Empirical research suggests that returns of broad based market indices as
the S&P 500 are predictable. This seems to contradict the efficient market
hypothesis. While it is controversial whether the predictability in returns is
economically significant - especially concerns related to data-snooping are
often expressed - studies on return volatility provide clear evidence against
constant volatility and therefore against the geometric Brownian motion of
asset prices. An extensive literature on excess volatility which was started
by Shiller (1981) and LeRoy and Porter (1981) claims that the volatility of
asset prices is too high to be consistent with classical asset pricing models.
Moreover, the occurrence of stock market crashes without any significant
news and the widespread use of technical analysis are often claimed to be
incompatible with rational, efficient markets.1 To explain these findings
many researchers argue in favor of investor irrationality and new behav-
ioral postulates. Other explanations rely on market imperfections such as
information costs which may explain herding and positive feedback trading.
Neither ”irrational” behavior nor market imperfections are needed to ex-
plain these characteristics. In this paper we show that a simple rational
expectations model based on a perfect capital market can explain these as-
set price characteristics if aggregate relative risk aversion is declining. If
there exists a representative investor, then her relative risk aversion would
equal aggregate relative risk aversion (Rubinstein, 1974). In this paper no
representative investor exists. Then aggregate relative risk aversion depends
on the equilibrium allocation and the relative risk aversion levels of the var-
ious investors. The level and variation of aggregate relative risk aversion is
controversial. Defining aggregate relative risk aversion as the negative elas-
ticity of the stochastic discount factor with respect to the asset price, recent
empirical studies estimate its level using option prices. The empirical results
documented in Ait-Sahalia and Lo (2000), Jackwerth (2000) and Rosenberg
and Engle (2002) suggest extreme bounds for aggregate relative risk aver-
sion. Ait-Sahalia and Lo (2000), for example, document levels up to 60 for
S&P 500 index values about 15 percent below the current future price. For
the lower bound, the work by Jackwerth suggests even negative aggregate
risk aversion, that is risk loving.2 But little is known on the level of aggre-
gate relative risk aversion for index values more than 15 percent above or
1 For an overview on return predictability and return volatility as well as a discussion of
the methodological problems, see Campbell et. al. (1997) and Cochrane (2001). Ghysels
et. al. (1996) provide an extensive overview on the characteristics of return volatility.
Shiller (2000) provides evidence that stock market crashes may occur without significant
news. For a recent study on the effectiveness of technical analysis see Lo et. al. (2000).
2Assuming constant aggregate relative risk aversion, Bliss and Panigirtzoglou (2003)
estimate aggregate relative risk aversion levels between 1.97 and 9.52. They find that risk
aversion declines with the forecast horizon and with the level of volatility. Analyzing the
cross section of industry portfolios Dittmar (2002) also provides evidence against constant
aggregate relative risk aversion.