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IPO Auctions: English, Dutch, ... French, and Internet

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Journal of Financial Intermediation 11, 9–36 (2002)<br />

doi:10.1006/jfin.2001.0319, available online at http://www.idealibrary.com on<br />

<strong>IPO</strong> <strong>Auctions</strong>: <strong>English</strong>, <strong>Dutch</strong>, ...<strong>French</strong>, <strong>and</strong> <strong>Internet</strong> ∗<br />

Bruno Biais<br />

Université de Toulouse, IDEI, Place Anatole France, 31200 Toulouse, France<br />

<strong>and</strong><br />

Anne Marie Faugeron-Crouzet<br />

Université de Paris Val de Marne, 61, avenue du Général de Gaulle, 94010 Créteil Cedex, France<br />

Received December 6, 1999<br />

Unseasoned shares are sold through the Book Building process in the United States <strong>and</strong><br />

the United Kingdom, fixed price offerings in several countries, uniform price auctions in<br />

Israel or the new internet-based Open <strong>IPO</strong> mechanism, <strong>and</strong> an auction-like mechanism called<br />

the Mise en Vente in France. We analyze <strong>and</strong> compare the performance of these various<br />

<strong>IPO</strong> mechanisms within the context of a unified theoretical model. Fixed price offerings<br />

lead to inefficient pricing <strong>and</strong> winner’s curse. <strong>Dutch</strong> auctions can also lead to inefficiencies,<br />

to the extent that they are conducive to tacit collusion by investors. The Book Building <strong>and</strong><br />

Mise en Vente can lead to optimal information elicitation <strong>and</strong> price discovery. We document<br />

empirically the similarity between the Book Building <strong>and</strong> the Mise en Vente. We discuss<br />

the implications of our analysis for the design of optimal <strong>Internet</strong> <strong>IPO</strong> auctions. Journal of<br />

Economic Literature Classification Numbers: G24, G3, D82. C○ 2002 Elsevier Science (USA)<br />

∗ Many thanks to Tom Chemmanur <strong>and</strong> the two referees for helpful comments, <strong>and</strong> to the Paris Bourse<br />

for financial support, access to data, <strong>and</strong> many insights, especially Jacky Billard, Martine Charbonnier,<br />

Didier Davydoff, Dominique Leblanc, Bernard Mirat, Alain Morice, <strong>and</strong> Pascal Samaran. We are also<br />

grateful for helpful discussions with Michael Fishman, Jean–Pierre Florens, Julian Franks, Sylvain<br />

Friedrich, David Goldreich, Richard Green, Michel Habib, Shmuel K<strong>and</strong>el, Kjell Nyborg, Pegaret<br />

Pichler, Jean Charles Rochet, Chester Spatt, Bill Wilhelm, Luigi Zingales, <strong>and</strong> seminar participants at<br />

the University of Chicago, the London Business School, the London School of Economics conference<br />

on trading markets for smaller companies, the Utah Winter Conference, the CEPR Summer Symposium<br />

on Financial Economics, the conference “Raising Capital in Different National Markets” in Frankfurt,<br />

the 2000 Meetings of the American Finance Association <strong>and</strong> the Journal of Financial Intermediation<br />

Conference on New Technologies, Financial Innovation <strong>and</strong> Intermediation at Boston College.<br />

9<br />

1042-9573/02 $35.00<br />

c○ 2002 Elsevier Science (USA)<br />

All rights reserved.


10 BIAIS AND FAUGERON-CROUZET<br />

1. INTRODUCTION<br />

One of the major benefits of public listing on stock exchanges is the rich flow<br />

of information, about the firm’s prospects <strong>and</strong> the investors’ willingness to hold<br />

its shares, that is reflected in prices <strong>and</strong> trades in the secondary market. Prior to<br />

the <strong>IPO</strong> very little such information is available. Consequently, the task of finding<br />

the <strong>IPO</strong> price is a difficult one. The auction by which the unseasoned shares are<br />

sold can therefore play an important role in eliciting information from the market<br />

participants about their valuation of the stock. Yet <strong>IPO</strong> auction mechanisms vary<br />

quite significantly across countries, <strong>and</strong> their ability to elicit information revelation<br />

from investors is likely to also vary (see Loughran et al. (1994) <strong>and</strong> Sherman<br />

(1999)):<br />

• In the United States <strong>and</strong> the United Kingdom, in the Book Building method,<br />

the investment banker elicits indications of interest from institutional investors <strong>and</strong><br />

uses these indications to set the <strong>IPO</strong> price <strong>and</strong> allocate the shares (see Benveniste<br />

<strong>and</strong> Spindt (1989), Benveniste <strong>and</strong> Wilhelm (1990 <strong>and</strong> 1997), Spatt <strong>and</strong> Srivastava<br />

(1991), Hanley (1993), Hanley <strong>and</strong> Wilhelm (1993), <strong>and</strong> Cornelli <strong>and</strong> Goldreich<br />

(1998)).<br />

• In Singapore, Finl<strong>and</strong>, <strong>and</strong> the United Kingdom, fixed price offers are used,<br />

whereby investors submit dem<strong>and</strong>s at the fixed price, <strong>and</strong> (possibly r<strong>and</strong>om) rationing<br />

rules are used to allocate the shares (see Koh <strong>and</strong> Walter (1989), Levis<br />

(1990), <strong>and</strong> Keloharju (1993)).<br />

• In Israel, <strong>IPO</strong>s are conducted according to the st<strong>and</strong>ard uniform price, market<br />

clearing, <strong>Dutch</strong> auction, whereby the price is set to equate supply <strong>and</strong> dem<strong>and</strong> (see<br />

K<strong>and</strong>el et al. (1997)).<br />

• In the Mise en Vente, an auction-like <strong>IPO</strong> method commonly used in France,<br />

investors submit limit orders <strong>and</strong> then the auctioneer sets the price as a function<br />

of aggregate dem<strong>and</strong> (the name of this auction procedure has been recently<br />

changed to Offre a Prix Minimum, but its workings have not been altered). In<br />

this <strong>IPO</strong> mechanism the price does not clear the market, <strong>and</strong> prorata rationing<br />

is used. For descriptions <strong>and</strong> analyses of this <strong>IPO</strong> method see Belletante <strong>and</strong><br />

Palliard (1993), Derrien <strong>and</strong> Womack (1999), Dubois (1989), Husson <strong>and</strong><br />

Jacquillat (1989), Jacquillat <strong>and</strong> Mac Donald (1974), Jacquillat et al. (1978),<br />

Leleux (1993), <strong>and</strong> Mirat (1983, 1984).<br />

The diversity of unseasoned shares selling mechanisms has actually even increased<br />

in the recent past as new, internet-based <strong>IPO</strong> auctions have been recently<br />

proposed (see Wilhelm (1999)):<br />

• Open <strong>IPO</strong> offers to sell unseasoned shares through a <strong>Dutch</strong> auction. In its<br />

advertising (for example on its website: www.openipo.com) it emphasizes that<br />

the use of this st<strong>and</strong>ard uniform price, market clearing auction ensures that “<strong>IPO</strong><br />

offfering prices are set by the market” <strong>and</strong> reflect “what people are truly willing to<br />

pay for the stock.” It also advises that “investors should make a bid at the maximum


<strong>IPO</strong> AUCTIONS 11<br />

TABLE 1<br />

<strong>IPO</strong> Selling Mechanisms in Different Countries<br />

U.K. U.S. Wit capital Singapore Finl<strong>and</strong> U.K. Israel Open <strong>IPO</strong> France<br />

Institution Book building Fixed price <strong>Dutch</strong> (uniform Mise en<br />

auction price) auction Vente<br />

Price set before after before after after<br />

of after<br />

dem<strong>and</strong><br />

Price clears no no yes no<br />

market<br />

Rationing rule discretionary prorata or — prorata<br />

r<strong>and</strong>om<br />

price at which they are comfortable owning shares of the issue.” In fact, Open <strong>IPO</strong><br />

has sometimes been presented as an alternative for the st<strong>and</strong>ard Book Building<br />

process, potentially more efficient than the latter, thanks to the use of the <strong>Dutch</strong><br />

auction mechanism.<br />

• Wit Capital follows a somewhat more st<strong>and</strong>ard strategy. It seeks to<br />

entice individual investors to bid in <strong>IPO</strong>s, but does not contribute in a major way<br />

to the price discovery mechanism. The latter is in large part operated by the<br />

lead managers of the <strong>IPO</strong>s in which Wit Capital participates. These lead<br />

managers, which are major investment banks such as Goldman Sachs, Morgan<br />

Stanley, or Merrill Lynch, determine the <strong>IPO</strong> price based on the traditional<br />

