IPO-mechanisms, monitoring and ownership ... - Semantic Scholar

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 share ownership and explores the role of underpricing and rationing in determining investors’ shareholdings. We focus on the agency problem that results when large institutions are the only investors capable of monitoring the firm whereas small shareholders free-ride on these activities. The major conclusion is that some well-known aspects of IPOs may be explained as rational responses by the issuer to the existence of regulatory constraints in public capital markets. There is a two-stage offering mechanism in which the investment banker, acting in the interests of the issuer, optimally rations the allotment of shares to small investors in order to capture the benefits associated with better monitoring by institutions. Importantly, in our model, the existence of underpricing (and oversubscription) is an indication that the issuer has received a higher ex ante price than would have been obtained through a competitive Walrasian-type offering process. ( 1998 Elsevier Science 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 firm value have attained recognition as an important topic in corporate finance.

* Corresponding author. Tel.: 949/824-5840; fax: 949/824-8469; e-mail: [email protected]. 1 We would like to thank the referee, Larry Benveniste, and the editor, William Schwert, as well as Bruno Biais, Patrik Bolton, Susanne Espenlaub, Michael Fishman, Thierry Foucault, Gunther 0304-405X/98/$19.00 ( 1998 Elsevier Science S.A. All rights reserved PII S 0 3 0 4 - 4 0 5 X ( 9 8 ) 0 0 0 1 7 - 8

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

Considerable attention has recently focused on the implications of heterogeneity of investors and equity ownership structure. This has led to a greater understanding of the links between corporate finance and the underlying institutional makeup of modern financial markets. In particular, there is a growing empirical literature on the relation between the fraction of shares owned by large investors such as pension funds and firm performance.2 A number of these studies conclude that institutional shareholdings do affect firms’ market values. Several recent papers derive theories of optimal institutional ownership levels.3 The main purpose of this paper is to address the question of how the initial public offering (IPO) process determines the equilibrium structure of shareholdings. More specifically, the paper analyzes the effect of different IPO mechanisms on share ownership and explores the role of underpricing and rationing as potentially rational responses to regulatory constraints and institutions.4 There is a rich empirical and theoretical literature describing the IPO underpricing phenomenon.5 This paper provides a theoretical justification for the existence of IPO underpricing that is based on moral hazard, rather than adverse selection or asymmetric information. The existing literature on IPOs does not document that the ownership structure per se affects firm value. Most papers focus on asymmetric information during the issue process and feature underpricing as a result. The basic philosophy behind these adverse selection papers is that underpricing is a cost to the issuer, which is borne from the need to extract 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 Roëll, Kristian Rydquist, Jean Tirole, Elu von Thadden, Ivo Welch, William Wilhelm, Joe Williams and Andrew Winton for helpful comments. This paper has been presented at the University of Alberta, Baruch College, the Free 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, Stockholm School of Economics, the University of British Columbia, UCLA, the University of Utah, the CEPR conferences in Tolouse and Gerzensee, the American Finance Association, the Western Finance Association and the European Finance Association. This paper was written while Stoughton visited the University of Vienna. He expresses his appreciation to the faculty and staff for an enjoyable stay. 2 Examples 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). 3 See Bhide (1993), Bolton and vonThadden (1995), Burkart et al. (1997), Kahn and Winton (1998) and Pagano and Roëll (1995). 4 We analyze the problem from the issuer’s perspective and therefore do not address the larger question of an optimal regulatory environment. 5 Examples include Allen and Faulhaber (1989), Benveniste and Spindt (1989), Benveniste and Wilhelm (1990), Chemmanur (1993), Grinblatt and Hwang (1989), Ritter (1987), Rock (1986), Tinic (1988) and Welch (1989).


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Ownership structure affects the efficiency of corporate governance and thus the intrinsic value of the firm. In our model, underpricing and rationing may be rational phenomena from the standpoint of the issuer. Rationing provides a mechanism whereby different classes of investors may be treated differentially, although they all purchase securities at a common price. We show that without the possibility of treating different classes of investors differently, the offering price and revenues raised would be reduced. In our model, the firm’s investment banker plays two key roles: (1) identifying investor classes and enforcing differential treatment; and (2) transferring value from the investors to the issuer. Both result from the continuing nature of the relationship between underwriters and institutions. There are several recent related papers.6 In an independently developed paper, Mello and Parsons (1998) study the optimal dynamic allocation process between active and passive investors. They similarly find that it may be optimal to favor large shareholders because of the public good created by external benefits of control. Mello and Parsons explore the implications of multiple rounds of share allocations in which the prices paid by investor classes can differ. In contrast, our paper develops a mechanism which maximizes revenues even when price discrimination between investor classes is not allowed. Brennan and Franks (1997) also discuss some of the implications of investor heterogeneity and the need for rationing. In their model, rationing favors small rather than large investors, and issuers are willing to permit underpricing because of nonpecuniary benefits of control.7 In our model, control considerations are absent. This may be consistent with some of the recent government privatizations and IPO’s in which initial owners plan to relinquish control.8 Benveniste and Spindt (1989) show that asymmetric information between the issuer and institutional investors may lead to underpricing and strategic rationing.9 In their model underpricing is a cost to the issuer and is necessary to adequately compensate institutional investors for supplying their private

6 A unique, but less directly related paper is that of Milne and Ritzberger (1991) whose model of IPO 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 the winner’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 of directors. In this case it appeared that the foundation wanted to reduce the chance that control considerations would negatively impact the firm value. Subsequently the firm was taken over by Glaxo. 9 See Sherman (1997) for an extension of the model by Benveniste and Spindt (1989) to the case in which the institution’s information acquisition is endogenized.

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information. Rationing in favor of institutional investors reduces required underpricing. In our model, strategic rationing and underpricing are positively correlated. If the issuer is not allowed to ration strategically, our model predicts zero underpricing but implies a lower intrinsic value due to lack of monitoring. Underpricing and rationing in favor of large shareholders lead to a higher intrinsic value of the firm which more than offsets the amount of underpricing. Another feature of our model is that large shareholders do not sell out in the secondary market in order to capture the gains from underpricing. This is consistent with recent empirical evidence reported by Hanley and Wilhelm (1995). They document a high degree of correlation between share ownership of institutions 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 paper a large investor can also affect firm value by monitoring. However, the initial endowment of shares is exogenous. We account for the endogeneity of the initial endowment and its interdependency with the IPO mechanism. The structure of the paper is as follows. The problem of an entrepreneur selling securities to large and small shareholders is introduced in Section 2. Section 3 establishes that in the presence of unobservable monitoring activities there exists a second-best optimal IPO mechanism. This serves as a benchmark for the alternative mechanisms. A Walrasian mechanism is analyzed in Section 4 and price discrimination in Section 5. A two-stage-rationing mechanism with underpricing is introduced in Section 6. Section 7 looks at the effects of secondary trading, and Section 8 concludes and discusses empirical implications.

