+ − −
ρ
ρ
γγσ ω σ γωσ
σ
e
f
f
e
bv
f
f
e
gg
t
t
g
DCCDCt
DDt
()/ E[()]
E ˆ ,
Ref=ρ−^1 gC− C^2
γγσ^22 /
,
262 BARBERIS, HUANG, SANTOS