Return Predictability and Stock Market Crashes in a Simple Rational Expectations Model



consistent with an equilibrium driven by a representative investor. They
show that such an equilibrium rules out widely used stochastic processes
such as the Ornstein-Uhlenbeck process and constant elasticity of variance
for market portfolio returns.

Many asset pricing models still assume constant aggregate relative risk aver-
sion. Among the few papers which analyze the impact of aggregate rela-
tive risk aversion on return characteristics is Stapleton and Subrahmanyam
(1990). They assume that the cash flow process is governed by a geomet-
ric [arithmetic] Brownian motion. They show that if aggregate relative risk
aversion [absolute risk aversion] is constant, the forward price is governed by
a geometric [arithmetic] Brownian motion. Franke et. al. (1999) show that
option prices are higher for declining than for constant aggregate relative
risk aversion and that asset returns are serially correlated in case of declining
aggregate relative risk aversion. Neither Franke et. al. (1999) nor Stapleton
and Subrahmanyam (1990) give a characterization of the volatility function
or the autocorrelation function. Also, they do not provide any quantification
of the effects of aggregate relative risk aversion on asset price process. Re-
cent papers have analyzed the implications of heterogeneous preferences on
aggregate relative risk aversion. Besides of Benninga and Mayshar (2000),
Chan and Kogan (2002) analyze a continuous time-economy with a contin-
uum of agents who have ”catching up with the Joneses” preferences and
differ in the level of constant relative risk aversion. Although they do not
provide an analytical solution for asset prices, they show that this kind of
heterogeneity can generate mean reversion in asset returns. None of these
papers, however, provides any rationale for stock market crashes.

Related to this paper is the research on the effect of learning on return
characteristics. Brennan and Xia (2002) assume that the representative in-
vestor cannot observe the growth rate of dividends but estimates it from
realized data. Their model can explain high volatility of stock prices. John-
son (2002) builds on their results to show that stochastic expected growth
rates of the dividend process lead to momentum. Brennan et. al. (2003)
and Brennan and Xia (2003) also work within a similar framework. They
emphasize the importance of a time-varying investment opportunity set to
explain the predictability of asset returns.3

Summarizing, we still lack a sound understanding of asset return characteris-
tics. This lack of knowledge exists even in the presence of the vast empirical
literature on asset returns, part of which has been criticized by Ang and Liu
(2004) for internal inconsistencies in asset return specifications.

The remainder of the paper is organized as follows. In Section 1 the model is
introduced and declining aggregate relative risk aversion is shown to be the

3See also Timmermann (1993), David (1997), Veronesi (2000) and Pastor and Veronesi
(2003) for the effect of learning on asset pricing.



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