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

10 The results are easily generalizable to a situation in which some fixed percentage less than 100% of the shares are sold.


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and influencing them for the benefit of all shareholders. For simplicity, each investor group is represented by a single composite investor.11 The entrepreneur in the model is able to elicit the assistance of an investment banker in selling securities to the public. We focus on the investment banker’s relationship with investor groups. In this respect it is critical that the investment banker be able to differentiate between large and small investors and to enforce agreements whether they are explicit or implicit. For simplicity, we neglect the investment banker’s compensation in the offering process. Equivalently, the investment banker’s compensation is equal to a constant amount in all mechanisms. We analyze a single-period model which is extended to two periods in Section 7. The single-period model can be interpreted as one in which the investment banker prevents the large investors from selling their securities in the secondary market. An explicit mechanism that is frequently used to discourage flipping of shares is penalty bids. This occurs whenever the managing underwriter requires syndicate members to forfeit their compensation when issued shares are repurchased to stabilize prices.12 Syndicate members therefore have an incentive to discourage their investors from flipping their shares in the secondary market. Since underwriters have some leverage over investors through the repeated nature of their relationship, penalty bids effectively insure against quick sales of initial allocations in the secondary market.13 The structure of the model is as follows. There is a single period. At the beginning of the period (the time of the public offer), some mechanism is used for allocating shares to investors L and S. We will discuss a number of mechanisms in this paper, each of which is differentiated by the type of involvement of the investment banker. The most general mechanism features a set of equity fractions and monetary transfers from the two types of investors to the entrepreneur. This is described by the pair (a, g ) representing the equity fraction, a, given to L L in exchange for total payment g , and (b, g ) representing the corresponding L S equity fraction, b, allocated to S in exchange for payment g . At the end of the S 11 By representing each group as a single investor we are not considering strategic effects between members of each group. This is justified if, for example, members within each class can achieve fully binding contracts with each other and if their risk preferences are derived from the same HARA class. Opler and Sokobin (1995) discuss the role of the Council of Institutional Investors as a coordinating body in the U.S. However, if a free rider problem exists within the group of large investors, then the relation between monitoring and share allocations would become more complex. This is an interesting avenue for further research. 12 For a detailed discussion and analysis of penalty bids and their role in reducing adverse selection costs, see Benveniste et al. (1996). 13 As mentioned by Benveniste et al. (1996), Prudential Securities, for example, decides on future share allocations on the basis of past purchases and retention of shares by a syndicate member’s clients in previous deals.

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period, the large investor employs a costly monitoring technology that increases the expected value of the end-of-period cash flow distribution. Monitoring includes any activity that creates value that is shared by all shareholders in proportion to their holdings. The basic problem facing the entrepreneur is to choose an appropriate mechanism given that the level of monitoring cannot be specified contractually between the entrepreneur and the two investors. Because monitoring is inherently unobservable and small investors can free-ride on these activities, the incentive for monitoring by L must be a function of the ownership proportions provided by the offering mechanism.14 We assume that ending cash flows are normally distributed and investor preferences are described by exponential utility (constant absolute risk aversion). We focus on a situation where there is a single risky firm and where the monitoring technology is ‘allocation-neutral’.15 Given the exponential-normal assumptions, preferences can be described by a certain-equivalent wealth with a 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 1 a2p2 º (a, g )"ak(m)! !C(m)!g , L L L 2 o

(1)

1 b2p2 º (b, g )"bk(m)! !g , S S S 2 q

(2)

and

where k(m) represents the expected cash flows of the firm as a function of the monitoring level, m; p2 is the variance of the ending cash flow distribution and is assumed to be unaffected by monitoring; o and q represent the risk tolerances of the large and small investors, respectively, and C(m) is the cost of monitoring. For concreteness, we further specify the benefits and costs of monitoring as follows: k(m)"k#m,

(3)

14 Many real-world examples of the positive influences provided by institutional investors are documented in Useem (1996). Another example told to one of the authors is an instance in which a pharmaceutical firm was forced by its institutional investors to rescind a poison pill(!). 15 Considering the firm in isolation from the rest of the market is essentially without loss of generality as long as the firm in question has no external effects on other firms. Given these preference and distribution assumptions, it is always possible to redefine cash flow risk relative to the market numeraire, i.e., as systematic risk and to adjust all risk parameters accordingly. An allocation-neutral monitoring technology, as defined in Admati et al. (1994), does not depend on the allocation of shares. That is, the cost and the benefit of monitoring only depend on m, the intensity of monitoring chosen by the large investor, not on holdings, a, directly.


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and (4) C(m)"1cm2, 2 where k is a constant and c represents the marginal cost coefficient of monitoring.16 Although we do not model potential agency problems between large investors such as pension funds and their clients, this could be one of the determinants of the cost function. From these assumptions, including the assumption that the variance of the cash flow distribution is unaffected by monitoring, it is clear that if there were complete contracting, the first-best level of monitoring would be m*"1/c. This is obtained by maximizing the benefit minus the cost. However, in our model monitoring is non-contractible and so the large investor, L, determines the (second-best) optimal amount of monitoring by solving the following problem: 1 a2p2 1 max a(k#m)! ! cm2!g , L 2 o 2 m whose solution is m"a/c.

(5)

(6)

That is, the second-best monitoring is always below the first-best by an amount that increases as the ownership share of the large investor decreases. In our environment, the small investor, S, always free-rides on the monitoring done by the large investor and there is an inherent inability to transfer the positive externality between the two investor groups. We now turn to the question of what mechanism form should be used by the entrepreneur in offering shares to the public. Several alternatives are considered, each of which is distinguished by the actions of the investment banker and the degree of outside regulatory influences on the entrepreneur.

