E[∆P 2 ∆P 3 ′]<0; (A50)
E[∆P 3 ′∆P 3 ]>0; (A51)
E[∆P 1 ∆P 3 ]<0, (A52)
The magnitude of E[∆P 2 ∆P 3 ′] varies nonmonotonically with q. As rrises
(the precision of s 3 ′is increased), direct calculation shows that E[∆P 2 ∆P 3 ′]
becomes more negative (increases in absolute value). As r→0.5, this co-
variance approaches zero. Thus, when the second noisy public signal is not
very informative, this negative single-lag covariance becomes arbitrarily
small in absolute value.
Confidence increases when s 2 confirms s 1 , but its effects are mitigated as
s 2 becomes more informative. Thus, an increase in the precision of s 2 has
an ambiguous effect on E[∆P 2 ∆P 3 ′]. This increase results in a greater likeli-
hood of overconfidence occurring, yet also places greater, rational, confi-
dence in s 2 itself, yielding less leverage to the effects of overconfidence. (At
the extreme, a value of qequal to one yields the greatest chances of s 2 con-
firming s 1 yet results in zero values for all covariances as the perfect infor-
mation of s 2 entirely determines all subsequent prices.) Based on simulation,
it appears that the greater information resulting from higher values of qtends
overshadow the increased likelihood of overconfidence, resulting in generally
lower absolute values for E[∆P 2 ∆P 3 ′].
Larger values of r, the precision of s 3 ′, result in more negative values of
E[∆P 2 ∆P 3 ′]. In this case, a more informative second noisy public signal can
only place less weight on previous signals and result in a stronger correc-
tion of the previous overreaction. Thus, the final one-period covariance is
more negative as the precision of s 3 ′rises.
INVESTOR PSYCHOLOGY 497