Book Building process, which is more focused toward large institutional<br />

investors.<br />

The overall diversity of <strong>IPO</strong> auction formats (summarized in Table 1) raises the<br />

following issues:<br />

• What is the optimal <strong>IPO</strong> mechanism in terms of expected proceeds, price<br />

discovery, <strong>and</strong> information elicitation from informed investors? How should <strong>IPO</strong><br />

prices be set, in response to investors’ dem<strong>and</strong>? Is the frequently used fixed price<br />

method optimal?<br />

• Or is the a priori appealing <strong>Dutch</strong> auction the optimal selling mechanism?<br />

• How do different auction-like <strong>IPO</strong> procedures, such as the Book Building, the<br />

Mise en Vente, <strong>and</strong> <strong>Dutch</strong> auctions compare?<br />

• How should <strong>Internet</strong>-based <strong>IPO</strong> auctions be designed?<br />

These questions are of interest to finance <strong>and</strong> economics scholars aiming<br />

to underst<strong>and</strong> price formation <strong>and</strong> the workings of auctions. They are also very<br />

relevant in practice for investors, shareholders, <strong>and</strong> investment bankers, whose<br />

profits can be significantly affected by the nature <strong>and</strong> efficiency of the <strong>IPO</strong><br />

mechanisms.


12 BIAIS AND FAUGERON-CROUZET<br />

To address these issues, this paper develops a unified theoretical model to analyze<br />

the workings of the different <strong>IPO</strong> mechanisms listed above: the Book Building<br />

method, the fixed price auction, the Mise en Vente, <strong>and</strong> the uniform price market<br />

clearing auction.<br />

The participants in the <strong>IPO</strong> process are the sellers, financial intermediaries, <strong>and</strong><br />

potential investors. In the model presented in Section 2 we assume the sellers<br />

seek to maximize the proceeds from the <strong>IPO</strong>, <strong>and</strong> the financial intermediary acts<br />

in their best interest. Some investors are large, strategic, institutional investors,<br />

with private information about the valuation of the stock in the secondary market.<br />

For simplicity, we assume that only the investors have private information,<br />

<strong>and</strong> abstract from the important problems arising when the sellers have private<br />

information (see, e.g., Allen <strong>and</strong> Faulhaber (1989), Grindblatt <strong>and</strong> Hwang (1989),<br />

Welch (1989), <strong>and</strong> Chemmanur (1993)). In addition to the large investors, there<br />

are smaller, <strong>and</strong> uninformed, but rational, investors. The funds available to these<br />

small investors are limited, hence they cannot absorb the whole issue. In Section 2,<br />

in the line of Benveniste <strong>and</strong> Spindt (1989), Benveniste <strong>and</strong> Wilhelm (1990), <strong>and</strong><br />

Spatt <strong>and</strong> Srivastava (1991), we consider the optimal direct mechanism, <strong>and</strong> its<br />

implementation within the context of the Book Building method.<br />

In Section 3, we show that, in the fixed price auction, since prices cannot adjust to<br />

dem<strong>and</strong>, winner’s curse problems, as in Rock (1986), lead to severe underpricing.<br />

Since the winner’s curse effect reflects the absence of adjustment of prices to<br />

dem<strong>and</strong> it is natural to expect that the market clearing uniform price auction<br />

should perform better. Yet, we show that this auction can be conducive to tacit<br />

collusion between bidders, as in Wilson (1979), leading to large underpricing. This<br />

provides an alternative interpretation for the underpricing empirically evidenced<br />

by K<strong>and</strong>el et al. (1997) in <strong>IPO</strong>s in Israel. In contrast, we show that the Mise en<br />

Vente can be structured to implement the optimal mechanism <strong>and</strong> to rule out tacit<br />

collusion, in contrast with the uniform price auction. In this auction, investors with<br />

good signals submit large dem<strong>and</strong>s, this drives prices up <strong>and</strong> thus enhances price<br />

discovery.<br />

In Section 4, we present empirical evidence from Mise en Vente auctions consistent<br />

with our theoretical result that it can implement the optimal mechanism,<br />

similar to the Book Building method. Hanley (1983) showed that, consistent with<br />

the implications from Benveniste <strong>and</strong> Spindt (1989) <strong>and</strong> Benveniste <strong>and</strong> Wilhelm<br />

(1990), prices somewhat underreact to dem<strong>and</strong>; i.e., the covariance between price<br />

adjustment <strong>and</strong> underpricing is positive. This is also the case empiricaly in the<br />

Mise en Vente. Cornelli <strong>and</strong> Goldreich (1999) show empirically that, in the Book<br />

Building method, prices are set deliberatey below the market clearing level <strong>and</strong><br />

that, anticipating this, investors inflate their dem<strong>and</strong>. This also arises in the Mise<br />

en Vente.<br />

Conclusions emerging from our analysis are the following:<br />

• Efficient price discovery in <strong>IPO</strong>s requires some adjustment of prices to dem<strong>and</strong>.<br />

Consequently, fixed price selling methods are inefficient. This is consistent


<strong>IPO</strong> AUCTIONS 13<br />

with the empirical finding by Loughran et al. (1994) that auction-like mechanisms<br />

lead to more efficient pricing than fixed price offers.<br />

• Yet, prices should not adjust to dem<strong>and</strong> too strongly, lest this should spur tacit<br />

collusion. Consequently, the st<strong>and</strong>ard market-clearing uniform price (or <strong>Dutch</strong>)<br />

auction is not the optimal mechanism. In this auction, bidders can tacitly collude<br />

by placing dem<strong>and</strong> functions such that the market clearing price is very low,<br />

<strong>and</strong> such that, any attempt to bid more aggressively, to gain market share, would<br />

push prices too high to be attractive. In the Mise en Vente, in contrast, since<br />

prices underreact to dem<strong>and</strong>, tacit collusion on low prices can be unravelled.<br />

Indeed, underreaction implies that, if the other bidders were to bid at low prices,<br />

one investor could gain a large market share, without impacting the price too<br />

much.<br />

• In spite of obvious differences in institutional characteristics, two auctions,<br />

the Mise en Vente <strong>and</strong> the Book Building method, can be designed to implement<br />

the optimal <strong>IPO</strong> mechanism. From a theoretical perspective, it is not unnatural that<br />

different institutions can be used to implement the same optimal direct mechanism.<br />

From an empirical perspective, it is interesting that, consistent with our theoretical<br />

finding that the two institutions are comparable, data generated by the Book<br />

Building method in the United States or the United Kingdom <strong>and</strong> by the Mise en<br />

Vente in France, exhibit the same observable patterns, in particular underreaction<br />

of prices to dem<strong>and</strong> <strong>and</strong> oversubscription.<br />

• This analysis has implications for the design of <strong>Internet</strong>-based <strong>IPO</strong> auctions.<br />

While the <strong>Dutch</strong> auction format proposed by Open <strong>IPO</strong> seems a priori attractive,<br />

our theoretical model shows that it can lead to tacit collusion on the part<br />

of bidders, <strong>and</strong> in that case it can be quite inefficient. In these collusive equilibria,<br />

the optimal strategy of the investors is to shade their bids rather than to<br />

“make a bid at the maximum price at which they are comfortable owning shares<br />

of the issue” as advised on Open <strong>IPO</strong>’s website. In fact, our analysis suggests<br />

that, in contrast with the <strong>Dutch</strong> auction, it can be optimal to let prices underreact<br />

to dem<strong>and</strong>. Note that, in a recent <strong>IPO</strong> (Andover.net, Inc.), Open <strong>IPO</strong> actually<br />

set the <strong>IPO</strong> price at a significant discount relative to the market clearing<br />

price, more in line with the rules governing the book building or the Mise en<br />

