ipo-mechanisms, monitoring and ownership...

Journal of Financial Economics 49 (1998) 45—77

IPO-mechanisms, monitoring and ownership structure1

Neal M. Stoughton*,!, Josef Zechner"! Graduate School of Management, University of California — Irvine, Irvine, CA 92697, USA

" University of Vienna, Department of Business Administration, A-1210 Vienna, Austria

Received 9 September 1996; received in revised form 26 September 1997

Abstract

This paper analyzes the effect of different IPO mechanisms on the structure of shareownership and explores the role of underpricing and rationing in determining investors’shareholdings. We focus on the agency problem that results when large institutions arethe only investors capable of monitoring the firm whereas small shareholders free-ride onthese activities. The major conclusion is that some well-known aspects of IPOs may beexplained as rational responses by the issuer to the existence of regulatory constraints inpublic capital markets. There is a two-stage offering mechanism in which the investmentbanker, acting in the interests of the issuer, optimally rations the allotment of shares tosmall investors in order to capture the benefits associated with better monitoring byinstitutions. Importantly, in our model, the existence of underpricing (and oversubscrip-tion) is an indication that the issuer has received a higher ex ante price than would havebeen obtained through a competitive Walrasian-type offering process. ( 1998 ElsevierScience S.A. All rights reserved.

JEL classification: G24; G32; G38

Keywords: IPOs; Monitoring; Institutions; Underwriting

1. Introduction

The interactions between ownership structure, corporate governance and firmvalue have attained recognition as an important topic in corporate finance.

*Corresponding author. Tel.: 949/824-5840; fax: 949/824-8469; e-mail: [email protected].

1We would like to thank the referee, Larry Benveniste, and the editor, William Schwert, as well asBruno Biais, Patrik Bolton, Susanne Espenlaub, Michael Fishman, Thierry Foucault, Gunther

0304-405X/98/$19.00 ( 1998 Elsevier Science S.A. All rights reservedPII S 0 3 0 4 - 4 0 5 X ( 9 8 ) 0 0 0 1 7 - 8

Considerable attention has recently focused on the implications of heterogeneityof investors and equity ownership structure. This has led to a greater under-standing of the links between corporate finance and the underlying institutionalmakeup of modern financial markets.

In particular, there is a growing empirical literature on the relation betweenthe fraction of shares owned by large investors such as pension funds and firmperformance.2 A number of these studies conclude that institutional sharehold-ings do affect firms’ market values. Several recent papers derive theories ofoptimal institutional ownership levels.3 The main purpose of this paper is toaddress the question of how the initial public offering (IPO) process determinesthe equilibrium structure of shareholdings. More specifically, the paper analyzesthe effect of different IPO mechanisms on share ownership and explores the roleof underpricing and rationing as potentially rational responses to regulatoryconstraints and institutions.4

There is a rich empirical and theoretical literature describing the IPO under-pricing phenomenon.5 This paper provides a theoretical justification for theexistence of IPO underpricing that is based on moral hazard, rather thanadverse selection or asymmetric information. The existing literature on IPOsdoes not document that the ownership structure per se affects firm value. Mostpapers focus on asymmetric information during the issue process and featureunderpricing as a result. The basic philosophy behind these adverse selectionpapers is that underpricing is a cost to the issuer, which is borne from the need toextract information from or signal value to outside investors.

Franke, Julian Franks, Mark Grinblatt, Jean Jacque Laffont, Alexander Ljungqvist, Ernst Maug,Gerhard Orosel, Pegaret Pichler, Raguram Rajan, Jay Ritter, Ailsa Roell, Kristian Rydquist, JeanTirole, Elu von Thadden, Ivo Welch, William Wilhelm, Joe Williams and Andrew Winton forhelpful comments. This paper has been presented at the University of Alberta, Baruch College, theFree University of Brussels, the University of Gothenburg, HEC, the University of California, Irvine,the University of Lausanne, the London School of Economics, the University of Odense, StockholmSchool of Economics, the University of British Columbia, UCLA, the University of Utah, the CEPRconferences in Tolouse and Gerzensee, the American Finance Association, the Western FinanceAssociation and the European Finance Association. This paper was written while Stoughton visitedthe University of Vienna. He expresses his appreciation to the faculty and staff for an enjoyable stay.

2Examples include Holthausen et al. (1990), Brickley et al. (1988), Jarrell and Poulson (1987),Nesbitt (1994), Opler and Sokobin (1995), Field (1995), Smith (1996) and Wruck (1989).

3See Bhide (1993), Bolton and vonThadden (1995), Burkart et al. (1997), Kahn and Winton (1998)and Pagano and Roell (1995).

4We analyze the problem from the issuer’s perspective and therefore do not address the largerquestion of an optimal regulatory environment.

5Examples include Allen and Faulhaber (1989), Benveniste and Spindt (1989), Benveniste andWilhelm (1990), Chemmanur (1993), Grinblatt and Hwang (1989), Ritter (1987), Rock (1986), Tinic(1988) and Welch (1989).

46 N.M. Stoughton, J. Zechner/Journal of Financial Economics 49 (1998) 45—77

Ownership structure affects the efficiency of corporate governance and thusthe intrinsic value of the firm. In our model, underpricing and rationing may berational phenomena from the standpoint of the issuer. Rationing providesa mechanism whereby different classes of investors may be treated differentially,although they all purchase securities at a common price. We show that withoutthe possibility of treating different classes of investors differently, the offeringprice and revenues raised would be reduced. In our model, the firm’s investmentbanker plays two key roles: (1) identifying investor classes and enforcing differ-ential treatment; and (2) transferring value from the investors to the issuer. Bothresult from the continuing nature of the relationship between underwriters andinstitutions.

There are several recent related papers.6 In an independently developedpaper, Mello and Parsons (1998) study the optimal dynamic allocation processbetween active and passive investors. They similarly find that it may be optimalto favor large shareholders because of the public good created by externalbenefits of control. Mello and Parsons explore the implications of multiplerounds of share allocations in which the prices paid by investor classes can differ.In contrast, our paper develops a mechanism which maximizes revenues evenwhen price discrimination between investor classes is not allowed. Brennan andFranks (1997) also discuss some of the implications of investor heterogeneityand the need for rationing. In their model, rationing favors small rather thanlarge investors, and issuers are willing to permit underpricing because of non-pecuniary benefits of control.7 In our model, control considerations are absent.This may be consistent with some of the recent government privatizations andIPO’s in which initial owners plan to relinquish control.8

Benveniste and Spindt (1989) show that asymmetric information between theissuer and institutional investors may lead to underpricing and strategicrationing.9 In their model underpricing is a cost to the issuer and is necessary toadequately compensate institutional investors for supplying their private

6A unique, but less directly related paper is that of Milne and Ritzberger (1991) whose model ofIPO underpricing stems partly from multiple equilibria in secondary market trading.

7 In Chowdhry and Sherman (1996), issuers may wish to favor small investors to reduce thewinner’s curse problem originally modelled by Rock (1986). Biais, Bossarts and Rochet (1996)investigate the optimal auction in this environment.

8 Julian Franks informed us of the interesting case of the Wellcome IPO in Britain. In that case,the original owners (a foundation) explicitly rationed the share allocation to members of the board ofdirectors. In this case it appeared that the foundation wanted to reduce the chance that controlconsiderations would negatively impact the firm value. Subsequently the firm was taken over byGlaxo.

9See Sherman (1997) for an extension of the model by Benveniste and Spindt (1989) to the case inwhich the institution’s information acquisition is endogenized.

