Book Building vs Fixed

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Bookbuilding vs. Fixed Price: An Analysis of Competing Strategies for Marketing IPOsAuthor(s): Lawrence M. Benveniste and Walid Y. BusabaSource: The Journal of Financial and Quantitative Analysis, Vol. 32, No. 4 (Dec., 1997), pp.383-403Published by: Cambridge University Press on behalf of the University of Washington School of Business

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JOURNALOFFINANCIALNDQUANTITATIVENALYSIS VOL.32, NO.4, DECEMBER997

Bookbuilding vs. Fixed Price: An Analysis ofCompeting Strategies for Marketing IPOsLawrence M. Benveniste and Walid Y. Busaba*

AbstractWe compare two mechanisms for selling IPOs, the fixed price method and American book?building, when investors have correlated information and can observe each other's sub?scription decisions. In this environment, the fixed price method is a strategy that can createcascading demand. Alternatively, an underwriter building a book aggregates investor infor?mation into the offer price. We find that bookbuilding generates higher expected proceedsbut exposes the issuer to greater uncertainty, and that it provides the option to sell additionalshares that are not underpriced on the margin.

I. IntroductionA debate has arisen in the international arena regarding the best way to priceand place Initial Public Offerings of Equity (IPOs). At the center of the debateis the fixed price method, which has historically been the dominant approach inthe UK and its former colonies (e.g., India and Singapore) and in most of Europe.

The debate has been fueled by an acceleration in the number of IPOs done in somemarkets and movements toward privatization that have resulted in some unusuallylarge issues. * Trends suggest that American bookbuilding is becoming the methodof choice.2

*FinanceDepartment,CarlsonSchool of Management,Universityof Minnesota,Minneapolis,MN55455, andFinanceDepartment,Collegeof Business andPublicAdministration,Universityof Arizona,Tucson,AZ 85721, respectively.We have benefitedfromthe commentsof Bhagwan Chowdhry thereferee),JeffColes, George Papaioannou, oseSuay,Bill Wilhelm,and seminarparticipants tBostonCollege, Rice University,Universityof Michigan, Universityof SouthernCalifornia,FederalReserveBank of New York,the 1995 meetingof the FinancialManagementAssociation,the 1996 ArizonaSymposiumat the Universityof Arizona,the 1996 meetingofthe WesternFinanceAssociation,andthe 1997 meetingofthe MultinationalFinanceSociety.^he handlingof the IPO of SingaporeTelecommunicationsPteLtd. is a good example. Tradi?tionally, IPOs in Singaporehave been done accordingto Britishcompanylaw, which mandates hatIPOs be distributedby the fixed price method(Koh and Walter(1989)). But GoldmanSachs, theglobal coordinator,placedapproximatelyone-halfof the issue using a book of orders. The rest wasdistributeddomestically according o the traditional ixedpriceevenhandedmanner TheWallStreetJournal,3/4/93 (A, 10:2), 8/18/93 (A, 7:6), and9/27/93 (B, 4D:6)).2See, forexample, "Goingby theBook,"TheEconomist,January ,1993, p. 72, "The1995 Guideto Germany,"publishedwith the April 1995 Issue of Euromoney,and "Don't Blame Us?It's theMarkets,"Euromoney,May 1995. See also Loughran,Ritter,andRydqvist(1994) for a discussion ofthe recentdevelopments n the newequitymarketsabroad.383

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384 Journal of Financial and Quantitative AnalysisThis paper compares the fixed price method and American bookbuilding wheninvestors have correlated information and can observe each other's subscriptiondecisions. In such an environment, the fixed price method is a strategy that can

create cascading demand. Alternatively, an underwriter building a book attemptsto aggregate investor information into the offer price before the offer is sold. Wefind that bookbuilding generates higher expected proceeds but exposes the issuerto greater uncertainty, and that it provides the option to sell additional shares thatare not underpriced on the margin.The challenge in any offering mechanism is price discovery: at what pricewill the issue sell? Consider, for example, the degree of price uncertainty inthe U.S. primary market. Preliminary prospectuses filed with the SEC for firmcommitment offerings specify an offer price range that, on average, spans 16%around the midpoint (Hanley (1993)). The main difference between the two sellingmethods lies in how they address the pricing challenge. Fixed price offerings arepriced without first soliciting investor interest. Investors then make subscriptiondecisions over a period that can typically range from two weeks to two months.In contrast, an underwriter building a book solicits non-binding contingent orders(indications of interest) during road shows, that provide information for setting thefinal offer price.3Our analysis builds on the market structure developed by Welch (1992), andour modeling of the fixed price method mirrors his. Welch models a fixed priceoffering to investors who possess equally valuable, correlated pieces of informationabout the true (common) after-market share value. Selling is sequential, allowingthe purchasing (or subscription) decisions of early investors to be informativefor, and, hence, to affect the decisions of, the later investors. As such, investorsapproached earlier in the selling process would inherently have greater marketpower and, as Welch illustrates, can generate cascades through their investmentdecisions. The fixed price method uniquely offers the potential to exploit thismarket structure (and avoid information aggregation) by pricing the issue lowenough to lure early investors and generate an immediate buying frenzy. Sequentialselling is also a way, as Welch argues, to avoid the winner's curse problem thatuninformed investors potentially face (Rock (1986)) when subscription decisionsare simultaneously made and rationing is a function of aggregate subscription.We compare the results of this pricing strategy to the results of using anunderwriter to sell the issue through bookbuilding to the same investors. Theunderwriter, by collecting and publicizing investor information, diffuses any pos?sibility of a cascade. And he has to pay a price, in the form of issue underpricing,to induce truthful indications of interest (Benveniste and Spindt (1989)). Yet, ouranalysis shows that the underpricing required to create a cascade is higher than thecost required to elicit investor information. We also find, however, that pricing anissue off a book may result in an offer price below that which creates a cascade in