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

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

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utilities are brought down to their reservation values. The second-best optimum is therefore a standard Pareto optimum problem as described by max g #g , L S a,b,gL,gS subject to Eq. (6) and

(7)

º *ºM (8) L L º *ºM , (9) S S for fixed reservation utility constraints on the large and small investors, ºM and L ºM .17 S It is clear that the reservation utility constraints are always binding, and since b"1!a, the second-best optimum problem may be rewritten as

A B

A B

a a2p2 a2 a (1!a)2p2 max a k# ! ! #(1!a) k# ! !ºM !ºM , L S 2o 2c 2q c c a (10) after substituting for the monitoring constraint (6). The first-order condition for this problem is18 1 ap2 a (1!a)p2 ! ! # "0, o q c c

(11)

which simplifies to 1#p2 (12) a**" c 2 q 2. 1#p #p c o q Inspection of Eq. (12) reveals that the second-best optimal share given to the large investor, L, is a decreasing function of the cost coefficient, c. If monitoring costs are near zero, then a** approaches one. In such circumstances the second-best optimal monitoring expenditures by the large investors approach those that would have occurred had monitoring been contractible (first-best). Intuitively, monitoring is relatively so cheap that the entrepreneur is better-off when most of the shares are allocated to the large investor. At the other extreme, when c is large a** approaches o/(o#q), the optimal equity ownership structure when only risk-sharing considerations are present.

17 Although not modeled here, the value of these constraints could be derived from other investment opportunities. 18 The maximand is globally concave, and therefore this condition is also sufficient.


53

This is also intuitive. In general, the second-best optimal equity share allocated to the large investor is increased above the risk-sharing amount in order for the entrepreneur to capture some of the externality created by the benefits enjoyed by small investors from monitoring activities. In order to implement the second-best optimal mechanism, the investment banker would have to make separate offers to each investor class. In fact, the investment banker would not be constrained to offer shares to each investor group with the same per-unit price. Although the per-unit prices cannot be specified without knowing the reservation utility levels, in general the large investors will be given a better price to encourage them to buy more equity than would be optimal when only risk-sharing considerations are present.

4. The Walrasian mechanism We now contrast the previous outcome with the results obtained without using the services of an investment banker. The mechanism we consider here is very simple. Investors participate under identical terms by purchasing at a fixed price. The large and small investors are assumed to be price-takers in the market for the initial public offer. The market clears at a price such that the demand by L, a, and the demand by S, b, clear the market. This is a Walrasian mechanism corresponding 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, they do not take into account the effect that their trades will have on the prices they pay. Defining p as the price of 100% of the shares, the expected utility of investors L and S are given by Eqs. (1) and (2) with ap replacing g and bp replacing g . L S Differentiating Eq. (2) with respect to b shows that the optimal amount of equity holding by the small investors equals:

A

b"q

B

k#a!p c . p2

(13)

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

A

B

p2 a2 a max a k# !p !a2 ! . (14) 2o 2c c a The first-order condition for this problem implies that the large investor’s inverse demand function is p"k#a

A

B

1 p2 ! . o c

(15)

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Note that the second-order condition holds if c'o/p2, i.e., the monitoring cost is not too small relative to the large investor’s risk tolerance. This second-order condition also implies that the inverse demand function is downward sloping.19 To solve for the equilibrium price, we substitute Eq. (15) into Eq. (13) and then use market clearing, a#b"1. After a number of algebraic manipulations, we arrive at the Walrasian equilibrium price: o!cp2 p*"k# . oc#qc

(16)

Of greater interest is the induced ownership structure in the Walrasian mechanism. Substituting the market-clearing price into Eq. (15), we see that the large investor purchases o a*" . o#q

(17)

This is the Pareto optimal risk-sharing amount, and it is independent of the cost of monitoring. Since a*(a**, the Walrasian mechanism always features less monitoring than the second-best optimum. Therefore, the Walrasian mechanism suffers from the major difficulty that there is an inability for the entrepreneur to extract any of the benefits associated with the positive externality on small investors. This is the inherent conflict between the form of the issuing process and the heterogeneity of investor groups. If the entrepreneur does not utilize the investment banking services of an underwriter, the price-taking process only allows risk-sharing to be achieved. But with monitoring, strict risk-sharing conflicts with the need to favor institutional shareholders in order to provide incentives for enhanced monitoring activities.

5. Price discrimination Having explored the two extremes of the second-best and the Walrasian mechanisms, we now consider two intermediate mechanisms. In these mechanisms underwriters are able to identify the types of investors through previous experience and continuing relationships. They are therefore able to price discriminate 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, as discussed in Admati et al. (1994). 20 Alternatively, price discrimination could be achieved via multiple rounds of share offerings, as analyzed by Mello and Parsons (1998).


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mechanism, it is assumed that the investment banker cannot negotiate directly with each investor. In Section 5.1, both types of investors are offered shares at a fixed price and may optimally choose the quantities they wish to purchase, taking prices as given. This corresponds to a situation where the investment banker acts as an underwriter and conducts a discriminatory auction among investor groups. Section 5.2 allows the investment banker to make a take-it-or-leave-it offer to the large investor. This can be motivated by the presence of an underwriter who has a long-term relationship with the large investor and may possibly exclude him from future distributions if he deviates from the equilibrium quantity. Hence, although both mechanisms feature discriminatory pricing, they differ in the amount of bargaining power that is exerted on the two investor types. While most jurisdictions, such as the U.S., prohibit price discrimination between investors in the security offering process, there may be ways in which issuers can effectively discriminate among different investor groups. Examples include the use of private placements, letter stock or restricted stock classes such as voting and non-voting shares which convey the same cash flow rights. In the U.S. such restricted securities are governed by SEC Regulation 144. This regulation specifies a minimum holding period of one year for non-affiliate investors.21 Moreover there are volume restrictions and mandatory disclosure requirements prior to security resales during the first two years. The expressed purpose of these regulations is to prevent issuers from circumventing the regulatory requirements on the public offering process through the use of non-registered securities. Therefore, the extent to which private placements can be 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 shares to the two types of investors at fixed but possibly different prices. Suppose that p denotes the price paid by large investors and p the price paid by small L S investors. Large and small investors both take price as given when computing their demands. Substituting these prices into Eqs. (13) and (15), we find that

A

B

1 p2 p "k#a ! , L o c and

A

(18)

B

a p2(1!a) p "k# ! . S c q

(19)