N.M. Stoughton, J. Zechner/Journal of Financial Economics 49 (1998) 45—77 47

information. Rationing in favor of institutional investors reduces requiredunderpricing. In our model, strategic rationing and underpricing are posit-ively correlated. If the issuer is not allowed to ration strategically, ourmodel predicts zero underpricing but implies a lower intrinsic value due tolack of monitoring. Underpricing and rationing in favor of large shareholderslead to a higher intrinsic value of the firm which more than offsets the amount ofunderpricing.

Another feature of our model is that large shareholders do not sell out in thesecondary market in order to capture the gains from underpricing. This isconsistent with recent empirical evidence reported by Hanley and Wilhelm(1995). They document a high degree of correlation between share ownership ofinstitutions at the IPO date and at the end of the subsequent quarter.

Our model is related to the analysis in Admati et al. (1994). In their papera large investor can also affect firm value by monitoring. However, the initialendowment of shares is exogenous. We account for the endogeneity of the initialendowment and its interdependency with the IPO mechanism.

The structure of the paper is as follows. The problem of an entrepre-neur selling securities to large and small shareholders is introduced in Section 2.Section 3 establishes that in the presence of unobservable monitoring activ-ities there exists a second-best optimal IPO mechanism. This serves as abenchmark for the alternative mechanisms. A Walrasian mechanism is ana-lyzed in Section 4 and price discrimination in Section 5. A two-stage-rationingmechanism with underpricing is introduced in Section 6. Section 7 looks at theeffects of secondary trading, and Section 8 concludes and discusses empiricalimplications.

2. Monitoring and the offering process

The model features an entrepreneur who plans to sell all his shares toa collection of outside investors.10 Alternatively, one can view this problem fromthe perspective of the venture capitalist who gives up control and sells his stakeat the time of the IPO. The outside investors are grouped in two classes: largeinvestors (L) and small investors (S). The major distinguishing feature betweenthe two classes is that large investors have the ability to monitor the activities ofmanagement in the firm while small investors do not. This is indicative ofthe practical situation in which large investors are essentially institutionalinvestors who have developed procedures for observing management activities

10The results are easily generalizable to a situation in which some fixed percentage less than100% of the shares are sold.


and influencing them for the benefit of all shareholders. For simplicity, eachinvestor group is represented by a single composite investor.11

The entrepreneur in the model is able to elicit the assistance of an investmentbanker in selling securities to the public. We focus on the investment banker’srelationship with investor groups. In this respect it is critical that the investmentbanker be able to differentiate between large and small investors and to enforceagreements whether they are explicit or implicit. For simplicity, we neglect theinvestment banker’s compensation in the offering process. Equivalently, theinvestment banker’s compensation is equal to a constant amount in all mecha-nisms.

We analyze a single-period model which is extended to two periods inSection 7. The single-period model can be interpreted as one in which theinvestment banker prevents the large investors from selling their securities in thesecondary market. An explicit mechanism that is frequently used to discourageflipping of shares is penalty bids. This occurs whenever the managing under-writer requires syndicate members to forfeit their compensation when issuedshares are repurchased to stabilize prices.12 Syndicate members therefore havean incentive to discourage their investors from flipping their shares in thesecondary market. Since underwriters have some leverage over investorsthrough the repeated nature of their relationship, penalty bids effectively insureagainst quick sales of initial allocations in the secondary market.13

The structure of the model is as follows. There is a single period. At thebeginning of the period (the time of the public offer), some mechanism is used forallocating shares to investors L and S. We will discuss a number of mechanismsin this paper, each of which is differentiated by the type of involvement of theinvestment banker. The most general mechanism features a set of equity frac-tions and monetary transfers from the two types of investors to the entrepreneur.This is described by the pair (a, g

L) representing the equity fraction, a, given to

L in exchange for total payment gL, and (b, g

S) representing the corresponding

equity fraction, b, allocated to S in exchange for payment gS. At the end of the

11By representing each group as a single investor we are not considering strategic effects betweenmembers of each group. This is justified if, for example, members within each class can achieve fullybinding contracts with each other and if their risk preferences are derived from the same HARAclass. Opler and Sokobin (1995) discuss the role of the Council of Institutional Investors asa coordinating body in the U.S. However, if a free rider problem exists within the group of largeinvestors, then the relation between monitoring and share allocations would become more complex.This is an interesting avenue for further research.

12For a detailed discussion and analysis of penalty bids and their role in reducing adverseselection costs, see Benveniste et al. (1996).

13As mentioned by Benveniste et al. (1996), Prudential Securities, for example, decides on futureshare allocations on the basis of past purchases and retention of shares by a syndicate member’sclients in previous deals.


period, the large investor employs a costly monitoring technology that increasesthe expected value of the end-of-period cash flow distribution. Monitoringincludes any activity that creates value that is shared by all shareholders inproportion to their holdings. The basic problem facing the entrepreneur is tochoose an appropriate mechanism given that the level of monitoring cannot bespecified contractually between the entrepreneur and the two investors. Becausemonitoring is inherently unobservable and small investors can free-ride on theseactivities, the incentive for monitoring by L must be a function of the ownershipproportions provided by the offering mechanism.14

We assume that ending cash flows are normally distributed and investorpreferences are described by exponential utility (constant absolute risk aver-sion). We focus on a situation where there is a single risky firm and where themonitoring technology is ‘allocation-neutral’.15 Given the exponential-normalassumptions, preferences can be described by a certain-equivalent wealth witha constant tradeoff between mean and variance of cash flows (see Varian 1992,pp. 189—190).

Preferences in the single-period model are therefore defined as

ºL(a, g

L)"ak(m)!

1

2

a2p2

o!C(m)!g

L, (1)

and

ºS(b, g

S)"bk(m)!

1

2

b2p2

q!g

S, (2)

where k(m) represents the expected cash flows of the firm as a function of themonitoring level, m; p2 is the variance of the ending cash flow distribution and isassumed to be unaffected by monitoring; o and q represent the risk tolerances ofthe large and small investors, respectively, and C(m) is the cost of monitoring.

For concreteness, we further specify the benefits and costs of monitoring asfollows:

k(m)"k#m, (3)

14Many real-world examples of the positive influences provided by institutional investors aredocumented in Useem (1996). Another example told to one of the authors is an instance in whicha pharmaceutical firm was forced by its institutional investors to rescind a poison pill(!).

15Considering the firm in isolation from the rest of the market is essentially without loss ofgenerality as long as the firm in question has no external effects on other firms. Given thesepreference and distribution assumptions, it is always possible to redefine cash flow risk relative to themarket numeraire, i.e., as systematic risk and to adjust all risk parameters accordingly. Anallocation-neutral monitoring technology, as defined in Admati et al. (1994), does not depend on theallocation of shares. That is, the cost and the benefit of monitoring only depend on m, the intensity ofmonitoring chosen by the large investor, not on holdings, a, directly.


and

C(m)"12cm2, (4)

where k is a constant and c represents the marginal cost coefficient of monitor-ing.16 Although we do not model potential agency problems between largeinvestors such as pension funds and their clients, this could be one of thedeterminants of the cost function. From these assumptions, including the as-sumption that the variance of the cash flow distribution is unaffected bymonitoring, it is clear that if there were complete contracting, the first-best levelof monitoring would be m*"1/c. This is obtained by maximizing the benefitminus the cost.

However, in our model monitoring is non-contractible and so the largeinvestor, L, determines the (second-best) optimal amount of monitoring bysolving the following problem:

maxm

a(k#m)!1

2

a2p2

o!

