In the benchmark case of constant aggregate RRA the asset price increases
linearly in the dividend. In specification 1, the rather mild decline in aggre-
gate RRA produces a convex curve which mildly contrasts with the bench-
mark case. Specifications 2 and 3 deviate strongly from the benchmark case.
For low dividends, the asset price increases very little with the dividend, then
around a dividend level of 4, it increases strongly and, thereafter, it increases
almost proportionally as in the benchmark case. Hence, specifications 2 and
3 show the potential for a stock market crash, in contrast to the benchmark
case and specification 1. If, given specification 3, the dividend declines from
4.3 to 3.8, then the price of the market portfolio crashes from about 1,400 to
around 260. A small decline (less than 12 percent) in the dividend, the fun-
damental variable, triggers a very strong decline in the market value (more
than 80 percent). The reason is that the stock market switches from a low
to a high risk aversion regime. The mildly risk averse investors dominating
the market in the high dividend range basically disappear from the market
and the very risk averse investors take over and dominate the market. They
strongly pull down the asset price. If the dividend happens to first increase
from 3.8 to 4.3 and then to fall back to 3.8, then the asset price increases
from about 260 to 1,400 and then falls back to about 260. This can be
viewed as a bubble. Technicians would call 260 a support level and 1,400 a
resistance level.
The crash potential of specifications 2 and 3 is also illustrated by the strong
variability in the elasticity of the asset price with respect to the dividend
as shown in Figure 5. This elasticity varies only little with levels between
1 and 2 in specification 1, but it increases dramatically to more than 16 in
specifications 2 and 3 around a dividend level of 4 so that the local return
volatility will be quite high.
- insert Figure 5 here -
Figure 4 also illustrates return predictability. This exists if expected asset
returns depend on the dividend level or on the asset price. In Figure 4, the
expected asset return is reflected in the slope of the asset price curve. This
slope varies except for the benchmark case, its variation is particularly strong
for specifications 2 and 3, due to the crash potential. Another indicator of
predictability is the Sharpe-ratio. The simulation shows that except for the
benchmark case the Sharpe-ratio declines with increasing dividend, similar
to the aggregate RRA. This decline is particularly strong for specifications
2and3.
Although the equity premium puzzle is not at the center of our study we
would like to point out that declining aggregate RRA may also explain this
puzzle. Note that for declining aggregate RRA Sharpe ratios are high for
17