21 The holding periods were shortened and a number of other changes were made in February 1997.

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The entrepreneur wants to maximize total revenue, so the problem is max a p #(1!a) p . (20) L S a subject to Eqs. (18) and (19). Substituting the price expressions from above and differentiating, we obtain the following expression for L’s optimal equity fraction, a0: 1#2p2 (21) a0" c 2 q 2. 2p #2p o q Notice that the second-order condition, c'o/p2, from L’s utility maximizing problem, implies that a(1. It is not surprising that the optimal equity ownership for the large investor in the price discrimination case exceeds that for the Walrasian mechanism, a0'a*. Since the Walrasian mechanism imposes the additional constraint that p "p "p, it is actually a special case of the price discrimination mechanism L S with an additional degree of freedom removed from the underwriter. This additional degree of freedom allows the underwriter to favor the large investor, which is optimal to encourage a greater level of ex post monitoring. Comparing Eqs. (21) and (12) we find that a0(a** if and only if 1/c(p2/o!p2/q, i.e., if the monitoring cost is sufficiently great. If the small investors have a large risk tolerance then this condition will hold, as it follows from the large investor’s second-order condition. On the other hand, if risk-sharing considerations are not important, then the underwriter may have an incentive to price the equity offering in such a favorable manner to the large investor that L’s ownership implies a larger monitoring expenditure. Given Eqs. (18) and (21), the expression for the price offered to the large investor is computed as oq2 #o!q !cp2 2 p "k#2p c . L cq#co

(22)

Comparing this price to that under the Walrasian equilibrium, we see that p (p* as long as L q o !1 (0, (23) 2 p2c

A

B

which follows from the second-order condition of L’s maximization problem. Not surprisingly, the price discrimination model predicts that L is given a lower price than he was under the Walrasian mechanism. On the other hand, S is charged a higher per-unit price. It is not hard to show that p !p "1/(2c), i.e., the greater the cost of monitoring, the lower the price S L


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discrepancy. Since the Walrasian mechanism is a special case of the price discrimination mechanism, it is clear that the entrepreneur always raises more revenue in the latter case. If this model of price discrimination is applied to the environment with different classes of stock as in the letter stock example, we predict that restricted stock will be priced lower than unrestricted stock. Interestingly, this pricing discrepancy does not arise due to restrictions on trading or differences in control rights, but rather as an inducement for the large investor to hold a larger fraction of the firm than would otherwise be the case. In contrast to the model of Longstaff (1995), we predict that the observed pricing discounts are not dependent on the volatility of prices, but rather on the potential gains from institutional monitoring. 5.2. Price discrimination with a negotiated offering Here we consider a hybrid between the price discrimination mechanism described in the previous subsection and the second-best mechanism. The second-best mechanism assumes that a take-it-or-leave-it offer can be made to the large and to each small investor. An intuitive justification for such an allocation is based on a repeated relationship which allows the investment banker to exclude an investor from future distributions if a deviation from the equilibrium quantities is observed. In practice such a repeated relationship may well exist between a large institutional investor and the investment banker, but is less likely to exist between the underwriter and small retail investors. We therefore investigate a mechanism involving discrimination, where small investors’ quantities are determined by their first-order conditions and the large investor is forced to his reservation utility by a take-it-or-leave-it offer. Suppose that p denotes the price of the shares given to the large investor and L p the price for the small investors. Given that the large investor is at the S reservation utility constraint, his utility is

A B

a a2p2 a2 a k# !(1/2) ! !ap "ºM . L L o 2c c

(24)

Hence,

A

B

a2 1 p2 ! . ap "!ºM #ak# L L o 2 c

(25)

Small investors’ price-taking demands are determined, as before, by Eq. (19). The problem of the entrepreneur is max ap #(1!a)p , L S a

(26)

58


or a2p2 (1!a)2p2 a2 (1!a)a !(1/2) ! . max !ºM #k#(1/2) # L o q c c a Solving the appropriate first-order condition for a yields

(27)

1#2p2 (28) aL " c 2 q 2. 1#p #2p c o q We can now compare Eq. (28) with the case of price discrimination through a fixed price offer in Eq. (21). It is easily verified that the second-order condition in Section 5.1, c'o/p2, implies that aL 'a0. Thus, because the investment banker has the bargaining power with the large investor, the investment banker can increase the optimal allocation to the large investor. Furthermore, inspection of Eq. (12) shows that the amount of share ownership allocated to the large investor is also greater than the second-best amount. Intuitively, if the investment banker can extract more surplus from the large investor, but not from small investors, it becomes optimal to forego possible risk sharing gains and instead increase the benefits from monitoring. This represents a major benefit to the entrepreneur from the relationships between investment bankers and institutional investors. In general, the price given to the large investor will depend on his reservation utility value. Using the expressions above for p and p , and substituting for L S aL from Eq. (28), it is easy to show that the difference in prices is bounded below by the difference in the fixed price case, i.e., p !p *1/(2c). That is, if the S L investment banker has greater bargaining power with the large investor, more price discrimination is implied.

6. Rationing Since many jurisdictions do not allow price discrimination, the entrepreneur cannot necessarily achieve the outcome of the previous section. However, a regulatory constraint disallowing price discrimination does not imply that the issuing process must be accomplished via the Walrasian mechanism. Indeed, the underwriter may still be able to utilize relationships with the large investors in order to enforce better overall terms for the entrepreneur. We therefore consider a mechanism involving rationing under which the entrepreneur can raise more revenue. Standard arguments would appear to imply that rationing is inefficient. After all, the first order effect of raising more revenue by increasing the price would seem to dominate the second-order effect of the reduction in monitoring activities. However, the rationing mechanism we propose does not imply that shares are offered to both large and small investors