1

2cm2!g

L, (5)

whose solution is

m"a/c. (6)

That is, the second-best monitoring is always below the first-best by an amountthat increases as the ownership share of the large investor decreases. In ourenvironment, the small investor, S, always free-rides on the monitoring done bythe large investor and there is an inherent inability to transfer the positiveexternality between the two investor groups.

We now turn to the question of what mechanism form should be used by theentrepreneur in offering shares to the public. Several alternatives are considered,each of which is distinguished by the actions of the investment banker and thedegree of outside regulatory influences on the entrepreneur.

3. Second-best mechanism

The second-best mechanism for offering securities represents the greatestbenefits the issuer can obtain from the investment banker, given that monitoringis non-contractable. Through the investment banker’s continuing relationships,investor types are identified and separate negotiations take place. As a result,

16Although we have chosen these functional forms for simplicity, our basic results are unalteredfor arbitrary functional forms as long as k(m) is weakly concave and C(m) is strictly convex.


utilities are brought down to their reservation values. The second-best optimumis therefore a standard Pareto optimum problem as described by

maxa,b,gL,gS

gL#g

S, (7)

subject to Eq. (6) and

ºL*ºM

L(8)

ºS*ºM

S, (9)

for fixed reservation utility constraints on the large and small investors, ºML

andºM

S.17It is clear that the reservation utility constraints are always binding, and since

b"1!a, the second-best optimum problem may be rewritten as

maxa

aAk#acB!

a2p2

2o!

a22c

#(1!a)Ak#acB!

(1!a)2p2

2q!ºM

L!ºM

S,

(10)

after substituting for the monitoring constraint (6). The first-order condition forthis problem is18

1

c!

ap2

o!

ac#

(1!a)p2

q"0, (11)

which simplifies to

a**"1c#p2

q1c#p2

o#p2

q. (12)

Inspection of Eq. (12) reveals that the second-best optimal share given to thelarge investor, L, is a decreasing function of the cost coefficient, c. If monitoringcosts are near zero, then a** approaches one. In such circumstances thesecond-best optimal monitoring expenditures by the large investors approachthose that would have occurred had monitoring been contractible (first-best).Intuitively, monitoring is relatively so cheap that the entrepreneur is better-offwhen most of the shares are allocated to the large investor.

At the other extreme, when c is large a** approaches o/(o#q), the optimalequity ownership structure when only risk-sharing considerations are present.

17Although not modeled here, the value of these constraints could be derived from otherinvestment opportunities.

18The maximand is globally concave, and therefore this condition is also sufficient.


This is also intuitive. In general, the second-best optimal equity share allocatedto the large investor is increased above the risk-sharing amount in order for theentrepreneur to capture some of the externality created by the benefits enjoyedby small investors from monitoring activities.

In order to implement the second-best optimal mechanism, the investmentbanker would have to make separate offers to each investor class. In fact, theinvestment banker would not be constrained to offer shares to each investorgroup with the same per-unit price. Although the per-unit prices cannot bespecified without knowing the reservation utility levels, in general the largeinvestors will be given a better price to encourage them to buy more equity thanwould be optimal when only risk-sharing considerations are present.

4. The Walrasian mechanism

We now contrast the previous outcome with the results obtained withoutusing the services of an investment banker. The mechanism we consider here isvery simple. Investors participate under identical terms by purchasing at a fixedprice. The large and small investors are assumed to be price-takers in the marketfor the initial public offer. The market clears at a price such that the demand byL, a, and the demand by S, b, clear the market. This is a Walrasian mechanismcorresponding to the ‘no last round of trade’ model in Admati et al. (1994).Although the large investors do account for how much monitoring they do, theydo not take into account the effect that their trades will have on the prices theypay.

Defining p as the price of 100% of the shares, the expected utility of investorsL and S are given by Eqs. (1) and (2) with ap replacing g

Land bp replacing g

S.

Differentiating Eq. (2) with respect to b shows that the optimal amount of equityholding by the small investors equals:

b"qAk#ac!p

p2 B. (13)

The large investors do take account of the effect of their induced monitoringexpenditure and therefore, inserting Eq. (6) into Eq. (1), we obtain the followingmaximization problem:

maxa

aAk#ac!pB!a2

p2

2o!

a22c

. (14)

The first-order condition for this problem implies that the large investor’sinverse demand function is

p"k#aA1

c!

p2

o B. (15)


Note that the second-order condition holds if c'o/p2, i.e., the monitoring costis not too small relative to the large investor’s risk tolerance. This second-ordercondition also implies that the inverse demand function is downward sloping.19

To solve for the equilibrium price, we substitute Eq. (15) into Eq. (13) andthen use market clearing, a#b"1. After a number of algebraic manipulations,we arrive at the Walrasian equilibrium price:

p*"k#o!cp2

oc#qc. (16)

Of greater interest is the induced ownership structure in the Walrasian mecha-nism. Substituting the market-clearing price into Eq. (15), we see that the largeinvestor purchases

a*"o

o#q. (17)

This is the Pareto optimal risk-sharing amount, and it is independent of the costof monitoring. Since a*(a**, the Walrasian mechanism always features lessmonitoring than the second-best optimum. Therefore, the Walrasian mecha-nism suffers from the major difficulty that there is an inability for the entrepre-neur to extract any of the benefits associated with the positive externality onsmall investors.

This is the inherent conflict between the form of the issuing process and theheterogeneity of investor groups. If the entrepreneur does not utilize the invest-ment banking services of an underwriter, the price-taking process only allowsrisk-sharing to be achieved. But with monitoring, strict risk-sharing conflictswith the need to favor institutional shareholders in order to provide incentivesfor enhanced monitoring activities.

5. Price discrimination

Having explored the two extremes of the second-best and the Walrasianmechanisms, we now consider two intermediate mechanisms. In these mecha-nisms underwriters are able to identify the types of investors through previousexperience and continuing relationships. They are therefore able to price dis-criminate between the large and small investors.20 In contrast to the second best

19 In addition if this condition is not satisfied, the Walrasian equilibrium does not exist, asdiscussed in Admati et al. (1994).

20Alternatively, price discrimination could be achieved via multiple rounds of share offerings, asanalyzed by Mello and Parsons (1998).


mechanism, it is assumed that the investment banker cannot negotiate directlywith each investor.

In Section 5.1, both types of investors are offered shares at a fixed price andmay optimally choose the quantities they wish to purchase, taking prices asgiven. This corresponds to a situation where the investment banker acts as anunderwriter and conducts a discriminatory auction among investor groups.Section 5.2 allows the investment banker to make a take-it-or-leave-it offer tothe large investor. This can be motivated by the presence of an underwriter whohas a long-term relationship with the large investor and may possibly excludehim from future distributions if he deviates from the equilibrium quantity.Hence, although both mechanisms feature discriminatory pricing, they differ inthe amount of bargaining power that is exerted on the two investor types.

While most jurisdictions, such as the U.S., prohibit price discriminationbetween investors in the security offering process, there may be ways in whichissuers can effectively discriminate among different investor groups. Examplesinclude the use of private placements, letter stock or restricted stock classes suchas voting and non-voting shares which convey the same cash flow rights. In theU.S. such restricted securities are governed by SEC Regulation 144. Thisregulation specifies a minimum holding period of one year for non-affiliateinvestors.21 Moreover there are volume restrictions and mandatory disclosurerequirements prior to security resales during the first two years. The expressedpurpose of these regulations is to prevent issuers from circumventing theregulatory requirements on the public offering process through the use ofnon-registered securities. Therefore, the extent to which private placements canbe used to overcome fair price rules is limited in the U.S.