3Therules for allocatingsharescan also differ. In fixed price offerings,shareallocations can benon-discretionarye.g., UK (offersforsale), Finland,HongKong,Taiwan,andSingapore)as well asdiscretionarye.g., Australia,Belgium,Brazil,Germany, taly,Japan pre-April1,1989), Korea post-June 1988), Sweden, Switzerland,and the US (best-effortscontracts)). See Rock (1986), and Kohand Walter 1989) forSingaporeandtheUK, andLoughran,Ritter,andRydqvist(1994) forthese andthe rest. Allocations arediscretionaryn thebookbuildingmethod. See also ChowdhryandSherman(1996) forananalysisofthe difference n the levels of oversubscription etweendifferentregimes.



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Benveniste and Busaba 385a fixed price offering. On the basis of these results, we conclude that the degree ofprice risk endogenous to the issue and the risk tolerance of the issuer are the keyelements in the issuing firm's preference regarding the offering method.

Additionally, we show that bookbuilding affords the issuing firm certain op?tions that are not available in the fixed price method. In particular, bookbuildingallows the issuer to exercise discretion over the offer size conditional on the out?come ofthe book. This discretion comes in two forms. First, the final issue size inU.S. firm commitment offerings?that are sold via bookbuilding?does not haveto be set until after the road shows when the final offering documents, includingthe offer price, are filed with the SEC (Ritter (1987)). Also, firm commitmentofferings typically carry a greenshoe (or over allotment) option that allows theissuance of up to 15% additional shares and can be exercised after the final offerprice has been established and selling is started. We show that the option to adjustissue size permits the issuing firm to offer added shares when demand is strong,and to do so at zero marginal underpricing cost.This result is based on the observation that underpricing in bookbuilding isa required sum of money necessary to induce investors with valuable positiveinformation to be truthful in their indications of interest. Our analysis showsthat the value of the required inducement is related only to i) the effect that falseindications can have on the offer price and ii) the allocation to investors falselyclaiming poor information. Filling the unfulfilled demand of investors with stronginterest has no effect on either of these factors and, hence, does not increase thedollar value of required underpricing. The result is that added shares are sold atfull marginal value.

II. Relation to Other WorkThe papers of Spatt and Srivastava (1991) and Benveniste and Wilhelm (1990)show in environments different from ours that bookbuilding generates higher ex?

pected proceeds than fixed price. Spatt and Srivastava work in a general auctionframework in which an IPO is viewed as an indivisible good, and argue that book?building stochastically dominates the fixed price method. Benveniste and Wilhelmreach a similar result when the winner's curse is possible in an environment thatadmits both informed and uninformed investors (as in Rock (1986)).

In both of these papers, however, sequential selling and the possibility thatinvestors can condition their demand on the demand of others are not permitted.We admit these possibilities and, by doing so, capture the real potential for the fixedprice method to generate demand cascades. As a result, bookbuilding no longerstochastically dominates fixed price. Our paper also is the first to demonstratethe option value in allowing the issuing firm to condition the offering size on theresults of the book.

Some markets abroad (in France, for instance) use formal auctions to sellIPOs. Both bookbuilding and fixed price, for that matter, can be viewed as specialcases ofthe general class of IPO auction mechanisms available. Rock (1986), forexample, modeled the fixed price method as an auction in which investors bid withtheir feet. To date, however, there are no general results on auctions that identify theoptimal IPO selling mechanism because an IPO is divisible. (See Back and Zender



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386 Journal of Financial and Quantitative Analysis(1993) and Wang and Zender (1996) for analyses of auctions of divisible goods.)This paper does not attempt to solve for the optimal IPO auction. Rather, attentionis focused on comparing two specific, commonly used IPO selling mechanisms.Yet we conjecture, based on Benveniste and Spindt (1989), that bookbuildinghas an added advantage over any formal auction because the underwriter dealsrepeatedly with the same pool of regular investors and can increase revenues to theissuer by conditioning future allocations on investors' current behavior as well.The rest of the paper is structured as follows. The next section presents thebasic elements of the model and Section IV develops the two competing market?ing strategies and compares their results. Section V discusses the option valueof bookbuilding and Section VI analyzes the firm's preferences with regard tomarketing method. The paper concludes in Section VII.

III. The ModelOur analysis will be carried out in a framework that most closely resemblesWelch's (1992) model. This section sketches the basic elements ofthe model and

includes the fundamental mathematical results that will be used later in the paper.The format and terminology will mirror those of Welch, but the notation will becloser to that of Benveniste and Spindt (1989).A. The Market Setting

In keeping with the marketing focus of the paper, our model centers on a firmselling a fixed fraction of ownership in the form of Q shares. The preliminaryoffering steps, such as due diligence, are assumed to be complete and all relevantinformation learned in the process already conveyed to the potential investors.More formally, we assume that the issuing firm knows nothing about its prospectsthat the potential investors do not also know.There is a total of H investors, with appetites for at most one share each,that make up the immediate market and to whom the issue must be placed to besuccessful. Each investor is endowed with a private signal conveying information(about the true share value) undiscovered in the due diligence period. The distin-guishing marketing strategies hinge on whether or not the issuing firm (representedby its underwriter) will try to ascertain the private information of investors priorto pricing and placing the issue.The true share value, V, is assumed to be uniformly distributed between Vuand VL, where Vu > VL. This prior distribution is common knowledge, as isthe issuer's reservation value Vp. Assume that Vp < VL on the grounds thatprivate owners may be ill-diversified or alternative sources of financing may beexpensive.4 We will use the same normalization as in Welch (1992), and define acorresponding unknown offering type as

e = (v-vL)/(vu -vL).4This assumptionis not critical for the fundamental esults of our paper(yet it is for Welch's

cascadesresult),but we retain t because it makes theexposition significantlysimpler.