59

on the same basis. The fact that observed per-unit prices are identical does not imply that investors are treated identically in the initial public offer. In practice the use of ‘book-building’ and other similar procedures by the underwriter imply that there is an interaction between the large investors and the investment banker. In this section, as in the previous subsection, we model the 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 the problem, we derive the result that the price allocation offer by the underwriter is equivalent to providing a linear demand schedule of IPO prices and share allocations to the large investors and allowing them to select their optimal share allocation from the schedule. The rationing mechanism we propose involves two stages. In the first stage, the underwriter dictates a price and allocation pair, (p, a) to the large investor. In the second stage, the small investors receive the remaining amount, 1!a at the identical per unit price paid by the large investors. When regulations imply that small investor participation is important, this twostage mechanism is shown below to indeed be a rationing mechanism, since the small investors would actually like to purchase more at the same per-unit price. In determining the optimal IPO price and allocation to L, the underwriter faces three constraints. First, the large investor’s reservation utility constraint must be satisfied, i.e., he must be willing to participate. Second, the price must be set so that small investors are willing to hold the balance of the equity not taken by the large investor. Third, small investors must be given some minimum participation in the offer as modeled here by a reservation utility constraint. We believe this participation constraint to be a realistic reflection of many regulatory considerations that require fairness in the offering of securities. For example, listing requirements of stock exchanges generally include a constraint that a certain percentage of each company’s stock must be widely held or that the stock have a minimum average trading volume. In addition, in an enhanced model of the offering process, the small investor’s utility constraint may simply reflect the issuer’s desire to have broad participation across investor classes. The optimal (rationing) mechanism is defined as the solution to the following problem for the entrepreneur: max p p,a

(29)

subject to º *0, L

(30)

60


where

A

B

a 1 a2p2 1 a2 º ,a k# !p ! ! , L c 2 o 2 c b*(1!a)

(31)

A

B

a b2p2 where b3argmax º ,b k# !p ! , S 2q c

(32)

º *ºM . (33) S S As is clear from comparing constraints (30)—(33), we view the regulatory environment as providing a more stringent requirement for small investor participation as compared to the large investor. We regard this assumption as a natural implication of protection for small investors. In any event, the impact on the nature of the optimum as ºM changes will be discussed below. S 6.1. Non-binding participation constraint for the large investor We first solve the problem when the participation constraint for the large investor is non-binding at the optimum. This occurs whenever the reservation utility constraint on small investors, ºM '0 is sufficiently large that large S 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 particular utility for the large investor. It is convenient here to consider the dual of this problem in which the utility of the large investor can be represented as arising from an optimal choice of share allocation along a linear demand schedule. ¸emma 1. Assume that the large investor’s participation constraint, (30), is nonbinding. 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 maximizing º subject to Eq. (31) along the line p(a)"a#ba. Moreover, the set of L feasible (p, a) values can be represented as p"k!ab#a

A

B

1 p2 ! . o c

(34)

Proof. Let º '0 represent a feasible value of the utility of the large investor in L the rationing mechanism. To show that this utility can be realized as the solution of maximizing º subject to p"a#ba, it is sufficient to show that the L indifference curves of the large investor in (p, a)-space are concave. Thus, any point along them can be generated as the point of tangency between the line p"a#ba and the indifference curve. Taking the total derivative of Eq. (31)


61

implies that

A

B

dp 1 a ap2 " k# !p! . o da a c

(35)

The second derivative can be simplified to give

A

A

BB

1 p2 d2p 1 "! 2(k!p)#a ! c da2 a2 o

.

(36)

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

A

B

a 1 p2 k!p# ! '0. o 2 c

(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 schedule instead of a take-it-or-leave it offer, without loss of generality. This representation simplifies the following analysis and allows an intuitive interpretation of the results. Eq. (34) represents the demand curve of the large investor and shows that the key parameter that links the IPO price, p, to the share allocation is b, the slope of the pricing schedule. We will show that b(0 for the optimal rationing mechanism. Hence, for fixed a, as the slope is made more negative the underwriter is able to extract a higher IPO price from the large investor. Substituting Eq. (34) into Eq. (31) and using the non-binding assumption on º , we find the following restriction on the slope of the pricing schedule: L

A

B

1 1 p2 b' ! . 2 c o

(38)

Returning to the solution of the rationing mechanism, we neglect the distribution constraint, (32), for the moment. This constraint will be subsequently verified. Thus, we set the realized allocation to small investors equal to b"1!a. Substituting Eq. (34) into the expression for º given by Eq. (32) with S b"1!a gives the following equivalent representation for the entrepreneur’s optimal mechanism:

A

B

1 p2 max p"k!ab#a ! , o c b,a

(39)

62


subject to

A

B

p2 (1!a)2p2 ! *ºM . (1!a)a b# S o 2q

(40)

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

A

B C D

A

B

1 p2 p2 #j (1!a)a b# max L"k!ab#a ! o o c b,a (1!a)2p2 ! !ºM . S 2q

(41)

Differentiating this expression with respect to b and solving for j yields 1 , j" 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 firstorder condition for the optimal large investor ownership share in the rationing mechanism, a: a 1 a p2 p2 ! b# ! # "0. q 1!a c 1!a o

(43)

6.2. Implications of the rationing mechanism The previous analysis provides some implications of the entrepreneur’s use of the rationing mechanism. Our first result shows that the entrepreneur will always want to induce the large investor to hold a greater equity ownership, and thereby perform more monitoring activities, than in the Walrasian mechanism. Proposition 1. Suppose that the ¼alrasian equilibrium, a*, leads to an allocation, º , such that inequality (33) is satisfied. ¹hen, the entrepreneur will always S 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 the rationing mechanism where the price schedule faced by the large investor is horizontal, i.e., b"0. Moreover, in the Walrasian mechanism, the large investor’s ownership share is equal to a*"o/(o#q). Evaluating the left hand side of the first-order condition Eq. (43) at b"0 and a"a* shows that the first-order


63

condition equals 1/c'0. Therefore, the Walrasian mechanism is inferior to the rationing mechanism and the entrepreneur would desire to increase the ownership share of the large investor. h Proposition 1 is intuitive. It implies that the entrepreneur need not settle for the lack of monitoring inherent in the Walrasian mechanism. Large investors can be induced to hold greater fractions of equity by varying the parameters of the 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-unit price 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 mechanism proposed here is indeed a rationing mechanism. Proposition 2. At the optimal a for the entrepreneur, the small shareholders are rationed. Proof. The unconstrained demand by the small shareholders is given by solving subproblem (32):

A

B

q a b" k# !p . p2 c

(44)

Substituting for p from Eq. (34) above yields

A

B

ap2 q ab# . b" o p2

(45)

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

A

B

1 p2 ap2 . ab# "(1!a) # q o c

(46)

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

A

B

q b"(1!a) 1# '(1!a). cp2

(47)

Thus, the small investors would demand more than the amount allotted to them by the entrepreneur. h Since the mechanism considered here allows only the large investors to choose their holdings optimally, the underwriter adjusts the schedule so that

