Risk aversion and asset prices

er.
if
O#ad,
on informzei availabie 23~the
ion operator mnditional
jht tith cm-refit consumption c,,
to comb
to compute utility at P, i.e.,
is specified as the CES form
?VhYWiX,
(c, z) =
[cp+ zyp,
c,zlO,
O#p<l,
Oqkl.
(4
us utility is defined recursively by
Q=
t2 o.
[c/‘+
P(Etv+l)P’a]l’p,
(3)
a
%is
czi
W
=
H
st-+
,t+B
”
.
s
--k
9
9
W
(a---
cave
ce
is
190
L 6. Epstein, Ri; k aversionand assetprices
comparative risk aversion analysis
change in prices is ambiguous if u
cas.
the issue of the circumstances u
artingale property. It is well
generally not a feature of
states ‘that the presence of
for current consumption is inconsistent
odel, even with 8,‘s correlated
see from (20) that only if a = p = 1 do we obtain the simple
discounting formulae
P(s,) = Bhh +PwL
erfect intertemporal substitutability (a = ao) and risk neutrality
( a = 1) are necessary for these relations to be valid.
f(0) > 0 ) f(co). Thus 3y* > 0, f( y*) = 0.
hus y* is the unique zero of f.
Step 2: Show that (22) possesses a unique solution. It suffices to prove
existence and uniqueness of
n_l
solving fqKi)=O, j=l,...,
(
&.l)p+ K*pqa-P)‘P
1
a soWion
(Si+pi(s))](p-l)‘p,
which is a form of ‘converse’ for (1
From (11)
,A(S)P/o-P)=
for some constant
derive
l+
3(
Substitute the latter equation into ( 03) and (10) to
192
LG. Epstein, Risk aversionand assetprices
intertemporal asset pricing model with stochastic consumption and
f Financial Economics 7,265296.
prices in a production economy, in: J.J.
rtainty (University of Chicago Press, Chi
stein, 1987, Non-expected utility preferences in a temporal framework
n to consumptionGavings haviour, Working paper 8701 (University of
intertemporal asset
aaldson, J.B. and Mehra, 1984, Comparative dynamics of an equihb
w of Economic Studies 51,491-508.
.E. Zin, 1987a, Substitution, risk aversion and the temporal behaviour of
asset returns I: A theorttical framework, Working paper 8715 (University of
Toronto, Toronto).
Epstein L.G. and S.E. Zin, 1987b, Substitution, risk aversion and the temporal behaviour of
consumption and asset returns II: An empirical analysis, Working paper 8718 (University of
Toronto, Toronto).
Farmer, R.E.A., 1987, Closed-form sohuions to dynamic stochastic choice problems (University of
Stochastic consumption, risk aversion, and the temporal
of PoIitical Economy 91,249-265.
1972, Capital markets: Theory and evidence, Bell JoumaI of Economics and
nt Science 3,357-398
Johnsen, T&I. and %.I%Donaldson, 1985, The structure of intertemporal preferences under
uncertainty and time consistent plans, Econometrica 53,1451-1458.
.J. lvfirman, 1974, Risk aversion with many commodities, Journal of
Kihlstrom, R
Economic
oopmans, T
aI utility and impatience, Econometrica 28,287-309.
Kreps, D.M. and E.L. Porteus, 1978, Temporal resolution of uncertainty and dynamic choice
Econometrica 46,185-200.
E
1986, Comparative dynamics and risk premia in an overlapping generations model,
evlew’bf Economic Studies 53,139-152.
ale property of stock prices, International
,
, Journal
an exchange economy, Econometrica 46,1429-1446.
Optimal growth with many consumers, Journal of Economic
:
A puzzle, Journal of Monetary Economics
onometrica 41,867-887.
: The case of homogeneous
aving under risk preference
aeo. (
ard University,