one case that we will consider in more detail later: b 0 =2, k=3. To obtain
it, we draw a long time series {t}50,000t= 1 of 50,000 independent draws from
the standard normal distribution and starting with z 0 =1, use the function
zt+ 1 =h(zt, t+ 1 ) described in subsection V.B to generate a time series for zt.
Note from the graph that the average ztis close to one, and this is no acci-
dent. The value of in equation (10) is chosen precisely to make the me-
dian value of ztas close to one as possible.
As we generate the time series for ztperiod by period, we also compute
the returns along the way using equation (20). We now present sample mo-
ments computed from these simulated returns. The time series is long
enough that sample moments should serve as good approximations to pop-
ulation moments.
Table 7.2 presents the important moments of stock returns for different
values of b 0 and k. In the top panel, we vary b 0 and set kto 3, which keeps
average loss aversion over time close to 2.25. At one extreme we have
b 0 =0, the classic case considered by Mehra and Prescott (1985). As we
push b 0 up, the asset return moments eventually reach a limit that is well
approximated with a b 0 of 100. The table also reports the investor’s aver-
age loss aversion, calculated in the way described in the Appendix.
Note that as we raise b 0 while keeping kfixed, the equity premium goes
up. There are two forces at work here. As b 0 gets larger, prior outcomes af-
fect the investor more, causing his risk aversion to vary more, and hence
generating more volatile stock returns. Moreover, as b 0 grows, loss aversion
becomes a more important feature of the investor’s preferences, pushing up
RPROSPECT THEORY AND ASSET PRICES 251Figure 7.4. Distribution of the state variable zt. The distribution is based on Economy
I with b 0 =2 and k=3.
(^)