5.1. Price discrimination with a fixed price auction

In this subsection, we allow the investment banker/underwriter to offer sharesto the two types of investors at fixed but possibly different prices. Suppose thatpL

denotes the price paid by large investors and pS

the price paid by smallinvestors. Large and small investors both take price as given when computingtheir demands. Substituting these prices into Eqs. (13) and (15), we find that

pL"k#aA

1

c!

p2

o B, (18)

and

pS"k#A

ac!

p2(1!a)

q B. (19)

21The holding periods were shortened and a number of other changes were made in February1997.


The entrepreneur wants to maximize total revenue, so the problem is

maxa

a pL#(1!a) p

S. (20)

subject to Eqs. (18) and (19). Substituting the price expressions from above anddifferentiating, we obtain the following expression for L’s optimal equity frac-tion, a0:

a0"1c#2p2

q2p2

o #2p2

q. (21)

Notice that the second-order condition, c'o/p2, from L’s utility maximizingproblem, implies that a(1.

It is not surprising that the optimal equity ownership for the large investor inthe price discrimination case exceeds that for the Walrasian mechanism,a0'a*. Since the Walrasian mechanism imposes the additional constraint thatpL"p

S"p, it is actually a special case of the price discrimination mechanism

with an additional degree of freedom removed from the underwriter. Thisadditional degree of freedom allows the underwriter to favor the large investor,which is optimal to encourage a greater level of ex post monitoring. ComparingEqs. (21) and (12) we find that a0(a** if and only if 1/c(p2/o!p2/q, i.e., ifthe monitoring cost is sufficiently great. If the small investors have a large risktolerance then this condition will hold, as it follows from the large investor’ssecond-order condition. On the other hand, if risk-sharing considerations arenot important, then the underwriter may have an incentive to price the equityoffering in such a favorable manner to the large investor that L’s ownershipimplies a larger monitoring expenditure.

Given Eqs. (18) and (21), the expression for the price offered to the largeinvestor is computed as

pL"k#

oq2p2c#o!q

2!cp2

cq#co. (22)

Comparing this price to that under the Walrasian equilibrium, we see thatpL(p* as long as

q2A

op2c

!1B(0, (23)

which follows from the second-order condition of L’s maximization problem.Not surprisingly, the price discrimination model predicts that L is given a lowerprice than he was under the Walrasian mechanism.

On the other hand, S is charged a higher per-unit price. It is not hard to showthat p

S!p

L"1/(2c), i.e., the greater the cost of monitoring, the lower the price


discrepancy. Since the Walrasian mechanism is a special case of the pricediscrimination mechanism, it is clear that the entrepreneur always raises morerevenue in the latter case. If this model of price discrimination is applied to theenvironment with different classes of stock as in the letter stock example, wepredict that restricted stock will be priced lower than unrestricted stock. Inter-estingly, this pricing discrepancy does not arise due to restrictions on trading ordifferences in control rights, but rather as an inducement for the large investor tohold a larger fraction of the firm than would otherwise be the case. In contrast tothe model of Longstaff (1995), we predict that the observed pricing discounts arenot dependent on the volatility of prices, but rather on the potential gains frominstitutional monitoring.

5.2. Price discrimination with a negotiated offering

Here we consider a hybrid between the price discrimination mechanismdescribed in the previous subsection and the second-best mechanism. Thesecond-best mechanism assumes that a take-it-or-leave-it offer can be made tothe large and to each small investor. An intuitive justification for such anallocation is based on a repeated relationship which allows the investmentbanker to exclude an investor from future distributions if a deviation from theequilibrium quantities is observed.

In practice such a repeated relationship may well exist between a largeinstitutional investor and the investment banker, but is less likely to existbetween the underwriter and small retail investors. We therefore investigatea mechanism involving discrimination, where small investors’ quantities aredetermined by their first-order conditions and the large investor is forced to hisreservation utility by a take-it-or-leave-it offer.

Suppose that pL

denotes the price of the shares given to the large investor andpS

the price for the small investors. Given that the large investor is at thereservation utility constraint, his utility is

aAk#acB!(1/2)

a2p2

o!

a22c

!apL"ºM

L. (24)

Hence,

apL"!ºM

L#ak#

a22 A

1

c!

p2

o B. (25)

Small investors’ price-taking demands are determined, as before, by Eq. (19).The problem of the entrepreneur is

maxa

apL#(1!a)p

S, (26)


or

maxa

!ºML#k#(1/2)

a2c#

(1!a)ac

!(1/2)a2p2

o!

(1!a)2p2

q. (27)

Solving the appropriate first-order condition for a yields

aL "1c#2p2

q1c#p2

o#2p2

q. (28)

We can now compare Eq. (28) with the case of price discrimination througha fixed price offer in Eq. (21). It is easily verified that the second-order conditionin Section 5.1, c'o/p2, implies that aL 'a0. Thus, because the investmentbanker has the bargaining power with the large investor, the investment bankercan increase the optimal allocation to the large investor. Furthermore, inspec-tion of Eq. (12) shows that the amount of share ownership allocated to the largeinvestor is also greater than the second-best amount. Intuitively, if the invest-ment banker can extract more surplus from the large investor, but not fromsmall investors, it becomes optimal to forego possible risk sharing gains andinstead increase the benefits from monitoring. This represents a major benefit tothe entrepreneur from the relationships between investment bankers and institu-tional investors.

In general, the price given to the large investor will depend on his reservationutility value. Using the expressions above for p

Land p

S, and substituting for

aL from Eq. (28), it is easy to show that the difference in prices is bounded belowby the difference in the fixed price case, i.e., p

S!p

L*1/(2c). That is, if the

investment banker has greater bargaining power with the large investor, moreprice discrimination is implied.

6. Rationing

Since many jurisdictions do not allow price discrimination, the entrepreneurcannot necessarily achieve the outcome of the previous section. However,a regulatory constraint disallowing price discrimination does not imply that theissuing process must be accomplished via the Walrasian mechanism. Indeed, theunderwriter may still be able to utilize relationships with the large investors inorder to enforce better overall terms for the entrepreneur.

We therefore consider a mechanism involving rationing under which theentrepreneur can raise more revenue. Standard arguments would appear toimply that rationing is inefficient. After all, the first order effect of raising morerevenue by increasing the price would seem to dominate the second-order effectof the reduction in monitoring activities. However, the rationing mechanism wepropose does not imply that shares are offered to both large and small investors


on the same basis. The fact that observed per-unit prices are identical does notimply that investors are treated identically in the initial public offer.

In practice the use of ‘book-building’ and other similar procedures by theunderwriter imply that there is an interaction between the large investors andthe investment banker. In this section, as in the previous subsection, we modelthe relationship as one that permits the underwriter to offer a ‘take-it-or-leave it’IPO price and share allocation to L. However, unlike the previous section,regulations require that the identical price be offered to S. After setting up theproblem, we derive the result that the price allocation offer by the underwriter isequivalent to providing a linear demand schedule of IPO prices and shareallocations to the large investors and allowing them to select their optimal shareallocation from the schedule.

The rationing mechanism we propose involves two stages. In the firststage, the underwriter dictates a price and allocation pair, (p, a) to the largeinvestor. In the second stage, the small investors receive the remainingamount, 1!a at the identical per unit price paid by the large investors. Whenregulations imply that small investor participation is important, this two-stage mechanism is shown below to indeed be a rationing mechanism, sincethe small investors would actually like to purchase more at the same per-unitprice.

