where

N(0, σ
^2 ) (so the signal precision is 1/σ
^2 ). The Us correctly assess
the error variance, but Is underestimate it to be σC^2 <σ
^2. The differing beliefs
about the noise variance are common knowledge to all.^7 Similarly, the date
2 public signal is

s 2 =θ+η, (2)

where the noise term η∼N(0, σp^2 ) is independent of θand
. Its variance σp^2
is correctly estimated by all investors.
Our simplifying assumption that all private information precedes all
public information is not needed for the model’s implications. It is essential
that at least some noisy public information arrives after a private signal.
The model’s implications stand if, more realistically, additional public in-
formation precedes or is contemporaneous with the private signal.
Since prices are set by the risk-neutral informed traders, the formal role
of the uninformed in this work is minimal. The rationale for the assump-
tion of overconfidence is that the investor has a personal attachment to his
own signal. This implies some other set of investors who do not receive the
same signal. Also, similar results will hold if both groups of investors are
risk averse, so that both groups influence price. We have verified this ana-
lytically in a simplified version of the model. So long as the uninformed are
not risk-neutral price setters, the overconfident informed will push price
away from fully rational values in the direction described here.

A. Equilibrium Prices and Trades

Since the informed traders are risk neutral, prices at each date satisfy

P 1 =EC[θθ+
] (3)

P 2 =EC[θθ+
, θ+η], (4)

where the subscript Cdenotes the fact that the expectation operator is cal-
culated based on the informed traders’ confident beliefs. Trivially, P 3 =θ.
By standard properties of normal variables (Anderson 1984, chapter 2)

(5)

(6)

where D≡++σσ σθ^22 ().Cp Cp^2 σσ^22

P

DDD

Cp p C

2

(^2222222)

• ++
  σσ σ
  θ
  σσ σσ
  η
  θθ() θ
  
  ,
  P
  C
  1
  2
  = (^22) + +
  σ
  σσ
  θ θ
  θ
  ()
  
  INVESTOR PSYCHOLOGY 467
  (^7) It is not crucial for the analysis that the Us correctly assess the private signal variance,
  only that they do not underestimate it as much as the informed do. Also, since the uninformed
  do not possess a signal to be overconfident about, they could alternatively be interpreted as