64


these investors are induced to hold larger fractions of equity. Small investors are treated fairly since they purchase at the same per-unit average price. They would like to purchase more at this price, but allowing them to do so would lower the amount of monitoring done by the large investors. The next proposition considers the important question of ‘underpricing’ in the initial public offer. In an empirical sense, underpricing is observed by comparing the offering price to the price when secondary trading opens. That is, underpricing is observed by a time-series comparison. The single-period model we have been using is not capable of providing time-series implications. However, it is extended 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 we define 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 exactly equal to what they are allocated in the rationing mechanism, 1!a. This therefore represents the price that would eventuate once trading opens, provided the opening of trading did not influence the initial ownership position taken by large investors. Proposition 3. ºnderpricing in the rationing mechanism exists with respect to the pseudo-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’ shadow price at which they demand exactly 1!a, that is

A

B

(48)

A

B

(49)

q a k# !pJ "1!a. p2 c

Thus, q a q k# !p #(p!pJ ) "1!a. p2 c p2

Using the pricing function Eq. (34) and the entrepreneur’s first-order condition Eq. (43), this can be rewritten as (1!a)q q (1!a)# #(p!pJ ) "(1!a). cp2 p2

(50)

(1!a) pJ !p" . c

(51)

Thus, h


65

This proposition can be used to see that the amount of underpricing is negatively related to the cost of monitoring, as might be expected.22 If monitoring activities are costly, then risk-sharing opportunities are relatively more valuable 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 the rationing mechanism. Proposition 4 establishes the interesting result that the rationing mechanism may actually lead to greater ownership by the large investors than the second-best optimal level. Proposition 4. ¹he entrepreneur’s optimal a satisfies 1#p2 c q a" . b#1#p2#p2 c o 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 on the slope of the pricing schedule. The more negative the slope of the pricing schedule 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-best optimum (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 Walrasian equilibrium are, respectively,

A

p"k!ab#a

A

p*"k#a*

B

1 p2 ! , o c

(53)

B

(54)

1 p2 ! . o c

Subtracting the second expression from the first yields, p!p*"!ab#(a!a*)

A

B

1 p2 ! '0, o c

(55)

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

66


which is positive since p is optimal and the Walrasian mechanism is feasible. Using Proposition 1, a'a*, and utilizing the maintained assumption of existence 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 axis depicts the equity allocated to the large investor, while the vertical axis depicts prices received by the entrepreneur. The Walrasian equilibrium is indicated by allocation a* and price p* and is determined by the intersection of the lower demand 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). Two demand curves are shown for each investor. The dotted curves represent the small investor’s indifference curves. The Walrasian equilibrium, (a*, p*), is determined by the intersection of the lower demand curves of the large and small investors. At this point, small investors are on their lower indifference curve. If the equity allocated to the large investor is increased so that the large investor’s holding is determined by the intersection of his upper demand curve with the upper indifference curve of the small investor, then small investors utility is decreased. Due to increased monitoring, the small investor’s demand curve shifts upward and the amount of underpricing is given by (pJ !p).


67

small investor is represented by the dotted curve passing through the Walrasian equilibrium. Note that the indifference curve of the small investor takes into account the impact of a change in a on subsequent monitoring, while the demand curve does not. As a result of this important effect, the demand curve at the Walrasian equilibrium passes through the indifference curve at a point of positive slope. This implies that small investors are willing to incur a price increase if it implies greater monitoring. Hence, the entrepreneur can increase price and a simultaneously. A possible instance of this is indicated by the movement along the original demand curve of the small investor to a point at the maximum of a higher indifference curve. This is accomplished by a rotation of the large investor’s demand curve to a point on the maximum of a higher indifference curve of the small investor. This is indicated as point a and price p, which is higher than the Walrasian equilibrium. Finally, due to the increased monitoring, the small investor’s demand curve shifts upward and the amount of underpricing is given by the difference between p and pJ , which is the point on the demand curve corresponding to the optimal allocation a. 6.3. Binding participation constraint for large investor We now turn to the implications for rationing and underpricing when the participation constraint of the large investor, Eq. (30), is binding. This occurs when the small investor’s reservation utility constraint, ºM , is small or zero. In S such situations, the prescribed minimum utility of small investors is insufficient to ensure that large investors are also willing to participate. When the large investor participation constraint is binding, º "0; from L Eq. (31), this becomes

A

B

a 1 p2 p"k# ! . 2 c o

(56)

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

A

B

1 1 p2 ! . b" o 2 c

(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 substituted from (57). The latter case holds when ºM is above some positive amount (but S smaller than in the previous subsection). In this case, the analysis of the previous subsection can be repeated to obtain analogues of Propositions 1—5. Equity ownership of the large investor is above the Walrasian level, the small shareholders are rationed (since their demand constraint is non-binding), there is

68


underpricing and the optimal a is determined by the intersection of the pricing function (56) and the indifference curve at ºM . S The second possibility occurs when ºM is in the neighborhood of zero. In this S instance the underwriter would like to obtain higher prices by moving along Eq. (56), i.e., lowering a. However, because of decreased monitoring, the small investors are no longer willing to hold the balance of the securities not purchased by the large investors. As a result, the optimum occurs at the intersection of 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 is there any underpricing. Nevertheless, it still is true that the optimal allocation, a, is above the Walrasian equilibrium. Solving for the small investor’s demand for shares using Eq. (56), we find that

A

B

aq 1 p2 b" # . p2 2c o

(58)

Thus,

AB

b q q q q p2 q " # ( # " , a 2o 2p2c 2o 2p2 o o

(59)

which implies that a'a*. The above inequality follows from the second-order condition for existence of a Walrasian equilibrium. It is interesting that optimal underpricing occurs when regulations require that a relatively large surplus be given to small investors. Their requests remain partly unfilled. However, if the regulatory environment dictates that small investor surplus is unimportant, they receive all they demand and entrepreneurial extraction of surplus is limited by the need to place all of the issue. Although direct regulation of surplus is difficult to enforce, it can be shown that when the large investor’s participation constraint is binding, a larger surplus is equivalent to regulating the minimum number of shares allocated to small investors.23 Thus, underpricing may be an implication of subtle pressures often observed to protect retail investors.

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

23 Specifically, the minimum utility of small investors is negatively impacted by the allocation given to large investors, i.e., dºM /da(0 using p from the pricing schedule (56) and substituting into S Eq. (32) if and only if a'a*.