In determining the optimal IPO price and allocation to L, the underwriterfaces three constraints. First, the large investor’s reservation utility constraintmust be satisfied, i.e., he must be willing to participate. Second, the price must beset so that small investors are willing to hold the balance of the equity not takenby the large investor. Third, small investors must be given some minimumparticipation in the offer as modeled here by a reservation utility constraint. Webelieve this participation constraint to be a realistic reflection of many regula-tory considerations that require fairness in the offering of securities. Forexample, listing requirements of stock exchanges generally include a con-straint that a certain percentage of each company’s stock must be widely held orthat the stock have a minimum average trading volume. In addition, in anenhanced model of the offering process, the small investor’s utility constraintmay simply reflect the issuer’s desire to have broad participation across investorclasses.

The optimal (rationing) mechanism is defined as the solution to the followingproblem for the entrepreneur:

maxp,a

p (29)

subject to

ºL*0, (30)


where

ºL,aAk#

ac!pB!

1

2

a2p2

o!

1

2

a2c

, (31)

b*(1!a) where b3argmaxºS,bAk#

ac!pB!

b2p2

2q, (32)

ºS*ºM

S. (33)

As is clear from comparing constraints (30)—(33), we view the regulatory environ-ment as providing a more stringent requirement for small investor participationas compared to the large investor. We regard this assumption as a naturalimplication of protection for small investors. In any event, the impact on thenature of the optimum as ºM

Schanges will be discussed below.

6.1. Non-binding participation constraint for the large investor

We first solve the problem when the participation constraint for the largeinvestor is non-binding at the optimum. This occurs whenever the reservationutility constraint on small investors, ºM

S'0 is sufficiently large that large

investors also earn a positive surplus at the optimum.In considering the solution to the rationing mechanism, it is apparent that in

choosing the price-allocation pair, the underwriter is essentially enforcing a par-ticular utility for the large investor. It is convenient here to consider the dual ofthis problem in which the utility of the large investor can be represented asarising from an optimal choice of share allocation along a linear demandschedule.

¸emma 1. Assume that the large investor’s participation constraint, (30), is non-binding. ¹hen there exist two parameters, a, and b, such that any feasible (p, a)value in the rationing mechanism may be represented as the solution to maximiz-ing º

Lsubject to Eq. (31) along the line p(a)"a#ba. Moreover, the set of

feasible (p, a) values can be represented as

p"k!ab#aA1

c!

p2

o B. (34)

Proof. Let ºL'0 represent a feasible value of the utility of the large investor in

the rationing mechanism. To show that this utility can be realized as thesolution of maximizing º

Lsubject to p"a#ba, it is sufficient to show that the

indifference curves of the large investor in (p, a)-space are concave. Thus, anypoint along them can be generated as the point of tangency between the linep"a#ba and the indifference curve. Taking the total derivative of Eq. (31)


implies that

dp

da"

1

aAk#ac!p!

ap2

o B. (35)

The second derivative can be simplified to give

d2p

da2"!

1

a2A2(k!p)#aA1

c!

p2

o BB. (36)

By the hypothesis of the lemma, ºL'0, which using Eq. (31) is equivalent to

k!p#a2A

1

c!

p2

o B'0. (37)

It is straightforward to see that this implies that the second derivative,d2p/da2(0.

Finally, given the linear schedule, p"a#ba and substituting into Eq. (31)and differentiating with respect to a yields Eq. (34). h

Lemma 1 shows that the underwriter can equivalently utilize a linear scheduleinstead of a take-it-or-leave it offer, without loss of generality. This representa-tion simplifies the following analysis and allows an intuitive interpretation of theresults. Eq. (34) represents the demand curve of the large investor and showsthat the key parameter that links the IPO price, p, to the share allocation is b, theslope of the pricing schedule. We will show that b(0 for the optimal rationingmechanism. Hence, for fixed a, as the slope is made more negative the under-writer is able to extract a higher IPO price from the large investor.

Substituting Eq. (34) into Eq. (31) and using the non-binding assumption onº

L, we find the following restriction on the slope of the pricing schedule:

b'1

2A1

c!

p2

o B. (38)

Returning to the solution of the rationing mechanism, we neglect the distribu-tion constraint, (32), for the moment. This constraint will be subsequentlyverified. Thus, we set the realized allocation to small investors equal tob"1!a. Substituting Eq. (34) into the expression for º

Sgiven by Eq. (32) with

b"1!a gives the following equivalent representation for the entrepreneur’soptimal mechanism:

maxb,a

p"k!ab#aA1

c!

p2

o B, (39)


subject to

(1!a)aAb#p2

o B!(1!a)2p2

2q*ºM

S. (40)

Introducing the Lagrange multiplier, j*0, for the constraint and usinga Kuhn—Tucker formulation, we have

maxb,a

L"k!ab#aA1

c!

p2

o B#jC(1!a)aAb#p2

o B!

(1!a)2p2

2q!ºM

SD. (41)

Differentiating this expression with respect to b and solving for j yields

j"1

1!a, (42)

showing that the small investor’s reservation utility constraint is binding. Next,differentiating L with respect to a and simplifying yields the following first-order condition for the optimal large investor ownership share in the rationingmechanism, a:

!

a1!a

b#1

c!

a1!a

p2

o#

p2

q"0. (43)

6.2. Implications of the rationing mechanism

The previous analysis provides some implications of the entrepreneur’s use ofthe rationing mechanism. Our first result shows that the entrepreneur willalways want to induce the large investor to hold a greater equity ownership, andthereby perform more monitoring activities, than in the Walrasian mechanism.

Proposition 1. Suppose that the ¼alrasian equilibrium, a*, leads to an alloca-tion, º

S, such that inequality (33) is satisfied. ¹hen, the entrepreneur will always

want to utilize the rationing mechanism instead of the ¼alrasian mechanism.Specifically, the entrepreneur always wants to increase a above a*.

Proof. Given that the Walrasian mechanism is feasible, it is a special case of therationing mechanism where the price schedule faced by the large investor ishorizontal, i.e., b"0. Moreover, in the Walrasian mechanism, the large inves-tor’s ownership share is equal to a*"o/(o#q). Evaluating the left hand side ofthe first-order condition Eq. (43) at b"0 and a"a* shows that the first-order


condition equals 1/c'0. Therefore, the Walrasian mechanism is inferior to therationing mechanism and the entrepreneur would desire to increase the owner-ship share of the large investor. h

Proposition 1 is intuitive. It implies that the entrepreneur need not settle forthe lack of monitoring inherent in the Walrasian mechanism. Large investorscan be induced to hold greater fractions of equity by varying the parameters ofthe price schedule, even if small investors are able to purchase at the same price.The power to provide L with a price schedule means that the marginal per-unitprice can be decreasing without lowering the average per-unit price. Thereby,total revenue is maximized.

The next proposition is critical. First, it shows that the omitted constraint,Eq. (32), is satisfied at the optimum and second, it establishes that the mecha-nism proposed here is indeed a rationing mechanism.

Proposition 2. At the optimal a for the entrepreneur, the small shareholders arerationed.

Proof. The unconstrained demand by the small shareholders is given by solvingsubproblem (32):

b"qp2Ak#

ac!pB. (44)

Substituting for p from Eq. (34) above yields

b"qp2Aab#

ap2

o B. (45)

The first-order condition of the entrepreneur’s problem (43) can be written as

ab#ap2

o"(1!a)A

1

c#

p2

q B. (46)

Substituting the right-hand side of Eq. (46) into Eq. (45) and simplifying gives

b"(1!a)A1#q

cp2B'(1!a). (47)

Thus, the small investors would demand more than the amount allotted to themby the entrepreneur. h

Since the mechanism considered here allows only the large investors tochoose their holdings optimally, the underwriter adjusts the schedule so that


these investors are induced to hold larger fractions of equity. Small investors aretreated fairly since they purchase at the same per-unit average price. They wouldlike to purchase more at this price, but allowing them to do so would lower theamount of monitoring done by the large investors.