Vente than with those of the <strong>Dutch</strong> auction. A challenge facing internet <strong>IPO</strong> auction<br />

designers is to translate into explicit computer algorithms the rather implicit<br />

rules that map dem<strong>and</strong> into prices in the Mise en Vente or the Book Building<br />

method.<br />

2. MODEL<br />

There are S unseasoned shares for sale. The seller faces N large, strategic,<br />

institutional investors with private information about the valuation of the firm by<br />

the market <strong>and</strong> large bidding capacity, <strong>and</strong> a fringe of small, retail investors who<br />

are uninformed <strong>and</strong> cannot absorb the whole issue. All agents are rational <strong>and</strong>


14 BIAIS AND FAUGERON-CROUZET<br />

risk neutral, <strong>and</strong> this is a common value auction. The objective of the seller is to<br />

maximize the proceeds from the sale.<br />

Each large investor can buy the whole issue <strong>and</strong> observes a private signal si, i =<br />

1,...N. The signals are identically <strong>and</strong> independently distributed <strong>and</strong> can be good<br />

(g), with probability π, or bad (b) with the complementary probability. The value v<br />

of the shares on the secondary market is increasing in the number of good signals n<br />

<strong>and</strong> its realization is denoted vn.<br />

The retail investors, as a whole, can purchase up to S(1 − k) shares, with k ∈<br />

[0, 1].<br />

The financial intermediary is assumed to act in the best interest of the seller.<br />

She is in contact with the large institutional investors, <strong>and</strong> she has a distribution<br />

network, collecting the orders from the retail investors.<br />

Consider the following direct mechanism. Each informed investor i sends a<br />

message mi ∈{g, b}. The mechanism maps these N messages into a price <strong>and</strong><br />

into allocations to the informed agents <strong>and</strong> the retail uninformed agents. The<br />

mechanism is subject to several constraints. First, the price must be the same for<br />

all. This is to reflect the constraint, observed in practice, that <strong>IPO</strong> auctions involve<br />

uniform pricing (it should be noted, however, that Benveniste <strong>and</strong> Wilhelm<br />

(1990) show that investment bankers acting in the best interest of the firm could<br />

increase expected proceeds by using price discrimination). Second, since we assume<br />

the N large traders are ex ante identical, the mechanism is symmetric. Hence<br />

the price is simply a function of the total number of investors who report good<br />

signals ˆn, <strong>and</strong> is correspondingly denoted p(ˆn), while the quantity allocated to informed<br />

agent i depends only on her message mi <strong>and</strong> the number of other informed<br />

agents who reported good signals, li. Correspondingly it is denoted q(mi; li). Similarly,<br />

the quantity allocated to the uninformed agents depends only on ˆn, <strong>and</strong><br />

it is denoted qu(ˆn). Third, the allocation must be such that exactly S shares are<br />

sold.<br />

∀{mi}i=1,....N , ˆn ∈{0,...N},<br />

N<br />

q(mi; li) + qu(ˆn) = S.<br />

The mechanism opens the possibility to allocate different quantities to investors<br />

reporting different signals. Indeed, quantity discrimination is crucial to obtain<br />

information revelation from the investors.<br />

The program of the mechanism designer is to maximize expected proceeds<br />

i=1<br />

Maxqi (.;.),qu(..),p(.)E(Sp(ˆn))<br />

under the incentive compatibility <strong>and</strong> participation constraints of the investors. The<br />

incentive compatibility constraint of the informed investor i is that she must be better<br />

off announcing her true signal than misreporting it, while rationally anticipating


<strong>IPO</strong> AUCTIONS 15<br />

that the others will truthfully report their own signals. When the investor has observed<br />

a good signal this amounts to<br />

N−1<br />

N−1<br />

πlq(g; l)(vl+1 − p(l + 1)) ≥ πlq(b; l)(vl+1 − p(l)),<br />

l=0<br />

where πl is the probability, from the point of view of the informed investor, that l<br />

out the N − 1 other investors have a good signal.<br />

We impose the rationality condition in its most dem<strong>and</strong>ing form. Investors must<br />

still be willing to participate to the mechanism ex post, i.e., after the messages of<br />

all the agents are known. This implies that the price set in the optimal mechanism<br />

must be lower than or equal to the value of the shares: p(n) ≤ vn.<br />

This problem is similar to the problem analyzed by Benveniste <strong>and</strong> Spindt (1989)<br />

<strong>and</strong> Benveniste <strong>and</strong> Wilhelm (1990). However, there are three differences. First<br />

<strong>and</strong> most importantly, in the present paper, the uninformed agent participates in<br />

the direct mechanism, along with the informed agents; the empirical analysis of<br />

the book-building process by Cornelli <strong>and</strong> Goldreich (1998) is consistent with<br />

this view. Considering the game in which both informed <strong>and</strong> uninformed agents<br />

participate enables us to nest in our analysis the study of winner’s curse effects as<br />

in Rock (1986) (see the analysis of the fixed price sale in the next section). Second,<br />

we do not impose the additive form used in Benveniste <strong>and</strong> Spindt (1989), where<br />

the value of the share is proportional to the number of good signals, which would<br />

imply, in our context that vn = αn, where α is a constant. Third, in contrast with<br />

Benveniste <strong>and</strong> Spindt (1989), we assume that each large investor could buy the<br />

whole issue. We think this is a reasonable assumption, given the bidding power<br />

of the large financial institutions participating regularly to <strong>IPO</strong>s, compared to the<br />

relatively small size of most of these operations. In addition this assumption simplifies<br />

the analysis. We discuss below how changing this assumption would alter our<br />

results.<br />

The optimal mechanism is given in the next proposition, with the proof of this<br />

proposition, as well as the following propositions, given in the Appendix.<br />

PROPOSITION 1. The optimal direct mechanism has the following characteristics:<br />

• If all informed investors report a bad signal, the <strong>IPO</strong> price is equal to the<br />

value of the shares: v0, the amount allocated to the retail investors is maximized,<br />

by setting qu(0) = S(1 − k), <strong>and</strong> the shares which cannot be sold to the retail<br />

investors are equally split between the informed investors: q(0; 0) = Sk<br />

N .<br />

• If there is at least one informed investor reporting a good signal, informed<br />

investors reporting a bad signal receive no shares, i.e., q(0, ˆn) = 0.<br />

• When some informed investors announce good signals, there is underpricing,<br />

<strong>and</strong> correspondingly expected proceeds are lower than the expected value of the<br />

l=0


16 BIAIS AND FAUGERON-CROUZET<br />

shares:<br />

E(p(n)) = E(vn) − kπ(1 − π) N−1 (v1 − v0).<br />

• The optimal mechanism can be implemented with the following price schedule:<br />

p(n) = vn, ∀n < N,<br />

<br />

1 − π<br />

p(N) = vN − k<br />

π<br />

N<br />

(v1 − p(0)).<br />

The proposition has a simple intuition. The mechanism designer must ensure<br />

that investors with a good signal announce their information truthfully rather<br />

than pretending they have a bad signal. To makes misrepresentation unattractive,<br />

the optimal mechanism minimizes the amount allocated to investors who<br />

announce bad information. This implies setting this amount equal to 0, except<br />

when it is not possible, because all informed investors announce bad signals.<br />

In that situation it is not possible to exclude all the informed agents, because<br />

the retail investors cannot absorb the whole issue. Hence underpricing must<br />

be used, in addition to quantity discrimination, to induce truthful revelation.<br />

This gives rise to informational rents for the large investors. The corresponding<br />

wedge between the expected proceeds <strong>and</strong> the expected value of the shares<br />

is proportional to the amount which the uninformed retail investors cannot buy<br />

(kS). Indeed, if the uninformed retail investors could buy all the shares, allocating<br />

them the whole issue would be a simple way to avoid adverse selection<br />

<strong>and</strong> sell all the shares at their a priori expected value, thus eliminating<br />

underpricing.<br />

Note that, as in Rock (1986), a winner’s curse problem, arises for the uninformed<br />

investors in the optimal mechanism, as the amount they are allocated is<br />

maximízed when the the value of the stock is lowest. Yet, they are still willing<br />

to participate to the auction, because the mechanism is designed to satisfy their<br />

individual rationality constraint.<br />

Next we discuss the extent to which our results are robust to the informational<br />

requirements of our approach:<br />

• In contrast with Allen <strong>and</strong> Faulhaber (1989), Welch (1989) or Chemmanur<br />