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Benveniste and Busaba 387In essence, 6 simultaneously normalizes both the magnitude and variabilityof possible share values. It has an implied prior distribution that is uniform overthe interval [0,1] with a mean of lA. The reader should note that although 6 is our

focus of analysis, expressing the solution in terms of original values will providea comparative analysis for characteristics such as the ex ante uncertainty in sharevalue.All parties?i.e., the issuing firm, its marketing agent (referred to as the

underwriter), and the investors?know the distribution ofthe true share value. Pri?vately, however, each investor costlessly observes an independently drawn signal/ e {U,L}. The information content of these signals is fully captured (and ex?plained below) by the assumption that for an offering of type 6, i is drawn froma Bernoulli variable {U,L} with the probability of U being 6. So, each signaladds valuable information and in sufficient number that the signals combined canidentify with high precision the true value of the shares (or equivalently, the truevalue of 6).

Communication among investors is important because it affects their invest?ment decisions through their reservation values. In this regard, we assume, likeWelch, that investors do not convey explicitly their private signals to one another,but do observe each other's purchasing decisions. Under some conditions, an in?vestor's purchasing decision may reveal his private signal and, as a result, impactsthe subjective valuation of investors who follow. We also assume though, in thespirit of Benveniste and Spindt, that the underwriter can privately ask each investorabout his signal and other investors cannot observe the answer.5Investors are assumed to be risk neutral. Their reservation prices are theexpected share values conditioned on their private signals and whatever additionalsignals they learned during the issuing process. The following subsection containsmathematical results on conditional expectations in this model that identify therelationship between reservation prices and information. Note that, formally, aninvestor's conditional expectation of 6 is equivalent to his reservation price.B. Mathematical FactsFact 1: An investor's expectation of 6, conditional on observing H signals of whichh are good (i.e., U signals), is given by the following Bayesian rule,(1) 6h = E(0\h;H) = (h+l)/(H + 2).Fact 2: Given a total of H signals, the number of good signals h can be any ofH+1 possible outcomes, {0,1,2,..., H}. Based on the prior uniform distributionof 0, each outcome is equally likely with a probability of

7rh = ?r(h;H) = l/(H+l), andPr(h>k;H) = (H-k+l)7rh = (H - k +l)/(H+1), h = 0,...,H.

5Relaxingthis assumptionby allowing investors o observeotherinvestors'answers reduces theproceeds rombookbuildingbutmaintains he samecomparative nalysisresultsbetweenbookbuildingandfixedprice.



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388 Journal of Financial and Quantitative AnalysisSince individual investors are endowed with private signals, we must con?sider how each investor perceives the distribution of signals among the remaininginvestors. The following results establish these subjective distributions.

Fact 3: Conditional on observing a U signal, an investor believes that there are hU signals with the remaining H ? 1 investors with probability(2a) 7rfh = Y>r(h;H-l\Usigm\) = **+ *) h = 0,...,H-l.ti\ti + 1)

Conditional on observing an L signal, however, this probability will be

(2b) < = Pr(h;H-l\L signal) =^"^,

h = 0,...,H- 1.

Proof. See the Appendix.

IV. The Marketing of New IssuesWe can now turn our attention to the analysis ofthe two competing marketing

strategies. We will start by presenting the results of doing the issue via fixed pricefollowing the approach of Welch (1992).A. The Fixed Price Method

We view a fixed price offering as an offering in which the offer price isestablished without first formally attempting to learn investor valuations. Thischaracterization obviously does not preclude learning from informal discussionswith and surveys of investors. Any information gleaned can be thought of ashaving been factored into the ex ante expectations about 6 and, hence, will havesimilar effects on both offering mechanisms. We assume that private informationpersists beyond such attempts to learn investor sentiment.

Establishing the offer price in this environment?when investors possess pri?vate information?involves weighing the benefits of raising the price against theincreased likelihood that the issue will not sell. We denote the offer price by P?and assume that unsold shares are worth the reservation value ofthe issuer, 6P (thenormalized value of Vp).Potential investors are lined up and selling is carried out sequentially. Eachinvestor at a time decides to purchase or not based on his reservation price. Weindex investors by their order in line, j, where j = \,...,H, and denote the reser?vation price and purchasing decision of each by Pj and dj, respectively. Formally,the reservation price of investor j can be expressed as a function of his signal ijand the observed purchasing decisions of the preceding j ? 1 investors,(3) Prj(ij*,dj-x,dj-2,...,dx) = E(e\ijmddj-l,dj-2,...,dl).Investor j decides to purchase shares only if Pj > P?.The following lemma identifies when an investor's purchasing decision isinformative about his signal and, hence, impacts the reservation prices of investorsdown the line.