The next proposition considers the important question of ‘underpricing’ in theinitial public offer. In an empirical sense, underpricing is observed by comparingthe offering price to the price when secondary trading opens. That is, underpric-ing is observed by a time-series comparison. The single-period model we havebeen using is not capable of providing time-series implications. However, it isextended in a straightforward manner in the next section to multiple periods.Nevertheless, it is instructive to define here a pseudo-secondary market price,and to compare this to the offering price, p. The pseudo-secondary price wedefine is the shadow price of the small investors. That is, it is the price which,when offered, would cause their optimal price-taking demands, b to be exactlyequal to what they are allocated in the rationing mechanism, 1!a. Thistherefore represents the price that would eventuate once trading opens, providedthe opening of trading did not influence the initial ownership position taken bylarge investors.

Proposition 3. ºnderpricing in the rationing mechanism exists with respect to thepseudo-secondary market price. ¹he amount of underpricing is equal to (1!a)/c.

Proof. Let pJ be the secondary market price, which is the small investors’ shadowprice at which they demand exactly 1!a, that is

Ak#ac!pJ B

qp2

"1!a. (48)

Thus,

Ak#ac!pB

qp2

#(p!pJ )qp2

"1!a. (49)

Using the pricing function Eq. (34) and the entrepreneur’s first-order conditionEq. (43), this can be rewritten as

(1!a)#(1!a)q

cp2#(p!pJ )

qp2

"(1!a). (50)

Thus,

pJ !p"(1!a)

c. h (51)


This proposition can be used to see that the amount of underpricing isnegatively related to the cost of monitoring, as might be expected.22 If monitor-ing activities are costly, then risk-sharing opportunities are relatively morevaluable and the entrepreneur will ration the small investors to a lesser degree.As a result, their shadow price will conform more to the offering price.

Finally, we turn to the specification of the optimal ownership fractions in therationing mechanism. Proposition 4 establishes the interesting result that therationing mechanism may actually lead to greater ownership by the largeinvestors than the second-best optimal level.

Proposition 4. ¹he entrepreneur’s optimal a satisfies

a"1c#p2

qb#1c#p2

o#p2

q. (52)

Proof. This is just a restatement of the first-order condition (43). h

Proposition 4 shows that the optimal equity share allotted to L depends onthe slope of the pricing schedule. The more negative the slope of the pricingschedule given to the large investor, the more equity is allocated to that investor.This implies that the monitoring level is actually greater than the second-bestoptimum (12) and closer to the first-best level.

Finally, Proposition 5 shows that the slope of the pricing schedule is negative.

Proposition 5. ¹he slope of the pricing schedule offered to the large investor, b(0.

Proof. The respective prices in the rationing mechanism and the Walrasianequilibrium are, respectively,

p"k!ab#aA1

c!

p2

o B, (53)

p*"k#a*A1

c!

p2

o B. (54)

Subtracting the second expression from the first yields,

p!p*"!ab#(a!a*)A1

c!

p2

o B'0, (55)

22This comparative static is obvious for large enough c since 1!a is bounded. It can also bedemonstrated for smaller values of c using the results of Proposition 4.


which is positive since p is optimal and the Walrasian mechanism is feasible.Using Proposition 1, a'a*, and utilizing the maintained assumption of exist-ence of a Walrasian equilibrium, c'o/p2, it can be seen that b(0. h

Fig. 1 illustrates the nature of the rationing mechanism. The horizontal axisdepicts the equity allocated to the large investor, while the vertical axis depictsprices received by the entrepreneur. The Walrasian equilibrium is indicated byallocation a* and price p* and is determined by the intersection of the lowerdemand curves of the large and small investors. The indifference curve of the

Fig. 1. The Rationing Mechanism. The market consists of 2 investors: large (L) and small (S). Twodemand curves are shown for each investor. The dotted curves represent the small investor’sindifference curves. The Walrasian equilibrium, (a*, p*), is determined by the intersection of thelower demand curves of the large and small investors. At this point, small investors are on theirlower indifference curve. If the equity allocated to the large investor is increased so that the largeinvestor’s holding is determined by the intersection of his upper demand curve with the upperindifference curve of the small investor, then small investors utility is decreased. Due to increasedmonitoring, the small investor’s demand curve shifts upward and the amount of underpricing isgiven by (pJ !p).


small investor is represented by the dotted curve passing through the Walrasianequilibrium. Note that the indifference curve of the small investor takes intoaccount the impact of a change in a on subsequent monitoring, while thedemand curve does not. As a result of this important effect, the demand curve atthe Walrasian equilibrium passes through the indifference curve at a point ofpositive slope. This implies that small investors are willing to incur a priceincrease if it implies greater monitoring.

Hence, the entrepreneur can increase price and a simultaneously. A possibleinstance of this is indicated by the movement along the original demand curve ofthe small investor to a point at the maximum of a higher indifference curve. Thisis accomplished by a rotation of the large investor’s demand curve to a point onthe maximum of a higher indifference curve of the small investor. This isindicated as point a and price p, which is higher than the Walrasian equilibrium.Finally, due to the increased monitoring, the small investor’s demand curveshifts upward and the amount of underpricing is given by the difference betweenp and pJ , which is the point on the demand curve corresponding to the optimalallocation a.

6.3. Binding participation constraint for large investor

We now turn to the implications for rationing and underpricing when theparticipation constraint of the large investor, Eq. (30), is binding. This occurswhen the small investor’s reservation utility constraint, ºM

S, is small or zero. In

such situations, the prescribed minimum utility of small investors is insufficientto ensure that large investors are also willing to participate.

When the large investor participation constraint is binding, ºL"0; from

Eq. (31), this becomes

p"k#a2A

1

c!

p2

o B. (56)

This is equivalent to the analysis of the previous subsection, but the slope of thepricing schedule, b, is fixed at

b"1

2A1

c!

p2

o B. (57)

There are two sub-cases that can occur. Either the distribution constraint, (32)or the reservation utility constraint (33) may be binding once b is substitutedfrom (57). The latter case holds when ºM

Sis above some positive amount (but

smaller than in the previous subsection). In this case, the analysis of the previoussubsection can be repeated to obtain analogues of Propositions 1—5. Equityownership of the large investor is above the Walrasian level, the small share-holders are rationed (since their demand constraint is non-binding), there is


underpricing and the optimal a is determined by the intersection of the pricingfunction (56) and the indifference curve at ºM

S.

The second possibility occurs when ºMSis in the neighborhood of zero. In this

instance the underwriter would like to obtain higher prices by moving alongEq. (56), i.e., lowering a. However, because of decreased monitoring, the smallinvestors are no longer willing to hold the balance of the securities not pur-chased by the large investors. As a result, the optimum occurs at the intersectionof the small investor’s demand curve and the pricing function (56). In this case,since small investors are on their demand curve, there is neither rationing, nor isthere any underpricing. Nevertheless, it still is true that the optimal allocation, a,is above the Walrasian equilibrium. Solving for the small investor’s demand forshares using Eq. (56), we find that

b"aqp2A

1

2c#

p2

o B. (58)

Thus,

ba"

q2o

#

q2p2c

(

q2o

#

q2p2A

p2

o B"qo, (59)

which implies that a'a*. The above inequality follows from the second-ordercondition for existence of a Walrasian equilibrium.