(1993), we do not assume that corporate insiders selling their shares in the <strong>IPO</strong> have<br />

private information about the market value of the stock. While clearly important<br />

<strong>and</strong> interesting, the case where there is two-way information asymmetry, i.e., both<br />

the sellers <strong>and</strong> the buyers have private signals, is beyond the scope of the present<br />

paper. Note that Chemmanur (1993) analyzes two-way information asymmetry, in<br />

the context of fixed-price offers.<br />

• In our framework, it is possible to exclude investors who report bad signals,<br />

except when all of them do so. This directly reflects our assumption that each large


<strong>IPO</strong> AUCTIONS 17<br />

investor has the potential to absorb the whole issue. If instead we assumed, like<br />

Benveniste <strong>and</strong> Spindt (1989) that the bidding capacity of the informed investors<br />

was below S, the threat to be excluded from the allocation would be less strong.<br />

Correspondingly, quantity discrimination would be a less powerful tool, <strong>and</strong> it<br />

would be necessary to rely on underpricing to a larger extent. In that context, the<br />

optimal price schedule would entail underpricing in several states, as in Benveniste<br />

<strong>and</strong> Spindt (1989).<br />

• In our model, underpricing is decreasing in the number of bidders, <strong>and</strong> the<br />

outcome of the mechanism goes to the competitive outcome (no underpricing) as<br />

the number of bidders goes to infinity. Note, however, that it would not be very<br />

reasonable to assume infinitely many bidders in our framework. In practice, there<br />

is only a limited number of professional investors who, like the large traders we<br />

consider in the model, have private information about the value of the shares <strong>and</strong><br />

have the capacity to absorb the whole issue.<br />

With the pricing schedule presented in Proposition 1, underpricing arises when<br />

the <strong>IPO</strong> price is high. This suggests that underpricing <strong>and</strong> <strong>IPO</strong> prices are likely to<br />

be positively correlated. Now, with this pricing schedule, the covariance between<br />

underpricing <strong>and</strong> <strong>IPO</strong> prices cov(v − p, p) simplifies to<br />

This is positive if<br />

π N (1 − π N )(vN − p(N))(p(N) − E(v | b)).<br />

E(v) − E(v | b)) > kπ(1 − π) N (v1 − v0),<br />

which is likely to hold, especially when k is relatively low. This positive covariance<br />

can be interpreted in terms of underreaction of prices to dem<strong>and</strong>. Note that, if<br />

no large investor could absorb the whole issue, <strong>and</strong> correspondingly there was<br />

underpricing in more states of the world, as in Benveniste <strong>and</strong> Spindt (1989),<br />

underreaction would also arise.<br />

Benveniste <strong>and</strong> Spindt (1989) <strong>and</strong> Benveniste <strong>and</strong> Wilhelm (1990) provide an<br />

interpretation of the Book Building method along the lines of this type of optimal<br />

mechanism. The indications of interest transmitted by investors to the investment<br />

bank are similar to messages about signals, <strong>and</strong> their reflection in the price adustment<br />

<strong>and</strong> discretionary allocation set by the intermediary are similar to the direct<br />

mechanism. Consistent with this theory, Hanley (1993) found positive correlation<br />

between price adjustment <strong>and</strong> underpricing in Book Building data.<br />

3. THEORETICAL ANALYSIS OF FIXED PRICE OFFERS, MARKET<br />

CLEARING AUCTIONS, AND MISES EN VENTE<br />

3.1. Fixed Price Auction<br />

Our analysis in this section is similar to Rock (1986). The differences are the<br />

following. First, unlike Rock (1986), we do not impose the condition that informed


18 BIAIS AND FAUGERON-CROUZET<br />

investors do not have enough funds to buy the whole <strong>IPO</strong>. This is more realistic,<br />

given the relatively small size of <strong>IPO</strong> issues, compared to the large bidding power<br />

of institutional investors. Second, we consider N informed investors, with different<br />

<strong>and</strong> imperfect signals, rather than a single, perfectly informed investor.<br />

In the case of fixed price offers, the only choice of the seller is to set the price, p.<br />

Since the uninformed agents cannot absorb the whole issue, <strong>and</strong> since the seller<br />

must sell the S shares, he must ensure that the informed agents are willing to bid<br />

for the shares, even when they have observed bad signals. Hence, the price must<br />

be set to satisfy the individual rationality constraint of the informed agent with a<br />

bad signal.<br />

We assume that informed investors can costlessly bid for up to S shares. If they<br />

want to bid for a larger amount, up to ¯Q > S, they incur cost c. As only S shares<br />

are for sale, such very large bids are expected not to be fully executed. They can<br />

be optimal, however, to the extent that they enable the investor to obtain a larger<br />

share of underpriced <strong>and</strong> overbid issues. The cost c can be thought of as the cost<br />

of immobilizing funds during the period of the <strong>IPO</strong> (Keloharju (1993) notes that<br />

in Finl<strong>and</strong> this period can be quite long).<br />

Consider the c<strong>and</strong>idate equilibrium where investors with good signals bid for<br />

a large amount ( ¯Q), while investors with a bad signal bid for a lower amount (S)<br />

<strong>and</strong> retail investors also participate to the <strong>IPO</strong>. In this context, the execution rate<br />

when there are n good signals is<br />

S<br />

τn =<br />

S(1 − k + N − n) + n ¯Q .<br />

Setting the expected gain of the informed with a bad signal bidding for S shares<br />

to 0<br />

E(Sτ(v − p) | b) = 0,<br />

pins down the <strong>IPO</strong> price. Correspondingly, we obtain the following proposition:<br />

PROPOSITION 2. If K1 ≤ c ≤ K2 (where K1 <strong>and</strong> K2 are constants defined in<br />

the proof ), then in the fixed price offer the highest possible <strong>IPO</strong> price is<br />

where,<br />

N−1<br />

p = λlv(l),<br />

λl =<br />

l=0<br />

πlτl<br />

N−1 l=0 πlτl<br />

,<br />

<strong>and</strong> the informed agent with a good signal bids for ¯Q, while the informed agent<br />

with a bad signal bids for S, <strong>and</strong> the uninformed agent bids for S(1 − k).


<strong>IPO</strong> AUCTIONS 19<br />

First note that consistent with empirical evidence (Koh <strong>and</strong> Walter (1989), Levis<br />

(1990), Keloharju (1993)) in the equilibrium described in Proposition 2, dem<strong>and</strong> is<br />

positively correlated with underpricing. Indeed the latter is equal to vn − p, while<br />

the former is equal to: S(1 − k + N − n) + nQ, so that both are increasing in n.<br />

Second, manipulating the 0 profit condition of the informed investors with a bad<br />

signal, the <strong>IPO</strong> price can be expressed as<br />

cov(τ,v − p | b)<br />

p = E(v | b) + .<br />

E(τ | b)<br />

As the execution rate is decreasing in the number of good signals (n), the covariance<br />

is negative. Hence, the <strong>IPO</strong> price is lower than the expectation of the value of the<br />

asset conditional on a bad signal (E(v | b)). Underpricing pricing is necessary to<br />

convince the investors with bad signals to participate to the offer, in spite of the<br />

winner’s curse problem they face (in the same spirit as in Rock (1986)). Indeed<br />

they obtain worse execution when the share is worth a lot, <strong>and</strong> many investors with<br />

good signals place large bids, resulting in low execution rates.<br />

Further note that the expected profit of the uninformed agent is greater than that<br />

of the investors with bad signals:<br />

E(τ(v − p)) > E(τ(v − p) | b) = 0.<br />

Hence retail investors earn positive expected profits in the fixed price offer.<br />

