two rows of Table 2 are positive indicating volatility clustering. Again, this
does not rule out varying signs of local autocorrelation.The autocorrelations
are small for specification 1, but quite high for specifications 2 and 3. The
high volatility in the crash region reinforces volatility clustering. To con-
clude, this section has demonstrated that declining aggregate RRA makes
excess returns overreact, makes expected excess returns and return volatil-
ities predictable, generates excess return volatility and volatility clustering,
and, perhaps most importantly, can explain stock market crashes.
5 Conclusion
This paper argues that in a perfect capital market with rational, heteroge-
neously risk averse investors asset pricing is likely to be characterized by
declining aggregate relative risk aversion (RRA). Therefore the paper ana-
lyzes the impact of declining aggregate RRA on asset returns in a simple
rational expectations model. If aggregate RRA is constant and the aggre-
gate dividend is the fundamental variable, driven by a geometric Brownian
motion, then asset prices are also governed by a geometric Brownian motion.
Declining aggregate RRA can lead to short-term momentum, long-term re-
versals as well as high and persistent volatility of excess returns. Declining
aggregate RRA even provides a rationale for chart analysis in an efficient
market. The asset price reaction to a dividend change depends on the divi-
dend level. In certain dividend ranges the asset price reaction is weak while
it can be quite strong in others. A small decline in the dividend can trigger
a strong decline in the price of the market portfolio as in a stock market
crash. This requires that aggregate RRA declines strongly in some dividend
range. It is likely to happen when there are two groups of investors, one
with a high level of RRA and the other one with a much lower level. Hence
explaining a stock market crash neither requires ”irrational behavior” nor
market imperfections.
The findings of the paper are consistent with many empirical findings on
stock returns. In contrast to mainly empirically motivated time-series mod-
els, the model in this paper has a solid economic foundation and in contrast
to many theoretical models analytical asset price functions are derived. How-
ever, the model setup is deliberately chosen to be simple to pinpoint the
importance of aggregate RRA for asset return processes. Therefore future
research is needed to investigate more complicated models taking into con-
sideration more realistic settings. For example, this model does not deal
explicitly with heterogeneous expectations of investors. Also, this model
only analyzes the return of the market portfolio neglecting single stocks.
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