ingredients are truly necessary. After all, Benartzi and Thaler (1995) show
that a loss-averse investor is very reluctant to allocate much of his portfolio
to stocks even when faced with the large historical equity premium. This
suggests that perhaps an equilibrium model with loss aversion alonewould
be enough to understand the data. Is it really necessary to incorporate the
effect of prior outcomes?
We answer this by examining the predictions of a version of the model of
section 2 which ignores the effect of prior outcomes. In particular, we make
the utility vof a gain or loss a function of the gain or loss Xt+ 1 alone, and
remove the dependence on the state variable zt. In this model, the degree of
loss aversion is the same in all circumstances, regardless of the investor’s
prior investment performance.
More formally, the investor chooses consumption Ctand an allocation to
the risky asset Stto maximize
(39)subject to the standard budget constraint, where
(40)and
(41)The next proposition presents the equations that govern equilibrium
prices in an economy like Economy II where consumption and dividends
vXX
XX
t Xt
tt
t() for
+.+
++
+=
≥(^1) <
1
1
1
1
0
λ 0
XSRSRttttft++11,=−,
E(),ρ
γ
ρ
γ
t t
t
t
t
t
C
bvX
1
1
1
0 1
−
=
∞
−
∑
PROSPECT THEORY AND ASSET PRICES 261Table 7.11
Sensitivity of Asset Returns to the Reference LevelEmpirical
0% −1% −2% ValueLog excess stock return
Mean 5.02 4.11 3.43 6.03
Standard deviation 23.84 24.25 25.20 20.02
Sharpe ratio 0.21 0.17 0.14 0.3
Average loss aversion 3.5 3.5 3.7
A “0%” reference level means that the investor compares the stock return with the risk-free
rate when measuring gains and losses. “−1%” means a reference level one percent lower than
the risk-free rate. Moments of asset returns are expressed as annual percentages. The results are
for Economy II with b 0 =2 and k=10; other parameters are fixed at the values in table 7.3.