These results emphasize that the lack of adjustment of prices to dem<strong>and</strong> leads to<br />

large rents, left both to the informed <strong>and</strong> the uninformed agents, <strong>and</strong> consequently<br />

large underpricing.<br />

3.2. Uniform Price Walrasian Auction<br />

In this mechanism, the seller sets a reservation price p, the investors submit<br />

dem<strong>and</strong> functions, <strong>and</strong> the <strong>IPO</strong> price is set to equate supply ¯ <strong>and</strong> dem<strong>and</strong>. In this<br />

market clearing uniform price auction, as in the analyses of Wilson (1979) <strong>and</strong><br />

Back <strong>and</strong> Zender (1993), there is scope for tacit collusion between investors, as<br />

stated in the next proposition:<br />

PROPOSITION 3. For any reservation price p ≥ E(v | b), there exists a<br />

Bayesian Nash equilibrium where investors’ dem<strong>and</strong>s ¯ are constant whatever the<br />

realization of the signals, <strong>and</strong> the resulting <strong>IPO</strong> price is equal to the reservation<br />

price. The equilibrium dem<strong>and</strong> of each investor is, at price p,<br />

⎧<br />

S ⎨ − σ (p − p<br />

N + 1<br />

¯ )<br />

⎩ with σ ≤<br />

1<br />

N(N + 1)<br />

S<br />

E(v | g) − p<br />

¯<br />

The intuition for this result is the following. The dem<strong>and</strong> functions have a relativelly<br />

small slope (σ ). Hence the residual supply function faced by each investor<br />

.


20 BIAIS AND FAUGERON-CROUZET<br />

is rather inelastic: It takes a big price increase to increase the residual supply. This<br />

large price impact makes it unattractive for each investor to attempt to increase<br />

her purchases. Our theoretical model provides an alternative interpretation for the<br />

thought-provoking empirical findings of K<strong>and</strong>el et al. (1997) on the uniform price,<br />

market clearing <strong>IPO</strong> mechanism used in Israel. In particular, K<strong>and</strong>el et al. (1997)<br />

find that (i) there is significant underpricing, <strong>and</strong> (ii) the (absolute value of the)<br />

slope of the dem<strong>and</strong> schedules is low, i.e., there is a flat, around the <strong>IPO</strong> price.<br />

This is consistent with our theoretical result that the slope of the dem<strong>and</strong> curve σ<br />

must be low in the tacit-collusion Bayes-Nash equilibrium.<br />

Because of the strategic complementarities between the actions of the bidders<br />

in this auction, there exist multiple equilibria, some of which do not involve tacit<br />

collusion. Yet, it is likely that the bidders will focus on the tacit collusion Nash<br />

equilibrium presented in the proposition, since it is the most advantageous for<br />

them.<br />

To cope with tacit collusion within this mechanism while satisfying the individual<br />

rationality condition of the informed investor with a bad signal, it is best for<br />

the seller to set p ¯ to E(v | b).<br />

To conclude this subsection, note that although underpricing is less severe in this<br />

auction than in the fixed price offer, it is still quite significant, due the possibility<br />

of tacit collusion it offers to the bidders.<br />

3.3. The Mise en Vente<br />

The Mise en Vente is an auction-like <strong>IPO</strong> procedure commonly used in France.<br />

It operates as follows. Five days prior to the <strong>IPO</strong> the quantity offered <strong>and</strong> the<br />

reservation price are set jointly by the bank, the broker, <strong>and</strong> the firm. On the<br />

day of the <strong>IPO</strong>, investors submit limit orders to their brokers. The latter transmit<br />

these orders to the stock exchange. The total dem<strong>and</strong> function is computed<br />

<strong>and</strong> graphically plotted by the auctioneer, who is a Bourse official. As a function<br />

of this dem<strong>and</strong>, the auctioneer sets the <strong>IPO</strong> price. As in the Book Building<br />

method, there is no formal explicit algorithm mapping dem<strong>and</strong> into prices. But<br />

price adjustment in the Mise en Vente exhibits strong empirical regularities, as<br />

shown in the next section. Eligible orders, above the <strong>IPO</strong> price, obtain prorata<br />

execution.<br />

To illustrate this description, consider the Mise en Vente of Partouche. On March<br />

29, 1995, 500,000 shares were offered. The reservation price was 185. The total<br />

dem<strong>and</strong>, expressed at all prices, amounted to 8.4 million shares, i.e., 16.29 times<br />

the supply. Figure 1 plots the dem<strong>and</strong> expressed at each price. The <strong>IPO</strong> price was<br />

set to 200, which corresponds to a percentage price adjustment of 8.1%. (Note<br />

that the price at which supply would have been equal to dem<strong>and</strong> was 220, i.e.,<br />

the <strong>IPO</strong> price was deliberately set below market clearing). Eligible orders, placed<br />

above 200, obtained prorata execution. The first secondary market price, set after a<br />

tâtonnement process which lasted two days, was equal to 215, which corresponds<br />

to 7.5% underpricing.


<strong>IPO</strong> AUCTIONS 21<br />

FIG. 1. Buy orders placed at the different prices for the Mise en Vente of Partouche, March 29, 1995.


22 BIAIS AND FAUGERON-CROUZET<br />

Denote D(p) the cumulated dem<strong>and</strong> stemming from limit orders placed at prices<br />

equal to or higher than p. The optimal Mise en Vente arising in our framework is<br />

described in the next proposition:<br />

PROPOSITION 4. If<br />

N−1 N − 1<br />

c < k(1 − π)<br />

N S<br />

¯Q − S<br />

(N − 1) ¯Q + S ′<br />

the optimal mechanism can be implemented with a Mise en Vente where (i) the reservation<br />

price is v0,(ii) investors place limit orders at prices p ∈{v0,v1,...,vN−1,<br />

pN }, (iii) the price schedule is<br />

if D(pN ) < S, then p = v0, while if D(pN ) ≥ S,<br />

<br />

then p = max p D(p) [ N ] +, min{p, s.t., D(p) = D(pN<br />

<br />

)} ,<br />

(where [.] + means that if the number within brackets is not an integer it is rounded<br />

up to the next integer), (iv) the equilibrium strategies of the investors are to dem<strong>and</strong><br />

Q shares at price pn for investors with good signals, to dem<strong>and</strong> S shares at price<br />

v0 for investors with bad signals, <strong>and</strong> to dem<strong>and</strong> S(1 − k) shares at price v0 for<br />

retail investors.<br />

In the optimal Mise en Vente, consistent with the workings of the actual mechanism,<br />

prices increase with total dem<strong>and</strong>, as the latter is equal to<br />

n ¯Q + (N − n + 1 − k)S.<br />

In equilibrium, in the optimal Mise en Vente, investors with good signals place<br />

more aggressive dem<strong>and</strong>s, as they are more eager to purchase the shares. Consequently,<br />

the higher the value of the asset, the better the private signals, the higher<br />

the dem<strong>and</strong>, <strong>and</strong> the higher the <strong>IPO</strong> price. This theoretical result is consistent with<br />

the empirical findings by Derrien <strong>and</strong> Womack (1999) that this auction-like <strong>IPO</strong><br />

method efficiently incorporates market information into <strong>IPO</strong> prices.<br />

Yet, the price set in this mechanism does not clear market in order to satisfy<br />

the incentive compatibility constraint. Correspondingly, there is oversubscription<br />

at the <strong>IPO</strong> price.<br />

Our analysis suggests that the Mise en Vente <strong>and</strong> the Book Building methods<br />

have similar incentive properties <strong>and</strong> can reach similar outcomes. This contrasts<br />

with the discussion in Benveniste <strong>and</strong> Wilhelm (1990) that, with uniform prices<br />

<strong>and</strong> even-h<strong>and</strong>ed allocations, information revelation should be impossible. The<br />

point is that, in the Mise en Vente, while the pro-rata allocation rule is indeed<br />

even-h<strong>and</strong>ed, it leads to investors with different signals being treated differently<br />

because they have placed different bids.