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Benveniste and Busaba 389Lemma 1. Investor/s purchasing decision reveals his private signal if and only if(4) P)(U;dj_x,dj-2,...,dx) > P? > P)(Udj-X,dj-2,...,dx).The intuition behind the condition is simple. When (4) is met, the investor'sdecision depends on his signal. Hence, a decision to purchase shares at P? reflectsa U signal while a decision to abstain reflects otherwise.When a point in the selling process is reached at which (4) is violated, acascade is created as all investors down the line ignore their signals and makethe same investment decision. If, for example, P? is lower than both conditionalreservation prices, investor j purchases regardless of his own signal. Investory-h1,having observed the purchasing decisions of the first j ? 1 investors, can verifythat (4) is not met for investor j and, as a result, cannot infer the investor's signalfrom his purchasing decision. He faces the same purchasing decision faced byinvestor j and, likewise, decides to buy shares. Similarly, all investors down theline decide to invest. If, on the other hand, (4) is violated by P? being higher thanboth conditional reservation prices, a negative cascade develops as investor j andothers down the line refrain from investing.The incidence of cascades, therefore, can be critical for the results of an issueand the possibility of their occurrence is expected to impact the pricing decision.An offer price of lA or below creates an immediate positive cascade?in which allinvestors buy?since the reservation price of the first investor in line is at least/s (the 6 value conditioned on the first investor's signal being L). Symmetrically,an offer price higher than %(the 6 value conditioned on the first investor's signalbeing U) creates an immediate negative cascade resulting in issue failure.For offer prices such that lA


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390 Journal of Financial and Quantitative Analysisin price beyond lA raises significantly the likelihood of a negative cascade. As aresult, the issuer is better off with sure success.

Going back to the non-normalized share values, the cascade price of lA rans-lates into a price of VL + (Vu ? VL)/3, and expected underpricing becomes(Vu ? VL)/6. Simple comparative static analysis illustrates that expected un?derpricing increases with (Vu ? VL), which measures ex ante uncertainty in theoffer value. Welch's Theorem 6, p. 706 shows that underpricing as a percentage ofthe offer price increases "when a mean-preserving spread is added to the commonprior" (Theorem 3 below shows that this is also true with bookbuilding).We turn next to analyzing the results of using the bookbuilding approach toprice and place this same issue. To accomplish this, we have adapted the approachof Benveniste and Spindt (1989) to the current framework.B. The Bookbuilding Method

In building a book, the underwriter conducts a pre-offer marketing effort inwhich it solicits non-binding indications of interest (or pre-orders) from potentialinvestors. The gathered indications provide an assessment of the demand for theissue that allows the underwriter to set an offer price that better reflects aggregate,or market, valuation. The issuing firm receives the gathered information before thefinal pricing decision, and this eliminates its informational disadvantage vis-a-visinvestors. Aggregate information is also revealed to potential investors, neutral-izing the power of any individual investor. But such benefits of the informationgathering effort come at a cost. Investors should be induced to be truthful in re?vealing their indications of interest, as they know that these will influence the offerprice.In the context of our model, we abstract from demand indications and assumethat investor responses during the pre-market are simply U or L. To secure honestresponses, the underwriter establishes a mechanism that conditions both the offerprice and share allocations on the outcome of the book (i.e., on individual andcumulative responses), and this mechanism is fully understood and anticipated byinvestors. The underwriter's objective is to maximize expected proceeds, subjectto investors' incentives. In light ofthe revelation principle, the underwriter restrictsits attention to price/allocation schedules that induce truthful indications of interest.In our model, the outcome of the pre-market is represented by the number hof investors who revealed U. The underwriter announces this outcome to investorsand then establishes a price/allocation schedule that is conditioned on both h andindividual responses (all investors with the same response are treated symmetri-cally). At that time, all investors revise their expectation of the true issue type to#/,, and this becomes their reservation value.

The following notation will be used to describe the candidate price allocationschedule:P?h = the offer price when h of the H investors reveal U signals;

qL,h = the allocation to an investor who reveals an L signal when h othersreveal U signals; andqu,h+\ = the allocation to an investor who indicates U when h others do thesame.



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Benveniste and Busaba 391Before setting the underwriter's problem and solving for the optimal price/allocation schedule, consider first the marginal value of an investor's signal. Aninvestor misrepresenting a U signal as L drives the perceived issue type from 0h+\

to Oh. Formally, the marginal value of private information is(5) 0/h-i ? Oh = H + 2 H + 2 H + Va decreasing function of the number of investors polled in the pre-market, H.

Assuming that the after-market price will efficiently incorporate information,and that the other H ? 1 investors are truthful, the expected profit for an investorwith a U signal who falsely reveals an L signal in the pre-market isH-\(6) Y,


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392 Journal of Financial and Quantitative AnalysisConstraints (11) reflect our assumption that any investor can buy only up toone share, and the requirement that the entire issue be placed.6 The solution tothis problem is described in the following theorem,

Theorem 2. The maximum expected proceeds are achieved if the following con?ditions are met:1. when h < Q, set qUjh = 1, qUh = (Q - h)/(H - h), and P?h= 0h;2. when h > Q, set qUjh = Q/h, qLh = 0, and P?h= 6h - uh where uh is given

by

E(uh) h=Q

The expected per share proceeds that result from this strategy are given byE(P?) = V2-E(uh).

Proof. See the Appendix.This price/allocation schedule minimizes the money that should be left onthe table for investors in payment for good information. Giving allocation priorityin all states to investors revealing good information and underpricing only whenthese investors can buy the whole issue ensures that underpricing?or the paymentfor information?is targeted solely at investors who provide favorable pre-market

response. Such price/allocation strategy, therefore, minimizes the benefit to in?vestors from falsely reporting L and, as a result, minimizes the level of underpricingrequired to satisfy the incentive compatibility constraint (8).

