will be insufficient volatility relative to the rational level, long-run return
continuation, and negative correlation between selective events such as re-
purchase and postevent returns. Of course, one could arbitrarily specify
whatever pattern of correlated noise is needed to match empirically ob-
served ex post price patterns. Such an exercise would merely be a relabeling
of the puzzle, not a theory. Instead, we examine a form of irrationality con-
sistent with well-documented psychological biases, and our key contribution
is to show that these biases induce several of the anomalous price patterns
documented in the empirical literature.
Some models of exogenous noise trades (e.g., DeLong, Shleifer, Summers,
and Waldmann 1990b, Campbell and Kyle 1993) also imply long-run re-
versals and excess volatility because of the time-varying risk premia induced
by these trades. Our approach additionally reconciles long-run reversals
with short-term momentum, explains event-based return predictability, and
offers several other distinct empirical predictions (see subsections 2.B.1–
2.B.3).
As noted in the introduction, a possible objection to models with imper-
fectly rational traders is that wealth may shift from foolish to rational
traders until price-setting is dominated by rational traders. For example, in
our model the overconfident informed traders lose money on average. This
outcome is similar to the standard result that informed investors cannot
profit from trading with uninformed investors unless there is some “noise”
or “supply shock.” However, recent literature has shown that in the long-
run rational traders may not predominate. DeLong, Shleifer, Summers, and
Waldman (1990b, 1991) point out that if traders are risk-averse, a trader
who underestimates risk will allocate more wealth to risky, high expected
return assets. If risk averse traders are overconfident about genuine infor-
mation signals (as in our model), overconfidence allows them to exploit in-
formation more effectively. Thus, the expected profits of the overconfident
can be greater than those of the fully rational (see Daniel, Hirshleifer, and
Subrahmanyam 2001).
Furthermore, owing to biased self-attribution, those who acquire wealth
through successful investment may becomemore overconfident (see also
Gervais and Odean 2001). Another distinct benefit of overconfidence is
that this can act like a commitment to trade aggressively. Since this may in-
timidate competing informed traders, those known to be overconfident
may earn higher returns (see Kyle and Wang 1997, and Benos 1998).
Recent evidence suggests that event-based return predictability varies
across stocks (e.g., Brav and Gompers 1997). Moving beyond the confines
of the formal model, we expect the effects of overconfidence to be more se-
vere in less liquid securities and assets. Suppose that all investors are risk
averse and that prices are not fully revealing (perhaps because of noisy liq-
uidity trading). If rational arbitrageurs face fixed setup costs of learning
about a stock, then large liquid stocks will tend to be better arbitraged
488 DANIEL, HIRSHLEIFER, SUBRAHMANYAM