It is interesting that optimal underpricing occurs when regulations requirethat a relatively large surplus be given to small investors. Their requests remainpartly unfilled. However, if the regulatory environment dictates that smallinvestor surplus is unimportant, they receive all they demand and entrepreneur-ial extraction of surplus is limited by the need to place all of the issue. Althoughdirect regulation of surplus is difficult to enforce, it can be shown that when thelarge investor’s participation constraint is binding, a larger surplus is equivalentto regulating the minimum number of shares allocated to small investors.23Thus, underpricing may be an implication of subtle pressures often observed toprotect retail investors.

7. Secondary trading

In the previous sections, a single-period model was used for tractability. Inthis model, the large investor was assumed to maintain the equity holdings

23Specifically, the minimum utility of small investors is negatively impacted by the allocationgiven to large investors, i.e., dºM

S/da(0 using p from the pricing schedule (56) and substituting into

Eq. (32) if and only if a'a*.


established by the offering mechanism. As discussed in Section 2, selling in thesecondary market may be prevented by the repeated nature of the relationshipbetween the underwriter and investors, possibly enforced by penalty bids. Inreality, some shares are traded even during the distribution period. Therefore itis important to extend the results of the single-period model to a multi-periodenvironment that permits the large investor to optimally engage in secondarymarket trading.

In this section we analyze the effect of secondary trading on the structure ofthe IPO and on the final ownership. If traders in the secondary market behavecompetitively and thus take prices as given, then the initial ownership structurechosen at the IPO stage becomes irrelevant. Assuming that equilibrium exists,investors trade until first-best risk sharing is obtained (see Admati et al., 1994).There is no incentive to choose an initial equity structure other than a"a*,since it would be undone in the secondary market. Thus, under pure price-taking in the secondary market, there is no way for the entrepreneur to do anybetter than the Walrasian outcome of Section 4.

However, there is strong reason to suspect that secondary market trading,especially at the outset, is not characterized by price-taking.24 As a result, ourmodel of secondary trading is characterized by imperfect competition, since weassume the large investor accounts for the effect of trading decisions on the price.There are a number of reasons why we feel this approach is justified. First, thereare problems with non-existence of a Walrasian equilibrium as documented inAdmati, Pfleiderer and Zechner. Second, if the entrepreneur is successful inemploying a mechanism that favors ownership by institutional investors, suchas the rationing mechanism, these investors have market power. This is becausetheir holdings constitute a large fraction of overall equity ownership. Third, byour definition large investors are those who are capable of monitoring. There-fore, they would be classified as insiders and therefore subject to regulation anddisclosure on their trading activities.25 Finally, and most importantly, theempirical evidence cited in Hanley and Wilhelm (1995) shows that institutionalinvestors do not engage in large-scale trades when the secondary market opens.In this section, we show that the major results of the previous single-periodmodel are preserved when non-price taking behavior of the large investors istaken into account.

To model the effect of secondary trading, we assume that information aboutthe firm’s final cash flow is received over time. The sequence of events is asfollows (Fig. 2). At time t

1the IPO takes place. At this time, k is unknown to all

and is distributed normally with mean k0

and variance p21. At time t

2, the

24 In the model of Mello and Parsons (1998) it is also important that price-taking not occur.

25For an analysis of the interaction between monitoring and insider trading, see Maug (1998).


Fig. 2. Sequence of events.

parameter k has been revealed to all market participants. Therefore, the firm’sfinal cash flow is distributed normally with mean k#m and variance p2

2. After

k has been revealed, shares can be traded on a stock market. At timet3

monitoring takes place and at time t4

the final cash flows are realized anddistributed to shareholders.

7.1. The secondary trading market

Analyzing the problem recursively, we first determine the equilibrium alloca-tions implied by the trading process at time t

2for a given initial allocation. At

time t2

the parameter k has been observed and the expected cash flows are, asbefore, k#a

2/c, where a

2is the final holding of the large investor and this

determines the amount of monitoring. Thus, the expected utility of the smallinvestor is given by

º2S"(1!a

2)Ak#

a2c!p

2B!1

2

(1!a2)2 p2

2q

#(1!a1)p

2, (60)

where 1!a2

represents the holdings of the small investor, p2

is the price ofshares at time t

2, and 1!a

1are the holdings from the initial time period. It is

easy to verify that the small shareholders’ demand as a function of the anticip-ated equity holdings is given by

p2(a

2)"k#

a2c!

(1!a2)p2

2q

, (61)

as long as these investors behave as price-takers.The institutional investor’s expected utility at time t

2is given by

º2L"a

2Ak#a2c!p

2(a

2)B!

1

2

a22

p22

o!

1

2

a22c#a

1p2(a

2). (62)

Substituting for p2(a

2) from Eq. (61) and differentiating with respect to a

2yields

a2"ka

1#

p22

q1c#p2

2

o#2p22

q, (63)


where

k"1c#p2

2

q1c#p2

2

o#2p22

q. (64)

This result shows that the large investor will generally trade from the initialholdings, a

1, toward the Walrasian equilibrium holdings, a*. If initial holdings

are above a*, then secondary market holdings will be as well. An importantproperty that we will use in the next subsection is that k(1, i.e., the effect of anincrease in initial equity holdings, a

1is attenuated somewhat by secondary

market trading.

7.2. Rationing in a multiperiod environment

Having now established the secondary market trading at time t2

for giveninitial holdings, we analyze the entrepreneur’s choice of an initial ownershipstructure. Based on Lemma 1 of the previous section, we consider a two-stagerationing mechanism where the large investors are offered a pricing schedule bythe investment banker, and the small investors’ demands are then filled at theaverage actual price paid by the large investor. For brevity, we focus only on thecase where the large investor’s participation constraint is not binding.

The institutional investor’s expected utility at time t1

can be expressed as

ºL"a

2Ak0#

a2c!pN

2(a

2)B!

1

2

a22p22

o!

1

2

a22c

#a1(pN

2(a

2)!p

1(a

1))!

1

2

a21p21

o, (65)

where pN (a2) represents the expected t

2price at t

1and we have substituted the

expected value of k as k0.

Next, we want to differentiate with respect to a1. First, we recognize that the

envelope theorem, from optimization in the secondary market, implies that

LºL

La2

da2

da1

#

LºL

LpN2

dpN2

da2

da2

da1

"0, (66)

and that dp1/da

1,b, the slope of the offering schedule. The first-order condi-

tion from maximizing ºL

with respect to a1

thus yields

p1(a

1)"pN

2(a

2)!a

1Ab#p21o B. (67)

Note the similarity with Eq. (34) from the previous section; the offering priceequals the expected next-period’s price minus an amount related to the slope ofthe offer schedule and the cash flow risk from time t

1to t

2.


As in the previous section, we assume that the entrepreneur attempts tomaximize revenues while taking into account a reservation utility constraint ofsmall investors. Since small investors trade optimally at time t

2, we only

consider the portion of utility from times t1to t

2as being subject to regulation in

the form of a minimum participation constraint. As before, this perspective onthe model is essentially a constraint ensuring broad small investor participationin the issue. Neglecting the full distribution constraint, the entrepreneur’soptimal mechanism design problem can be specified as follows:

maxa1,b

p1(a

1)"pN

2(a

2)!a

1Ab#p21o B (68)

subject to

º1S"(1!a

1)((pN

2(a

2)!p

1(a

1))!