Simple comparative static analysis illustrates the following two properties ofunderpricing.Corollary 1. For a given offer size, Q, expected underpricing decreases with H.Proof. Substituting for ir'h n E(uh) from Fact 3, the proof becomes straightforward.

As H increases, both the marginal value of information and the expectedallocation to investors revealing bad information drop, reducing the expected gainsfrom cheating (the RHS of (8)). In the limit, when the number of investors isinfinite, required underpricing drops to zero.7Corollary 2. Expected underpricing increases with (Vu ? VL).

6AUowing he underwriter o place less thanQ shareseliminatesthe need forunderpricingincetheunderwriter analwaysset qLh = 0 and drive(6) to zero. Tocircumventhisartificial olution,weview Q as the minimumnumberof shares heunderwriter eeds to placeforthe issueto be successful.ViewingQ this way only strengthens he cascade result ofthe fixedpricemethod.7Wedo notobserve,however, hat underwriters re-marketo aninfinitenumberof investors. Thiscould be explained n therepeatedgameframeworkbetweenunderwritersndtheirregularnvestors)suggested by Benveniste andSpindt(1989). Also, thereare directcosts thatrelateto the numberofinvestors n the pre-marketing rocess.



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Benveniste and Busaba 393Proof. Using original values, the marginal value of information (5) becomes(Vu ? VL)/(H + 2), and expected underpricing, given in Theorem 2, becomes(Vu - VL)E(uh), which clearly is increasing in (Vu - VL).

This result is not surprising because when ex ante uncertainty increases, thevalue of private information increases. Thus, the incentive to falsely reveal badinformation in the pre-market rises, and the underwriter must promise deeperunderpricing to induce honest indications of interest. The following theoremshows that, as in the case of cascades, underpricing as a percentage ofthe offer priceincreases with ex ante risk. This is consistent with the theoretical (Proposition 1)and empirical results of Beatty and Ritter (1986).Theorem 3. The ratio of underpricing to the offer price increases with a mean-preserving spread of (Vu ? VL).Proof. See the Appendix.C. Comparing the Results

The analysis above illustrates that a fixed price offering must be discountedin order to neutralize the potential adverse effect of weak early investor interest.Bookbuilding provides an alternative method for eliminating the threat of negativecascades. It allows the issuing firm to buy investor information prior to pricing andplacing the issue. The following theorem compares the results ofthe two marketingmethods. In Section V, we consider other potential benefits of collecting investorinformation prior to selling an IPO.Theorem 4. Relative to a fixed price issue, the proceeds of an issue priced and soldwith a book of pre-orders will1. have a strictly higher expected value if H > 1, but will also

2. have higher ex ante variability,if the expected proceeds maximizing strategy is followed.Proof. See the Appendix.

Theorem 4 demonstrates that the cost of acquiring information in bookbuild?ing is lower than that of shedding the risk of negative cascades in a fixed priceoffering. Two factors underlie this result. First, the level of underpricing requiredin a fixed price offering is determined by the full value of the private signal ofthe first investor in line. In comparison, an underwriter building a book aggre-gates information and, hence, pays only for the marginal value of investor signals.Since investor signals are correlated, the marginal value of any of them drops withthe number of signals aggregated (see (5)). Second, the payment for informa?tion in bookbuilding is further reduced by the underwriter's ability to discriminatein share allocations against investors showing weak interest. The theorem alsoshows, however, that the proceeds are riskier with bookbuilding because they arecontingent on investor interest that is revealed in the pre-market. Also, it should benoted here that the distribution of proceeds under bookbuilding does not first-orderstochastically dominate the sure cascade proceeds. For H > 2, the cascade price



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394 Journal of Financial and Quantitative Analysisof /a is strictly greater than, for example, 00i the offer price in bookbuilding whenh = 0. Theorem 4 suggests the following empirical implications.Implication 1. Average (or expected) underpricing is lower for IPOs sold off abook vs. those sold via the fixed price method.Implication 2. Abstracting from the degree of underpricing, the absolute levelof the price adjustment in the immediate after-market, or equivalently, the cross-sectional variance of initial returns, is larger for fixed price offerings than forofferings sold off a book.

The intuition behind Implication 2 follows from the fact that, unlike the offerprice of a pre-marketed issue, the cascade offer price does not reflect investors'private valuation. Hence, the price of a fixed price issue should adjust in the(immediate) after-market to incorporate such information.The fact that firm commitment offerings in the U.S. are typically sold usingbookbuilding while best-effort offerings resemble fixed price offerings providesone way to test these implications. Chalk and Peavy (1987) study a sample ofIPOs from the period 1975-1982, and consistent with our first prediction, theyfind that average underpricing (measured by initial day return) was 19.61% forfirm commitment offerings and 37.81% for best-efforts offerings. Ritter (1987)further controls for offer size and still finds similar contract effect. He also reports,indirectly consistent with Implication 2, that the time-series after-market standarddeviation of returns is significantly higher for best-efforts offerings.