<strong>IPO</strong> AUCTIONS 23<br />

Consistent with our theoretical result, a recent empirical study of the Book Building<br />

method in the United Kingdom, by Cornelli <strong>and</strong> Goldreich (1998), shows that<br />

in this <strong>IPO</strong> institution: (i) the <strong>IPO</strong> price is deliberately set below market clearing,<br />

so that there is oversubscription at the <strong>IPO</strong> price, (ii) good deals are underpriced,<br />

<strong>and</strong> (iii) rationally anticipating this, investors inflate their dem<strong>and</strong> <strong>and</strong> apply for<br />

more shares than they actually desire to buy. All these features are exhibited in our<br />

theoretical model of the Mise en Vente. This highlights that, in spite of institutional<br />

differences, Book Building <strong>and</strong> Mise en Vente can have similar properties.<br />

In the uniform price market clearing auction, there exists a tacit collusion Nash<br />

equilibrium whereby the bidders place dem<strong>and</strong>s such that the <strong>IPO</strong> price is always<br />

equal to the reservation price. The issue arises, therefore, if such tacit collusion<br />

equilibria exist in the Mise en Vente. The following proposition states that it is not<br />

the case.<br />

PROPOSITION 5. If<br />

E(v | g) − v1 ><br />

1<br />

(E(v | g) − v0),<br />

N + 1 − k<br />

then tacit collusion (such that the <strong>IPO</strong> price is equal to the reservation price<br />

irrespective of the signal) is not a Bayesian Nash equilibrium in the optimal Mise<br />

en Vente.<br />

In contrast with the case of the market clearing uniform price auction, tacit<br />

collusion can be unravelled in the case of the Mise en Vente. This is because in the<br />

Mise en Vente prices respond less strongly to dem<strong>and</strong> than in the market clearing<br />

case. This is conducive to outbidding, since the investors can increase their market<br />

share, by raising their dem<strong>and</strong>, without affecting the price too much.<br />

The condition stated in Proposition 5 is not very dem<strong>and</strong>ing. For example, in the<br />

linear parametrization assumed in Benveniste <strong>and</strong> Spindt (1989), where vn = αn,<br />

the condition holds.<br />

4. EMPIRICAL ANALYSIS OF THE MISE EN VENTE<br />

To assess the empirical relevance of our theoretical analysis we confront it to a<br />

sample of 92 Mises en Vente which took place between 1983 <strong>and</strong> 1996. Our data<br />

corresponds to firms listed on the “Second Marché” an intermediary tier of the<br />

stock market created in France in 1983 for growth companies <strong>and</strong> for which the<br />

listing requirements are less stringent than for the first tier (the “Cote Officielle”<br />

or Official List). Practically all <strong>IPO</strong>s between 1983 <strong>and</strong> 1996 have taken place<br />

on the “Second Marché” (only a few exceptions, including privatizations, are on<br />

the Official List). This contrasts with the United Kingdom where <strong>IPO</strong>s are more<br />

frequently on the Official List than on the Unlisted Securities Market (see Levis<br />

(1990)). In Finl<strong>and</strong>, there are <strong>IPO</strong>s on the Helsinki Stock Exchange or on the


24 BIAIS AND FAUGERON-CROUZET<br />

TABLE 2<br />

Summary Statistics on 92 Mises en Ventes, 1983–1996<br />

Variable Average St<strong>and</strong>ard deviation<br />

Underpricing =<br />

ln(stock market<br />

clearing price/<strong>IPO</strong> price)<br />

13% 16.52%<br />

ln(<br />

Total dem<strong>and</strong><br />

Supply<br />

) 55 74<br />

Supply (number of shares) 159262 141401<br />

Price adjustment =<br />

ln(<strong>IPO</strong> price/<br />

reservation price)<br />

17.36% 10.66%<br />

Sales year before <strong>IPO</strong>∗ FF 635, 805, 979 1, 377, 289, 794<br />

Age at time of <strong>IPO</strong>∗ 28.32 21.7<br />

∗ Statistics based on 68 observations between 1983 <strong>and</strong> 1994.<br />

OTC market (see Keloharju (1993)). In 1996, an additional tier of the <strong>French</strong><br />

equity market, the “Nouveau Marché,” was created. It aims at attracting younger<br />

companies to the Bourse. Because the companies listing on this market are quite<br />

different from those listing on the “Second Marché” they are not included in the<br />

present analysis.<br />

For the <strong>IPO</strong>s in our sample we observe:<br />

• the <strong>IPO</strong> price, the reservation price, <strong>and</strong> the secondary market clearing price,<br />

• the number of shares sold,<br />

• the total number of shares dem<strong>and</strong>ed,<br />

• the age of the firm at the time of <strong>IPO</strong>, <strong>and</strong> the sales during the year prior to<br />

<strong>IPO</strong> (these variables were available only for the period up to 1994).<br />

Table 2 reports summary statistics on these variables. In particular, note that the<br />

firms going public in France are relatively older than their U.S. counterparts (a<br />

feature shared with firms going public in other European countries). Note also that<br />

underpricing is on average equal to 13%, a figure very similar to those observed in<br />

the United States in the context of the Book Building procedure, while on average<br />

the price adjustment is 17.36%.<br />

Our theoretical analysis implies that the adjustment of the <strong>IPO</strong> price over the<br />

reservation price should increase with total dem<strong>and</strong>. To test this hypothesis, we<br />

regressed price adjustment on the strength of dem<strong>and</strong> <strong>and</strong> estimated the following<br />

regression<br />

ln(Pj/R j) = a + b ln(D j/S j) + e j,<br />

where Pj is the price of <strong>IPO</strong> j, R j is the initial reservation price for this <strong>IPO</strong>,<br />

D j is the total dem<strong>and</strong> (i.e., sum of the quantities of all the orders placed at<br />

all prices in this <strong>IPO</strong>) <strong>and</strong> S j is the number of shares sold. The results are in<br />

Table 3. The first column in Table 3 presents the simple OLS results, for which<br />

the slope is significantly positive. The second <strong>and</strong> third columns present estimates


<strong>IPO</strong> AUCTIONS 25<br />

TABLE 3<br />

<strong>IPO</strong> price<br />

Regression of Price Adjustment (ln( reservation price )) on Dem<strong>and</strong> <strong>and</strong> Control<br />

Variables (t Statistics Are in Parentheses)<br />

Sample period 1983–1996 1983–1996 1983–1994 ∗<br />

Number of observations 92 92 68<br />

Estimation method OLS White correction<br />

for heteroschedasticity<br />

OLS<br />

Constant −0.027 −0.03 −0.1<br />

(−1.47) (−1.88) (−0.79)<br />

ln (<br />

Total dem<strong>and</strong><br />

Supply<br />

) 0.061 0.053 0.06<br />

(11.79) (72.8) (12.1)<br />

ln (sales year before <strong>IPO</strong>) — — 0.0008<br />

(0.13)<br />

ln (age at time of <strong>IPO</strong>) — — 0.01<br />

(1.77)<br />

∗ Statistics based on 68 observations between 1983 <strong>and</strong> 1994.<br />

obtained after correcting for heteroskedasticity, using the White adjustment, <strong>and</strong><br />

after controlling for exogenous variables such as the age of the firm <strong>and</strong> the level of<br />

its sales. The estimates obtained in these regressions are similar to those obtained<br />

in the simplest version of the test, <strong>and</strong> the coefficient of total sales is significantly<br />

positive in the three specifications. Figure 2 illustrates this analysis by plotting<br />

price adjustment (measured as the logarithm of the ratio of the <strong>IPO</strong> price to the<br />

initial reservation price) against total dem<strong>and</strong> (measured as the logarithm of the<br />

ratio of total dem<strong>and</strong> to supply).<br />

Our maintained hypothesis is that the Mise en Vente implements the optimal<br />

mechanism, like the Book Building method. Under this hypothesis, it should exhibit<br />

empirical regularities which are characteristic of this mechanism, <strong>and</strong> which<br />

are also observed in the Book Building method. One such empirical regularity is<br />

the underadjustment of prices to dem<strong>and</strong>, which manifests itself in positive covariance<br />

between price adjustment <strong>and</strong> underpricing, <strong>and</strong> which was documented<br />

empirically in the case of the Book Building method by Hanley (1993). To test<br />

this hypothesis, we regressed underpricing on price adjustment, as<br />

ln(v j/Pj) = a + b ln(Pj/R j) + e j,<br />

where v j is the first market clearing price after the <strong>IPO</strong>, Pj is the price of<br />

<strong>IPO</strong> j, <strong>and</strong> R j is the initial reservation price for this <strong>IPO</strong>. The results are in<br />

Table 4. As in the previous regression we estimated a simple OLS specification, as<br />

well as two other specifications, one correcting for heteroskedasticity <strong>and</strong> the other<br />

controlling for age <strong>and</strong> sales. Consistent with the underadjustment hypothesis, the<br />

slope is significantly positive, in all three specifications. Figure 3 illustrates this<br />

analysis by plotting underpricing (measured as the logarithm of the ratio of the<br />

first market clearing price to the <strong>IPO</strong> price) against price adjustment.