69

established by the offering mechanism. As discussed in Section 2, selling in the secondary market may be prevented by the repeated nature of the relationship between the underwriter and investors, possibly enforced by penalty bids. In reality, some shares are traded even during the distribution period. Therefore it is important to extend the results of the single-period model to a multi-period environment that permits the large investor to optimally engage in secondary market trading. In this section we analyze the effect of secondary trading on the structure of the IPO and on the final ownership. If traders in the secondary market behave competitively and thus take prices as given, then the initial ownership structure chosen 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 pricetaking in the secondary market, there is no way for the entrepreneur to do any better 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, our model of secondary trading is characterized by imperfect competition, since we assume 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, there are problems with non-existence of a Walrasian equilibrium as documented in Admati, Pfleiderer and Zechner. Second, if the entrepreneur is successful in employing a mechanism that favors ownership by institutional investors, such as the rationing mechanism, these investors have market power. This is because their holdings constitute a large fraction of overall equity ownership. Third, by our definition large investors are those who are capable of monitoring. Therefore, they would be classified as insiders and therefore subject to regulation and disclosure on their trading activities.25 Finally, and most importantly, the empirical evidence cited in Hanley and Wilhelm (1995) shows that institutional investors 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-period model are preserved when non-price taking behavior of the large investors is taken into account. To model the effect of secondary trading, we assume that information about the firm’s final cash flow is received over time. The sequence of events is as follows (Fig. 2). At time t the IPO takes place. At this time, k is unknown to all 1 and is distributed normally with mean k and variance p2. At time t , the 1 2 0

24 In the model of Mello and Parsons (1998) it is also important that price-taking not occur. 25 For an analysis of the interaction between monitoring and insider trading, see Maug (1998).

70


Fig. 2. Sequence of events.

parameter k has been revealed to all market participants. Therefore, the firm’s final cash flow is distributed normally with mean k#m and variance p2. After 2 k has been revealed, shares can be traded on a stock market. At time t monitoring takes place and at time t the final cash flows are realized and 3 4 distributed to shareholders. 7.1. The secondary trading market Analyzing the problem recursively, we first determine the equilibrium allocations implied by the trading process at time t for a given initial allocation. At 2 time t the parameter k has been observed and the expected cash flows are, as 2 before, k#a /c, where a is the final holding of the large investor and this 2 2 determines the amount of monitoring. Thus, the expected utility of the small investor is given by

A

B

a 1 (1!a )2 p2 2 2#(1!a )p , º2"(1!a ) k# 2!p ! S 2 2 1 2 q c 2

(60)

where 1!a represents the holdings of the small investor, p is the price of 2 2 shares at time t , and 1!a are the holdings from the initial time period. It is 2 1 easy to verify that the small shareholders’ demand as a function of the anticipated equity holdings is given by a (1!a )p2 2 2, p (a )"k# 2! 2 2 c q

(61)

as long as these investors behave as price-takers. The institutional investor’s expected utility at time t is given by 2

A

B

a 1 a2 p2 1 a2 º2"a k# 2!p (a ) ! 2 2! 2#a p (a ). L 2 2 2 1 2 2 c 2 o 2 c

(62)

Substituting for p (a ) from Eq. (61) and differentiating with respect to a yields 2 2 2 2

p2 q a "ka # , 2 1 1#p22#2p22 c o q

(63)


71

where 2

1#p2 (64) k" c 2 q 2 . 1#p2#2p2 c o q This result shows that the large investor will generally trade from the initial holdings, a , toward the Walrasian equilibrium holdings, a*. If initial holdings 1 are above a*, then secondary market holdings will be as well. An important property that we will use in the next subsection is that k(1, i.e., the effect of an increase in initial equity holdings, a is attenuated somewhat by secondary 1 market trading. 7.2. Rationing in a multiperiod environment Having now established the secondary market trading at time t for given 2 initial holdings, we analyze the entrepreneur’s choice of an initial ownership structure. Based on Lemma 1 of the previous section, we consider a two-stage rationing mechanism where the large investors are offered a pricing schedule by the investment banker, and the small investors’ demands are then filled at the average actual price paid by the large investor. For brevity, we focus only on the case where the large investor’s participation constraint is not binding. The institutional investor’s expected utility at time t can be expressed as 1 a 1 a2p2 1 a2 º "a k # 2!pN (a ) ! 2 2! 2 L 2 0 2 2 c 2 o 2 c

A

B

1 a2p2 #a (pN (a )!p (a ))! 1 1, 1 2 2 1 1 2 o

(65)

where pN (a ) represents the expected t price at t and we have substituted the 2 2 1 expected value of k as k . 0 Next, we want to differentiate with respect to a . First, we recognize that the 1 envelope theorem, from optimization in the secondary market, implies that Lº da Lº dpN da L 2# L 2 2"0, (66) La da LpN da da 2 1 2 2 1 and that dp /da ,b, the slope of the offering schedule. The first-order condi1 1 tion from maximizing º with respect to a thus yields L 1 p2 p (a )"pN (a )!a b# 1 . (67) 1 1 2 2 1 o

A

B

Note the similarity with Eq. (34) from the previous section; the offering price equals the expected next-period’s price minus an amount related to the slope of the offer schedule and the cash flow risk from time t to t . 1 2

72


As in the previous section, we assume that the entrepreneur attempts to maximize revenues while taking into account a reservation utility constraint of small investors. Since small investors trade optimally at time t , we only 2 consider the portion of utility from times t to t as being subject to regulation in 1 2 the form of a minimum participation constraint. As before, this perspective on the model is essentially a constraint ensuring broad small investor participation in the issue. Neglecting the full distribution constraint, the entrepreneur’s optimal mechanism design problem can be specified as follows:

A

p2 max p (a )"pN (a )!a b# 1 1 1 2 2 1 o a1,b subject to

B

(68)

1 (1!a )2p2 1 1*ºM 1. º1"(1!a )((pN (a )!p (a ))! S S 1 2 2 1 1 q 2

(69)

Substituting for p (a ) from Eq. (61) and introducing a Lagrangian multiplier, 2 1 j yields

A

a (1!a )p2 p2 2 1!a b# 1 L"kN # 2! 0 1 q o c

C

A

B

B

D

p2 (1!a )2p2 1 1!ºM 1 . #j (1!a ) a b# 1 ! S 1 1 o 2q

(70)

