loss aversion remains in the aggregate and, moreover, that aggregate loss
aversion still varies with prior stock market movements. If these two ele-
ments are still present, our model should still be able to generate a high pre-
mium, volatility, and predictability.
One form of heterogeneity does aggregate satisfactorily: this is the case
where investors have different wealth levels, but identical wealth to income
ratios. We can model this by having several cohorts of investors, each co-
hort containing a continuum of equally wealthy investors. Since wealth is
not a nontrivial state variable, all our results go through.^24
There is reason to hope that our intuition will also survive other forms of
heterogeneity. For example, it is possible that investors differ in the extent
of their prior gains or losses, perhaps because they entered the stock market
at different times. In other words, investors may have different zts.
Note that even if ztvaries across investors, each individual investor is still
more sensitive to losses than to gains, and there is no reason to believe that
this will be lost in the aggregate. Hence there is no reason to think that the
equity premium will be much reduced in the presence of this kind of hetero-
geneity. Furthermore, if the stock market experiences a sustained rise, this
will increase prior gains for most investors, making them less risk averse.
Therefore, it is very reasonable to think that risk aversion will also fall in
the aggregate. If aggregate loss aversion still varies over time, our model
should still be able to generate substantial volatility and predictability.
5 .Numerical Results and Further DiscussionIn this section we present price/dividend ratios f(zt) that solve equations
(24) and (34). We then create a long time series of simulated data and use it
to compute various moments of asset returns which can be compared with
historical numbers. We do this for both economies described in section 4:
Economy I, where stocks are modeled as a claim to the consumption
stream; and the more realistic Economy II where stocks are a claim to divi-
dends, which are no longer the same as consumption.
A. Parameter ValuesTable 7.1 summarizes our choice of parameter values for Economy I. For gC
and σC, the mean and standard deviation of log consumption growth, we
follow Cecchetti, Lam, and Mark (1990) who obtain gC=1.84 percent and
σC=3.79 percent from a time series of annual data from 1889 to 1985.
PROSPECT THEORY AND ASSET PRICES 247(^24) The only subtlety is that since aggregate consumption enters preferences, we need to
assume that people use the average consumption of a reference group of people with identical
wealth to set Ct, rather than average consumption in the economy as a whole.
Ct