while the single-period price change single-lag autocorrelation that straddles
the extremum is negative.^17
Under appropriate parameter assumptions, the negative single-lag auto-
correlation surrounding the extremum will be arbitrarily close to zero. This
will occur if either the extra overreaction or the start of the correction is
weak (or both). The extra overreaction is small if confidence is boosted only
slightly (k>0 small) when an investor’s trade is confirmed by public news.
The initial correction is slight if the further noisy public signal is not very in-
formative (ση^2 large). When parameter values are such that this straddling
autocorrelation is not too large, it will be outweighed by the positive auto-
correlations during the hearts of the overreaction or correction phases. In
other words, an econometrician calculating autocorrelations uncondition-
ally would find, in a large sample, a positive single-lag autocorrelation. In
contrast, longer-lag pairs of price changes that straddle the extremum of the
impulse response function will tend to be opposed, because a price change
drawn from the overreaction phase tends to be negatively correlated with a
price change drawn from the correction phase. Thus, the overconfidence
theory provides a joint explanation for both short-term momentum and
long-term reversals.
Proposition 7.If investor confidence changes owing to biased self-
attribution, and if overreaction or correction is sufficiently gradual,
then stock price changes will exhibit unconditional short-lag posi-
tive autocorrelation (“momentum”) and long-lag negative autocor-
relation (“reversal”).According to Jegadeesh and Titman (1993), their momentum evidence is
“consistent with delayed price reactions to firm-specific information.”
Proposition 7 offers a very different possible interpretation, namely, that
momentum occurs not because the market is slow to react to news, but be-
cause the market initially overreacts to the news, and later public news trig-
gers further overreaction to the initial private signal. More generally,
Proposition 7 refutes the common casual equating of positive versus nega-
tive autocorrelations with underreaction versus overreaction to new infor-
mation. While negative autocorrelations result from overreaction in the
model, positive autocorrelations also result from continuing overreaction
(followed by underreaction in the correction of this error).
Evidence from the psychological literature suggests that individuals tend
to be more overconfident in settings where feedback on their information
or decisions is slow or inconclusive than where the feedback is clear and
rapid (Einhorn 1980). Thus, mispricing should be stronger in stocks which
480 DANIEL, HIRSHLEIFER, SUBRAHMANYAM
(^17) Formally, cov(P 2 −P 1 ,P 1 −P 0 )>0, cov(P 3 −P 3 ′,P 3 ′−P 2 )>0, and cov(P 3 ′−P 2 ,P 2 −
P 1 )<0. See the appendix of Daniel, Hirshleifer, and Subrahmanyam (1998).