Differentiating with respect to b yields 1 . (71) j" 1!a 1 Substituting for a from Eq. (63) and taking expectations in Eq. (61), the first1 order condition with respect to a is given by 1 k kp2 a p2 p2 # 1! 1 b# 1 # 1"0. (72) q 1!a o q c 1 This expression illustrates the essential change from the single-period analysis. Comparing Eq. (72) to Eq. (43), (k/c)#(kp2)/q replaces 1/c.26 There are two 1 effects. First, the marginal benefit of monitoring is reduced since k(1. This reduction in the marginal benefit of monitoring is due to the fact that the large investor trades down from the initial holdings toward the Walrasian level. As a result, the entrepreneur is unable to sustain as high a level of monitoring

A

B

26 Since the relevant measure of risk is related to the amount of uncertainty revealed over the period until trading begins, the change from p to p is merely notational. 1


73

activity in the multi-period model. The second effect, which is driven by enhanced risk-sharing possibilities with an additional round of trading, works in the opposite direction. Increasing initial equity-holdings of the large investor is less costly because the entrepreneur knows that a fraction will be sold once secondary trading opens. 7.3. Results of the multiperiod model The essence of the results from the single-period model obtain in the multiperiod model as well.27 Propositions 1 and 2 hold in a straightforward manner. The entrepreneur prefers rationing small investors to a Walrasian offering mechanism. Similarly, allowing for secondary trading does not change the essential aspects of Proposition 3 concerning underpricing of IPOs. The underpricing result now has a more natural interpretation since it can be measured relative to the price in the secondary market. Combining Eqs. (61) and (72) we see that the expected price increase between the IPO price and the price in the secondary market is k kp2 p2 pN !p "(1!a ) # 1# 1 . (73) 2 1 1 c q q

A

B

The expected price is larger in the secondary market as compared to the offering price. This is due to both the marginal benefits of monitoring as well as a risk premium. The risk premium is measured by the last two terms. These effects are lower as the variance of information declines and/or the small investors are more risk tolerant. The first term, (1!a )(k/c), is analogous to the result of 1 Proposition 3 and shows that the degree of underpricing will be positively related to less costly monitoring activities on the part of institutional shareholders. However, the existence of secondary trading does attenuate the underpricing effect since k(1. Again, however, if monitoring is relatively more important than risk-sharing, then k is large and underpricing is more significant. Finally, the analogous expression to Proposition 4 holds except that k/c#(kp2)/q replaces 1/c. Initial holdings by large investors may be either larger 1 or smaller than in the single period model depending on whether the increased risk-sharing benefits outweigh the decreased monitoring expenditures.

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

74


8. Conclusion The major conclusion of this paper is that the value of a firm’s IPO is determined by the ownership structure resulting from the offering mechanism. The basic premise of our argument is that investors are not homogeneous in their ability to monitor management of the newly public firm. Large investors have an advantage in this regard because of the establishment of institutional mechanisms that facilitate such activities. Moreover, they benefit from participatory relationships and other complementarities that small investors do not enjoy. Nevertheless, since monitoring activities are difficult to observe and therefore to contract on, a free-rider problem exists. The existence of this agency problem creates a tension between risk-sharing and information production. We find that these two goals must be traded-off against one another. As a result, the optimal offering process will, to the extent that regulations allow, give favored treatment to the large investor class. A common form of a regulatory constraint ensures that all investors purchase shares at the same per-unit price. We show that this regulation still gives the issuer some latitude in setting quantity restrictions and therefore in rationing small investors. In our model, rationing can be optimal because of the positive externality enjoyed by small investors from the monitoring activities of large investors. However, rationing cannot be accomplished through a competitive trading mechanism such as a Walrasian auction. It requires the imposition of a negotiated offer schedule between the underwriter and large investors. We believe 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 investment banker or underwriter than other papers on IPOs. We view the investment banker as a broker with an active and continuing relationship with the institutional investment community. The nature of this relationship provides two benefits to the entrepreneur. First, the investment banker is able to identify those investors capable of monitoring and provide favored treatment, either in price terms, or if that is disallowed, in terms of priority. Second, the nature of the repeated relationship allows the investment banker to negotiate directly with the large investor, providing for greater extraction of surplus to the benefit of the entrepreneur. Our theory generates several empirical predictions. First, the ability to ration in favor of large shareholders should be positively correlated with underpricing. One way of testing this prediction is to compare underpricing in different jurisdictions. Whenever pro-rata allocation regulations are imposed, one should expect less underpricing. Loughran et al. (1994) provide evidence on underpricing in different countries. Although the results are not conclusive, countries with little strategic rationing such as France or Finland exhibit low underpricing.


75

Second, the model also predicts a positive relation between underpricing and strategic rationing within a given regulatory environment. Consistent with this prediction, Koh and Walters (1989) report, for their sample of IPOs in Singapore, a negative correlation between underpricing and the proportion of the issue allocated to small investors. Supportive evidence is also reported in Hanley and Wilhelm (1995). Third, underpricing should be larger for companies with high benefit-to-cost ratios for monitoring activities, such as high-tech firms. By contrast, firms with long operating histories are likely to exhibit less scope for monitoring, and should therefore be less underpriced. Some empirical support for this can be found in Loughran et al. (1994). Fourth, when regulations require significant participation of small investors then IPO’s should be more underpriced. For tractability reasons, we have modeled the negotiation process between the investment banker and the large investor as optimal from the entrepreneur’s perspective. The actual process clearly involves a substantial amount of bargaining. Obviously, the existence of bargaining power on the part of large investors is likely to create lower revenue for the entrepreneur. But it is also just as likely to enhance the results involving favored treatment for institutions and relatively large equity percentages at the time of offering. If large investors internalize more of the benefits from monitoring through greater participation in the proceeds from issuance, then they are more likely to want a higher degree of ownership. Underpricing would be even more pronounced. Therefore, the assumption in the paper that the schedule is optimally chosen from the entrepreneur’s perspective is a conservative assumption when it comes to an underpricing prediction. We believe that considering the form of institutional mechanisms such as the rationing process we have described here is an important objective of future research. With heterogeneity of investor groups and inherent agency problems, market features other than purely competitive markets may actually be beneficial both from the standpoint of the firm issuing securities as well as those who provide the participatory capital. The recent privatization programs in Eastern and Western Europe along with the concomitant design of capital markets provide important examples.

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