V. The Option Value of BookbuildingOur focus to this point has been on the distinctions in the cost and quality ofthe information garnished by the issuing firm in the two offering mechanisms. The

comparison, though, has ignored the additional benefits an issuing firm can realizefrom the information acquired. Such benefits can be numerous, ranging fromfundamental benefits in evaluating the firm's strategy (Benveniste and Busaba(1995)) to capital cost benefits, such as permitting the firm to raise additionalcapital at a lower cost. In this section, we demonstrate how the option to adjustoffer size based on investor information provides an inexpensive method for usingsuch information to raise additional capital.Casual observation of the IPO market and empirical work indicate that sig?nificant adjustments to the size of firm commitment offerings do take place beforethe final prospectus is published. Ritter (1987) analyzes the degree of price andquantity adjustments that the 1982 firm commitment issues experienced betweenthe preliminary and final prospectuses. He reports an average change in expectedproceeds of 23.8%. Likewise, Hanley (1993) documents the incidence of suchpre-offer adjustments.To formalize the value of the option to adjust offer size, we now relax theassumption that this size is fixed but maintain the issuer's objective unchanged. Theissuer's objective in the analysis so far has been to maximize expected proceeds(expression (10)). But when the offer size is fixed, this objective is identical



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Benveniste and Busaba 395to maximizing the expected offer price, or minimizing the expected per-shareunderpricing.We assume in this section that offer size can vary from a minimum of Q sharesto a maximum of Q+s shares and the issuer's objective is to maximize the expectedproceeds per offered share.8 For convenience, but without loss of generality (aswe illustrate in footnote 9), we model the option to adjust issue size as the optionto increase issue size from Q to Q + s?h,where 0 < s?h< s. Hence, s?h s a choicevariable that determines the optimal offer size in state h.

Establishing that the option to adjust offer size has no added value in a fixedprice offering is straightforward. Exercising this option during the selling process,for example, by increasing the offer size from Q to Q + s shares, is identical tochoosing the larger offering in the first place. The optimal offer price when sellingQ + s shares would still be the cascade price and the added shares would sell ifenough investors are there.

By contrast, we show below that an option to increase issue size attached toan issue done with bookbuilding can actually increase the average offer price. Infact, we suggest an optimal strategy for exercising this option and show that iteffectively allows the sale of the additional shares at no discount. This strategyunderlies our proposition that information acquired during a new equity issue canbe used by the issuing firm to raise additional capital more cheaply.

The intuition behind this result follows from the observation that the under?pricing required to ensure the success of the bookbuilding effort is determined bythe value of private information, \/(H + 2) from (5), and the allocation expectedby an investor who reveals weak interest. While the first factor is exogenous, acareful choice of when to increase issue size can ensure that the second factoris unchanged. In particular, if the underwriter exercises the option only to fulfillunfulfilled demand of investors with good information, the required level of to?tal underpricing need not be changed, i.e., the extra shares can be sold withoutincreasing the expected dollar value of underpricing.To mathematically develop this intuition, we state below the underwriter'smaximization problem (in which issue size is a control variable and the objectiveis to maximize the expected offer price),

H(10') maximize Vtt, {0h - {6h -P?h)} ,{^umvh^ h=0subject to constraints (8) and (9), and(110 0 < qUh < 1, h = 0,...,H-l,

0 < qu,h< 1, h=l,...,H,hqiJM+ (H-K)quh = Q + s?h, h = 0,...,H,0 < s?h < s, h = 0,...,H.

8Webelieve thatthis objectiveis realistic. A counterexamplewill illustratewhy. Assume thatan issuing firm canget $50 million forone-thirdof its total threemillion sharesoutstanding i.e., $50pershare). If the firm'sobjectivewereto maximizetotalproceedsfromthe issue, selling the entire 3million sharesfor$51 million (ormerely$17 pershare)would be a dominant elling strategy.



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396 Journal of Financial and Quantitative AnalysisTheorem 5 describes the solution to this problem, including the optimal ex?ercise strategy ofthe option to adjust offer size.

Theorem 5. The maximum expected proceeds are achieved if the following con?ditions are met:1. optimal exercise strategy of the option to increase issue size:

s?h= 0 when h < Q,s?h= min(h ? Q, s) when h>Q;

2. optimal price/allocation schedule:when h Q, set qUJh= (Q + s?h)/h, qUh - 0, and P? = 0h- vh where vhis given by

h=Q x v 7/ h=0 x 7Proof See the Appendix.

The optimal pricing/allocation strategy is identical to that derived in Theorem2 and the underlying intuition is the same. As to the option to increase issue size, thegoal behind the exercise strategy described in Theorem 5 is to allow the underwriterto increase issue size without increasing the allocations to investors indicating L.This goal is achieved by setting s?h> 0 only in states of high demand (i.e., whenh > Q) in which all of the additional shares can be allocated to investors whorevealed strong interest.

Increasing issue size while keeping the allocation to investors with weakinterest unchanged improves the outcome of the IPO to the issuing firm. Aswe argued earlier, the optimal exercise strategy we identify for the option keepsunchanged the expected profit from misrepresenting signals in the pre-market and,hence, the total underpricing required for truth-telling (constraint (8)). On the otherhand, the issue size is increased in states of high demand when underpricing occursand, as a result, less underpricing per share is needed.9 In fact, the additional sharessold will generate full value and, hence, will not be underpriced on the margin.We formalize this result in Theorem 6.Theorem 6. Average underpricing per share of an issue sold off a book is reducedin the presence of an option to adjust issue size. The added proceeds in each statethe issue size is increased (h > Q) are 0hS?h,he full value ofthe additional sharessold.Proof See the Appendix.

Our analysis of the option to adjust issue size during the pre-market canpossibly extend to the over-allotment option that is offered on virtually every IPOthat is done under a firm commitment contract in the U.S. To the extent thatthe pre-offer indications of interest are not binding and, hence, some uncertainty

9If we interpretedQ as the expectedissue size andallowed the actual size to varyfromQ ? s toQ+ s, then the same result(of increasing heaverageofferprice)can be achievedby choosingan offersize below Q when demand s weak and aboveQto fulfillunfulfilleddemand.