1

2

(1!a1)2p2

1q

*ºM 1S. (69)

Substituting for p2(a

1) from Eq. (61) and introducing a Lagrangian multiplier,

j yields

L"kN0#

a2c!

(1!a2)p2

1q

!a1Ab#

p21o B

#jC(1!a1) a

1Ab#p21o B!

(1!a1)2p2

12q

!ºM 1SD. (70)

Differentiating with respect to b yields

j"1

1!a1

. (71)

Substituting for a1

from Eq. (63) and taking expectations in Eq. (61), the first-order condition with respect to a

1is given by

k

c#

kp21

q!

a1

1!a1Ab#

p21o B#

p21q"0. (72)

This expression illustrates the essential change from the single-period analysis.Comparing Eq. (72) to Eq. (43), (k/c)#(kp2

1)/q replaces 1/c.26 There are two

effects. First, the marginal benefit of monitoring is reduced since k(1. Thisreduction in the marginal benefit of monitoring is due to the fact that the largeinvestor trades down from the initial holdings toward the Walrasian level. Asa result, the entrepreneur is unable to sustain as high a level of monitoring

26Since the relevant measure of risk is related to the amount of uncertainty revealed over theperiod until trading begins, the change from p to p

1is merely notational.


activity in the multi-period model. The second effect, which is driven by en-hanced risk-sharing possibilities with an additional round of trading, works inthe opposite direction. Increasing initial equity-holdings of the large investor isless costly because the entrepreneur knows that a fraction will be sold oncesecondary trading opens.

7.3. Results of the multiperiod model

The essence of the results from the single-period model obtain in the multi-period model as well.27 Propositions 1 and 2 hold in a straightforward manner.The entrepreneur prefers rationing small investors to a Walrasian offeringmechanism.

Similarly, allowing for secondary trading does not change the essentialaspects of Proposition 3 concerning underpricing of IPOs. The underpricingresult now has a more natural interpretation since it can be measured relative tothe price in the secondary market. Combining Eqs. (61) and (72) we see that theexpected price increase between the IPO price and the price in the secondarymarket is

pN2!p

1"(1!a

1)A

k

c#

kp21

q#

p21q B. (73)

The expected price is larger in the secondary market as compared to the offeringprice. This is due to both the marginal benefits of monitoring as well as a riskpremium. The risk premium is measured by the last two terms. These effects arelower as the variance of information declines and/or the small investors aremore risk tolerant. The first term, (1!a

1)(k/c), is analogous to the result of

Proposition 3 and shows that the degree of underpricing will be positivelyrelated to less costly monitoring activities on the part of institutional share-holders. However, the existence of secondary trading does attenuate the under-pricing effect since k(1. Again, however, if monitoring is relatively moreimportant than risk-sharing, then k is large and underpricing is more significant.

Finally, the analogous expression to Proposition 4 holds except thatk/c#(kp2

1)/q replaces 1/c. Initial holdings by large investors may be either larger

or smaller than in the single period model depending on whether the increasedrisk-sharing benefits outweigh the decreased monitoring expenditures.

27We conjecture that extension to an even greater number of periods would not change theresults. Once given an initial equity stake above the Walrasian equilibrium, the large investor is likea durable goods monopolist. It is well-known in such situations that commitment to not selling untilthe last possible time is advantageous. Thus, with a finite number of trading rounds, the largeinvestor holds the initial equity stake until the last period before final cash flows are revealed. Ourresults would only be affected if somehow there is never a time before the time of monitoring whentrading is halted, i.e., no last round of trade.


8. Conclusion

The major conclusion of this paper is that the value of a firm’s IPO isdetermined by the ownership structure resulting from the offering mechanism.

The basic premise of our argument is that investors are not homogeneous intheir ability to monitor management of the newly public firm. Large investorshave an advantage in this regard because of the establishment of institutionalmechanisms that facilitate such activities. Moreover, they benefit from participa-tory relationships and other complementarities that small investors do notenjoy. Nevertheless, since monitoring activities are difficult to observe andtherefore to contract on, a free-rider problem exists. The existence of this agencyproblem creates a tension between risk-sharing and information production. Wefind that these two goals must be traded-off against one another. As a result, theoptimal offering process will, to the extent that regulations allow, give favoredtreatment to the large investor class.

A common form of a regulatory constraint ensures that all investors purchaseshares at the same per-unit price. We show that this regulation still gives theissuer some latitude in setting quantity restrictions and therefore in rationingsmall investors. In our model, rationing can be optimal because of the positiveexternality enjoyed by small investors from the monitoring activities of largeinvestors. However, rationing cannot be accomplished through a competitivetrading mechanism such as a Walrasian auction. It requires the imposition ofa negotiated offer schedule between the underwriter and large investors. Webelieve this offer schedule represents the essential elements of the ‘book-building’process by which equity participation is generated.

This paper features a different perspective on the contributions of the invest-ment banker or underwriter than other papers on IPOs. We view the investmentbanker as a broker with an active and continuing relationship with the institu-tional investment community. The nature of this relationship provides twobenefits to the entrepreneur. First, the investment banker is able to identify thoseinvestors capable of monitoring and provide favored treatment, either in priceterms, or if that is disallowed, in terms of priority. Second, the nature of therepeated relationship allows the investment banker to negotiate directly with thelarge investor, providing for greater extraction of surplus to the benefit of theentrepreneur.

Our theory generates several empirical predictions. First, the ability to rationin favor of large shareholders should be positively correlated with under-pricing. One way of testing this prediction is to compare underpricing indifferent jurisdictions. Whenever pro-rata allocation regulations are imposed,one should expect less underpricing. Loughran et al. (1994) provide evidence onunderpricing in different countries. Although the results are not conclusive,countries with little strategic rationing such as France or Finland exhibit lowunderpricing.


Second, the model also predicts a positive relation between underpricing andstrategic rationing within a given regulatory environment. Consistent with thisprediction, Koh and Walters (1989) report, for their sample of IPOs in Sin-gapore, a negative correlation between underpricing and the proportion of theissue allocated to small investors. Supportive evidence is also reported in Hanleyand Wilhelm (1995).

Third, underpricing should be larger for companies with high benefit-to-costratios for monitoring activities, such as high-tech firms. By contrast, firms withlong operating histories are likely to exhibit less scope for monitoring, andshould therefore be less underpriced. Some empirical support for this can befound in Loughran et al. (1994).

Fourth, when regulations require significant participation of small investorsthen IPO’s should be more underpriced.

For tractability reasons, we have modeled the negotiation process between theinvestment banker and the large investor as optimal from the entrepreneur’sperspective. The actual process clearly involves a substantial amount of bargain-ing. Obviously, the existence of bargaining power on the part of large investors islikely to create lower revenue for the entrepreneur. But it is also just as likely toenhance the results involving favored treatment for institutions and relativelylarge equity percentages at the time of offering. If large investors internalize moreof the benefits from monitoring through greater participation in the pro-ceeds from issuance, then they are more likely to want a higher degree ofownership. Underpricing would be even more pronounced. Therefore, the as-sumption in the paper that the schedule is optimally chosen from the entrepre-neur’s perspective is a conservative assumption when it comes to an underpricingprediction.

We believe that considering the form of institutional mechanisms such as therationing process we have described here is an important objective of futureresearch. With heterogeneity of investor groups and inherent agency problems,market features other than purely competitive markets may actually be benefi-cial both from the standpoint of the firm issuing securities as well as those whoprovide the participatory capital. The recent privatization programs in Easternand Western Europe along with the concomitant design of capital marketsprovide important examples.

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