26 BIAIS AND FAUGERON-CROUZET<br />

FIG. 2. OLS regression of price adjustment on strength of dem<strong>and</strong>, 92 Mises en Vente, 1983–1996.


<strong>IPO</strong> AUCTIONS 27<br />

FIG. 3. OLS regression of underpricing on price adjustment, 92 Mises en Vente, 1983–1996.


28 BIAIS AND FAUGERON-CROUZET<br />

TABLE 4<br />

stock market clearing price<br />

Regression of Underpricing (ln ( <strong>IPO</strong> price )) on Price Adjustment <strong>and</strong><br />

Control Variables (t Statistics Are in Parentheses)<br />

Sample period 1983–1996 1983–1996 1983–1994 ∗<br />

Number of observations 92 92 68<br />

Estimation method OLS White correction for<br />

heteroschedasticity<br />

OLS<br />

Constant −0.03 −0.5 0.32<br />

(−1.15) (−3.28) (1.04)<br />

<strong>IPO</strong> price<br />

ln ( reservation price ) 0.91 0.77 0.97<br />

(6.92) (80.3) (3.2)<br />

ln (sales year before <strong>IPO</strong>) — — −0.01<br />

(−0.87)<br />

ln (age at time of <strong>IPO</strong>) — — −0.03<br />

(−1.7)<br />

ln (<br />

Total dem<strong>and</strong><br />

Supply<br />

) — — −0.00024<br />

(−0.009)<br />

∗ Statistics based on 68 observations between 1983 <strong>and</strong> 1994.<br />

5. CONCLUSION<br />

Our analysis suggests that it is important to organize <strong>IPO</strong> auctions so that<br />

the <strong>IPO</strong> price reflects the information held by investors. If this is not the case,<br />

as in fixed price offers, underpricing is bound to be large <strong>and</strong> very little information<br />

can be generated about the value of the stock during the <strong>IPO</strong> process.<br />

Yet, our analysis suggests that the optimal auction may not be the (a priori natural)<br />

Walrasian uniform price auction. In such an auction, the strong reaction<br />

of prices to dem<strong>and</strong> can lead to tacit collusion between bidders, as in Wilson<br />

(1979), which leads to large underpricing. For optimal information elicitation<br />

to be immune to tacit collusion, some form of underadjustment of prices to<br />

the informational content of dem<strong>and</strong> is required. Such information elicitation<br />

can be achieved in similar ways by apparently very different institutions: the<br />

Book Building method used in the United States <strong>and</strong> the Mise en Vente used in<br />

France.<br />

While our analysis suggests that the <strong>Dutch</strong> auction used by Open <strong>IPO</strong> may not<br />

be optimal, it raises—but does not resolve—the issue how to translate into explicit<br />

computerizable rules the mapping of dem<strong>and</strong> into prices that occurs in the Mise<br />

en Vente or the Book Building.<br />

While the present paper emphasizes the similarities between the Book Building<br />

method <strong>and</strong> the Mise en Vente auction, there are some important potential differences<br />

between the two systems. In the Mise en Vente, bids are anonymous, while<br />

in the Book Building the investment banker observes (<strong>and</strong> has entire discretion to<br />

condition on) the identity of the investors sending indications of interest. Lack of


<strong>IPO</strong> AUCTIONS 29<br />

investor’s anonymity <strong>and</strong> discretionary allocation in the Book Building can have<br />

positive consequences, as they can be used to enhance the ability to extract information<br />

from the bidders. Indeed, Benveniste <strong>and</strong> Spindt (1989) analyze how long<br />

term nonanonymous relationship can be used efficiently in the <strong>IPO</strong> process, while<br />

Sherman (1999) analyzes the superiority of the book building over auction mechanisms<br />

(see also Sherman (2000)). On the other h<strong>and</strong>, if the investment banker is not<br />

acting in the best interest of the seller, discretionary allocations can have negative<br />

consequences. In particular, they can worsen winner’s curse problems for retail<br />

investors <strong>and</strong> consequently reduce their participation in auctions. In this context,<br />

the anonymity <strong>and</strong> nondiscretionary rules used in auctions can be attractive. This<br />

may well be why Open <strong>IPO</strong> insists that its <strong>Dutch</strong> auction mecanism “levels the<br />

playing field” <strong>and</strong> “ensures that all bidders are on equal footing.” Mechanisms other<br />

than the <strong>Dutch</strong> auction could potentially be used to “level the playing field.” Biais<br />

et al. (2002) analyzed the case where the investment bank <strong>and</strong> the institutional<br />

investors can collude (so that the investment bankers are tempted to treat large<br />

institutional investors more favorably than retail investors). They showed theoretically<br />

<strong>and</strong> econometrically that the Mise en Vente can be an efficient mechanism<br />

in this context.<br />

Wilhelm (1999) discussed that, while traditional investment banking was<br />

based on relationships with a small number of large investors, <strong>Internet</strong> technology<br />

could potentially allow one to sell unseasoned shares to a large number of<br />

relatively small investors, with no or litttle relationship with the investment bank.<br />

An interesting avenue of further research could be to investigate the consequences<br />

of this evolution for the optimal pricing <strong>and</strong> allocation of <strong>IPO</strong>s. In particular,<br />

it would be interesting to analyze price discovery, information elicitation, <strong>and</strong><br />

strategic issues in the context of <strong>Internet</strong>–based sales to a large diffuse investor<br />

base.<br />

APPENDIX: PROOFS<br />

Proof of Proposition 1. As is typical in such two-type mechanism design problems,<br />

the incentive compatibility condition of the informed investor with bad news<br />

is redundant, <strong>and</strong> only the incentive compatibility condition of the informed agent<br />

with a good signal is binding.<br />

The constraint that all shares be sold is<br />

∀l = 0,...N − 1, (l + 1)q(g; l) + (N − l − 1)q(b; l + 1) + qu(l + 1) = S,<br />

which can be rewritten as<br />

∀l, q(g; l) = S − qu(l + 1) − (N − (l + 1))q(b; l + 1)<br />

.<br />

l + 1


30 BIAIS AND FAUGERON-CROUZET<br />

Substituting this value of q(g; l) in the incentive compatibility condition becomes<br />

N−1<br />

l=0<br />

πl<br />

S − qu(l + 1) − (N − (l + 1))q(b; l + 1)<br />

(vl+1 − p(l + 1))<br />

l + 1<br />

N−1<br />

≥ πlq(b; l)(vl+1 − p(l)).<br />

l=0<br />

To relax this condition, minimize qu(l + 1), for l = 0,...N − 1, by setting it<br />

equal to 0, <strong>and</strong> minimize q(b; l), l = 0,...N, by setting: q(b; l) = 0, for l > 0,<br />

<strong>and</strong> q(b;0)= Sk<br />

. Thus the incentive compatibility condition simplifies to<br />

N<br />

N−1<br />

l=0<br />

πl<br />

S<br />

l + 1 (vl+1<br />

Sk<br />

− p(l + 1) ≥ π0<br />

N (v1 − p(0)).<br />

Treating this constraint as an equality, p(N) can be written as a function of the<br />

other prices<br />

πN−1 p(N) = πN−1vN +<br />

N−2<br />

l=0<br />

− π0k(v1 − p(0)).<br />

N πl<br />

l + 1 (vl+1 − p(l + 1))<br />

Now, the objective of the mechanism designer is to maximize (under the incentive<br />

compatibility <strong>and</strong> individual rationality conditions) the expected proceeds, which<br />

can be written as<br />

N−1<br />

n=0<br />

N−2<br />

µn p(n) = µN p(N) +<br />

<br />

µn p(n),<br />

where µn denotes the probability that n signals out of N are good. Noting that µN =<br />