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Benveniste and Busaba 397about market demand persists beyond the pre-market, the underwriter (working onbehalf of the issuing firm) can benefit from an option to adjust the offer size in theafter-market. The over-allotment option permits the underwriter to short sell anadded number of shares (typically 15% of the issue) at the offer price and cover theposition with additional shares issued. Our analysis suggests that such an optionhas value to an issuing firm only if a mechanism is used in which informationis acquired in conjunction with setting the offer price, such as the bookbuildingmechanism.10 If the exercise strategy we outline in Theorem 5 is used with theover-allotment option, average underpricing per share will be reduced.The optimal exercise strategy we identify is consistent with the empiricalregularity that the over-allotment option is exercised more often when indicationsof interest are strong. Hanley (1993) studies the frequency of use of the optionfrom 1985 to 1987 and finds that "85% of the issues with offer prices above theoffer price range exercise the over-allotment option, compared to 68% and 54% forissues with offer prices within and below the offer range, respectively" (p. 243).In her study, the position of the offer price relative to the offer range is a directmeasure of the level of investor demand.

Benveniste and Spindt (1989) originally hinted that the over-allotment optioncan potentially reduce underpricing by giving the underwriter more flexibility inthe allocation of shares. Our results are much stronger, however. We show that theadditional shares can be sold at full value, suggesting (contrary to Hansen, Fuller,and Janjigian (1987) who view the over-allotment option as a floatation cost) thatthe option can provide firms with a very inexpensive source of additional capital.This feature is particularly valuable in light of the fact that between one-third andone-fourth of firms going public come back to market for new financing withinthree years of their IPO (Michaely and Shaw (1994)).We turn next to the comparison ofthe two competing marketing mechanisms.Section VI contains a discussion of how our results reflect on both the choice ofindividual issuing firms and the debate regarding the optimal method of placement.

VI. Bookbuilding vs. Fixed PriceOur analysis illustrates that the issuing firm has some control over the resultsof its initial public offering through its choice ofthe marketing method used to placethe offering. Bookbuilding generates higher expected proceeds and exclusively

provides an opportunity to sell additional shares at full value but, in the process,exposes the issuer to greater risk. In comparison, fixed price offerings priced atthe cascade price guarantee the issuer certain proceeds.The certainty ofthe proceeds ofa fixed price offering sold at the cascade priceis an advantage of the fixed price method that seems to have been overlooked inlight of the literature's overwhelming focus on the level of proceeds. We argue

10Thereferee suggested that, because the issuer has the option to adjustissue size duringthepre-market, he formallystatedover-allotmentoptionthat can be exercisedin the after-marketmayhave other roles. Onerole that comes to mind stems from the possibleassociationbetweenthe over-allotmentoption and underwriters'price stabilization n the after-marketBenveniste,Busaba, andWilhelm(1996) and Schultzand Zaman(1994)). Such a possiblerole, however,does not reducetheoption'svalueidentified n Theorem6.



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398 Journal of Financial and Quantitative Analysisbelow that this feature may be attractive for risk-averse issuers who are uncertainabout the market valuation of their issues.

A. The Effect of Risk AversionIt is straightforward to extend our analysis to apply to a risk-averse issuerwhose objective is to maximize expected utility from proceeds. The optimal pric?

ing strategies for both fixed price and bookbuilding are invariant to this extension.The cascade price generates certain proceeds and, hence, is consistent with maxi?mizing expected utility from proceeds. And the optimal price/allocation schedulewe identified in Theorem 2 for the bookbuilding method first-order stochasticallydominates any other state-contingent pricing scheme. This is because the optimalpricing schedule maximizes the offer price state by state.

Although risk aversion on the part of the issuer has no bearing on the resultsof the marketing methods, it may affect the issuing firms' preference of the twomethods. For some concave utility function, the expected utility from the surecascades proceeds may exceed the certainty equivalence of the state-contingentproceeds of bookbuilding. Since neither strategy dominates?in the sense thatbookbuilding generates higher proceeds but exposes the issuer to higher risk?theissuer's preference should be governed by the risk of its issue and the level of itsrisk tolerance. In this regard, we state the following:1. firms with more price uncertainty are more likely to prefer a fixed priceoffering,2. firms with greater concern for risk are also more likely to prefer a fixedprice offering, and3. firms with greater future capital needs (who benefit from the over-allotmentoption) are more likely to prefer bookbuilding.

Predictions 2 and 3 follow from Theorems 4 and 6, respectively. Prediction1 is less evident. Expected underpricing in both marketing methods is directlyproportional to (Vu ? VL). However, increases in (Vu ? VL) raise the uncertaintyonly in bookbuilding proceeds, increasing the likelihood that the sure cascade priceexceeds the certainty equivalence of the bookbuilding state-contingent price.As to the international debate regarding the best way to price and place anIPO, our results show that both the fixed price and bookbuilding methods can beoptimal and, hence, challenge any policy that restricts the underwriting process toone method or the other. Many countries, especially former British colonies, stilloperate under variants ofthe British company law and require that IPOs be placedin a manner that eliminates the potential for bookbuilding. Such restrictions createinefficiencies and handicap firms that might prefer this marketing approach.B. The Effect of Issue Size and Marketing Costs

It should be noted here that the above predictions hold for otherwise identicalissues and issuers. There are other, possibly dominant factors that determine thechoice of marketing method. One obvious factor is cost. As the role of the under?writers in bookbuilding is rather involved, including identifying potential investorsand conducting road shows, the cost ofthe process might be prohibitive for smaller



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Benveniste and Busaba 399issues. Thus, small issues are likely to be placed by the fixed price mechanismsimply to avoid the fixed cost of bookbuilding. Ritter (1987) documents consistentsize difference between best-efforts and firm commitment offerings.

