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18 BIAIS AND FAUGERON-CROUZET
investors do not have enough funds to buy the whole IPO. This is more realistic,
given the relatively small size of IPO issues, compared to the large bidding power
of institutional investors. Second, we consider N informed investors, with different
and imperfect signals, rather than a single, perfectly informed investor.
In the case of fixed price offers, the only choice of the seller is to set the price, p.
Since the uninformed agents cannot absorb the whole issue, and since the seller
must sell the S shares, he must ensure that the informed agents are willing to bid
for the shares, even when they have observed bad signals. Hence, the price must
be set to satisfy the individual rationality constraint of the informed agent with a
bad signal.
We assume that informed investors can costlessly bid for up to S shares. If they
want to bid for a larger amount, up to ¯Q > S, they incur cost c. As only S shares
are for sale, such very large bids are expected not to be fully executed. They can
be optimal, however, to the extent that they enable the investor to obtain a larger
share of underpriced and overbid issues. The cost c can be thought of as the cost
of immobilizing funds during the period of the IPO (Keloharju (1993) notes that
in Finland this period can be quite long).
Consider the candidate equilibrium where investors with good signals bid for
a large amount ( ¯Q), while investors with a bad signal bid for a lower amount (S)
and retail investors also participate to the IPO. In this context, the execution rate
when there are n good signals is
S
τn =
S(1 − k + N − n) + n ¯Q .
Setting the expected gain of the informed with a bad signal bidding for S shares
to 0
E(Sτ(v − p) | b) = 0,
pins down the IPO price. Correspondingly, we obtain the following proposition:
PROPOSITION 2. If K1 ≤ c ≤ K2 (where K1 and K2 are constants defined in
the proof ), then in the fixed price offer the highest possible IPO price is
where,
N−1
p = λlv(l),
λl =
l=0
πlτl
N−1 l=0 πlτl
,
and the informed agent with a good signal bids for ¯Q, while the informed agent
with a bad signal bids for S, and the uninformed agent bids for S(1 − k).