ππN , <strong>and</strong> substituting the incentive compatibility condition into the objective, the<br />

latter becomes<br />

π<br />

<br />

πN−1vN +<br />

N−1<br />

+<br />

n=1<br />

N−2<br />

l=0<br />

µn p(n) + µ0 p(0).<br />

<br />

N πl<br />

l + 1 vl+1<br />

N−2<br />

−<br />

l=0<br />

n=0<br />

N πl<br />

l + 1 p(l + 1) − π0k(v1 − p(0))<br />

Noting that µn+1 = ππn N<br />

, <strong>and</strong> that because of the participation constraint:<br />

n+1


p(0) = v0, this can be rewritten as<br />

<br />

N−1<br />

µN vN +<br />

<strong>IPO</strong> AUCTIONS 31<br />

<br />

N−2<br />

µnvn − µn+1 p(n + 1) − ππ0k(v1 − v0)<br />

n=1<br />

n=0<br />

N−2<br />

+ µn+1 p(n + 1) + µ0v0.<br />

n=0<br />

Noting that π0 = (1 − π) N−1 , the expected proceeds are equal to<br />

E(vn) − kπ(1 − π) N−1 (v1 − v0).<br />

Note that prices do not appear in this expression. Hence, prices are indeterminate,<br />

as long as the incentive compatibility condition is satisfied. One possible solution<br />

is to set<br />

<strong>and</strong><br />

p(l) = vl, ∀l = 1,...,N − 1,<br />

<br />

1 − π<br />

p(N) = vN −<br />

π<br />

N−1<br />

k(v1 − v0).<br />

Note that, for this solution, the quantity allocated to the retail investors qu(n), n =<br />

1,...N − 1, is no longer relevant since it is multiplied by 0 in the incentive<br />

compatibility condition. Thus, for the price solution above, the optimal mechanism<br />

does not require that the retail investors receive 0 shares for vn, n = 1,...<br />

N − 1.<br />

Proof of Proposition 2. This participation constraint of the informed investor<br />

with a bad signal, E(Sτ(v − p) | b) = 0, can be rewritten more explicitly as<br />

N−1<br />

πl[v(l − p]τl = 0.<br />

l=0<br />

Hence, the <strong>IPO</strong> price can be written as<br />

p =<br />

N−1<br />

l=0<br />

πlτl<br />

N−1 l=0 πlτl<br />

vl =<br />

N−1<br />

λlvl.<br />

l=0


32 BIAIS AND FAUGERON-CROUZET<br />

The investor with a bad signal is better off bidding for S shares than for ¯Q if<br />

c > ¯Q<br />

N−1<br />

<br />

<br />

S<br />

πl[v(l) − p]<br />

.<br />

S(1 − k + N − (l + 1)) + (l + 1) ¯Q<br />

l=0<br />

Denote K1 the right-h<strong>and</strong> side of this inequality.<br />

Now consider the informed investor with a good signal. She is better off bidding<br />

for ¯Q than for S shares if<br />

That is, if<br />

N−1<br />

<br />

<br />

¯Q<br />

S<br />

πl[vl+1 − p]<br />

− c<br />

S(1 − k + N − (l + 1)) + (l + 1) ¯Q<br />

l=0<br />

<br />

N−1<br />

S<br />

> S πl[vl+1 − p]<br />

.<br />

S(1 − k + N − l) + (l) ¯Q<br />

l=0<br />

N−1<br />

πl[vl+1 − p]S<br />

l=0<br />

<br />

¯Q<br />

×<br />

S(1 − k + N − l) + l ¯Q + ¯Q −<br />

<br />

S<br />

> c.<br />

S(1 − k + N − l) + l ¯Q + S<br />

Denote K2 the left-h<strong>and</strong> side of the inequality. Note that it is indeed positive,<br />

since<br />

¯Q<br />

S(1 − k + N − l) + l ¯Q + ¯Q ><br />

S<br />

S(1 − k + N − l) + l ¯Q + S .<br />

Proof of Proposition 3. To establish that the strategies stated in the proposition<br />

form an equilibrium, we need to prove that the investor with a good signal, anticipating<br />

that the other investors follow the equilibrium strategy, prefers to purchase<br />

S/(N + 1) shares at price p ¯ , rather than bidding more aggressively, to increase her<br />

market share. Indeed, if she does not want to do so, then a fortiori, the uninformed<br />

investor or the informed investor with bad news do not want to undercut, while<br />

they are still willing to buy a constant amount at p ¯ .<br />

Anticipating that the other investors follow their equilibrium strategies, she faces<br />

the residual supply curve:<br />

<br />

S<br />

S − N<br />

N + 1 − σ (p − p ¯ )<br />

<br />

.


<strong>IPO</strong> AUCTIONS 33<br />

Her task is to choose the price p which maximizes her expected profit, (p),<br />

where<br />

<br />

S<br />

(p) = + Nσ (p − p) (E(v | g) − p),<br />

N + 1<br />

which is equal to the product of the residual supply curve by the unit profit. To<br />

prove that she finds it optimal to purchase S/(N + 1) shares at price p ¯ , we need to<br />

show that this is decreasing for all prices above p ¯ .Now<br />

∂(p)<br />

p<br />

<br />

S<br />

= Nσ (E(v | g) − p) − + Nσ (p − p)<br />

N + 1<br />

is decreasing in p. Hence, to show that it is negative for all prices larger than or<br />

equal to p ¯ , we only need to show that it is negative for p ¯ , i.e.,<br />

that is<br />

<br />

S<br />

Nσ (E(v | g) − p) − < 0,<br />

¯ N + 1<br />

σ<<br />

1<br />

N(N + 1)<br />

S<br />

E(v | g) − p ¯<br />

Proof of Proposition 4. First, consider the case of the informed investor with<br />

a good signal. Her equilibrium expected gain is<br />

π N−1 (vn − p) S<br />

− c.<br />

N<br />

Could she obtain more by deviating from her equilibrium strategy? First, suppose<br />

she dem<strong>and</strong>s a lower amount q, still at price pn. Ifq > S, her expected gain is<br />

strictly lower than in equilibrium, since she just obtains less shares. If q ≤ S, then<br />

her expected gain is<br />

π N−1 S<br />

(vn − p)S<br />

(N − 1) ¯Q + S ′<br />

which is lower than her equilibrium gain if<br />

π N−1 <br />

N − 1 ( ¯Q<br />

<br />

− S)<br />

(vn − p)S<br />

N (N − 1) ¯Q + S<br />

.<br />

> c.<br />

Second, suppose she places a bid at a lower price than pn, say P.IfP < pn−1, the<br />

<strong>IPO</strong> price is pn−1, while if P ≥ pn−1, then the <strong>IPO</strong> price is above P. In both cases<br />

she obtains 0 shares.


34 BIAIS AND FAUGERON-CROUZET<br />

The retail investors <strong>and</strong> the informed investor with a bad signal obtain 0-expected<br />

gains in equilibrium <strong>and</strong> it is straightforward to see that they cannot obtain positive<br />

profits by deviating.<br />

Proof of Proposition 5. Consider a c<strong>and</strong>idate equilibrium, whereby tacit collusion<br />

would prevail, <strong>and</strong> in which the <strong>IPO</strong> price would always equal v0. In such<br />

an equilibrium the investors would bid as much as possible while not pushing the<br />

price above v0 <strong>and</strong> still deterring the other investor from competing away market<br />

shares. To avoid pushing the price above v0, they place bids for (slightly less than)<br />

S<br />

N shares at pN <strong>and</strong> for S(1 − 1/N) atv0. The expected profit from such tacit<br />

collusion after observing a good signal is<br />

S<br />

[E(v | g) − v0].<br />

N + 1 − k<br />

If, she expects the others to follow this strategy, the informed investor placing a<br />

bid for S shares at p1 = v1 expects to gain<br />

S[E(v | g) − v1].<br />

Hence, she prefers to follow that strategy rather than to implicitly collude if<br />

E(v | g) − v1 ><br />

1<br />

[E(v | g) − v0].<br />

N + 1 − k<br />

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