Loughran, Ritter, and Rydqvist (1994) suggest yet another reason for whysmaller issues are more often underwritten by best-effort contracts. They state that,for liquidity purposes, such issues are typically placed with individual investors(rather than institutional investors), who are unlikely to possess information rele?vant for valuation. As a result, bookbuilding is not justified in these cases.

VII. Summary and ConclusionThis paper analyzes and compares the results of two commonly used meth?

ods for marketing IPOs, the fixed price offer and American bookbuilding, in anequity market where investors' information is correlated and investors can havevarying degrees of market power. The paper builds upon the formalization of thebookbuilding approach in Benveniste and Spindt (1989) and the modeling of thefixed price approach in Welch (1992). The analysis shows that both methods canbe optimal, depending on the characteristics ofthe issuing firms, and suggests thatregulation restricting the underwriting process to one method or the other may becausing inefficiencies in new equity markets.The debate in the international forum regarding the best method to sell IPOsis complicated, however, by the policy question as to whose welfare should beparamount in determining the method of placement. For example, many IPOs donein Great Britain over the past 15 years have been privatizations of nationally ownedfirms. Government policy there has established that citizens should benefit directlyfrom the privatization by giving them priority in the allocation of issues and, inmany cases, at promotional prices. To the extent that such equity considerationsare important in the pricing and allocation decisions, our results may be of second-order relevance.

AppendixProof of Fact 3:The proof builds on Lemma 3 of Welch (1992) which, using our notation,derives the probability of observing h U signals in H signals given the observationof i U signals in another sample (from the same distribution) of m signals,

CH x Cm ( m + 1 \prob(fct/sintf|;t/sinm) = -^-^ ^___ j ,

where C" denotes the combinations of H outcomes, h by h, and is given byC? =h h\(H-h)V

In our case, i = m= 1, and the investor will be calculating the probability that theremaining H ? 1 investors hold h U signals,

CH~X x C1 / 2 \n'h =prob(A;//-l|l;l)= * ^ ' ^?j , h = 0,...,H-l,



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400 Journal of Financial and Quantitative Analysiswhich, upon simplification, yields the result in Fact 3. The conditional probabilitieswhen / = 0 are similarly derived,

tt? = prob(A;ff-l|0;l) = C? ^ C? (jff[) > h = 0,...,H-l.CHProof of Theorem 2:From the definitions of irh> and ir^,

Kh+\ = H -7rfh and nh = H h = 0,...,H-l.2(h+l) n " 2(H-h)Using these identities, and noting that qu,o = qun = 0, we can rewrite the term

HY, *? { [hqu,h + (H- h)qL,h] (0h - P?h)} ,h=0

which appears in the objective function, as

(A-l)H-\h=0 ^ (oh+x

- K+l) qvMi + Y^h~ *$ qL'hThe incentive compatibility constraint (8) will hold with equality at the optimumsince the underwriter does not have to underprice by more than necessary. Using(8) to substitute for the first term within brackets in (A-l), we can write (A-l) as

which simplifies toH-

(A-2)h=0

12 \H + 2 (Oh-n) qL,h-

To maximize expected proceeds (the objective function), the underwriter hasto minimize (A-2), which represents (the issuer's expected loss to cheaters or)expected underpricing. The underwriter should minimize qL^ and should setP?h= Ohwhenever q^h > 0. The price/allocation schedule detailed in the theoremachieves this goal.Substituting these results into (A-2) gives the minimum total expected under?pricing,

knowing that the second term under the summation in (A-2) will always be identicalto zero. Noting that underpricing occurs only in states h = Q,...,H, and denotingunderpricing per share by uh = 0h? P?h,we can write



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Benveniste and Busaba 401

h / 1 \ e-

Dividing through by Q, we obtain the expression for expected underpricing pershare, E(uh), stated in the theorem.Substituting constraint (11) in the objective function (10) and dividing through

by Q give the following expression for expected proceeds per share,H H

E(P?) = ]T7r^-]T^(^-P?).h=Q h=0Using the proceeds-maximizing price/allocation schedule from above and notingthat X^=o Kh6h = % we obtain the expression for the maximum expected proceedsper share in the theorem.Proof of Theorem 3:In the V space, the gain from cheating is (Vu - VL)[\/(H + 2)], and un?derpricing per share is (Vu ? VL)uh. Underpricing as a ratio of the offer priceis

uh (Vu - VL)uhpo VL + (Vl,-VL)PJ, ^"" *

Increasing Vu by S and decreasing VLby 6, i.e., applying a mean-preserving spreadto the prior distribution of V, makes relative underpricing equal to?* (Vu-VL)uh + 28uhP?h VL + (VU -VL)P?h + 8{2P?h-\y

U"'" *

Differentiating with respect to 8 givesn (Uh\ 2uhVL + (Vu-VL)uh

n) [VL + (Vu - VL)P?h+ 6 (2P?h - 1)]The numerator ofDs(uh/P?h) is positive. Hence, Ds(uh/P?h) > 0.Proof of Theorem 4:Part 1. We start with the H = Q case, in which pre-marketing underpricing isthe highest, and then use Corollary 1 to generalize. IfH=Q, underpricing occursonly in one state, when h = H = Q. Substituting H = Q in (A-4) and dividingby Q give the expected underpricing per share l/(2(H + 2)), which will be equalto cascade underpricing, % when H = 1, but will be smaller when H > 1. Inlight of Corollary 1, this result carries over to the H > Q case and, hence, we cangeneralize.Part 2. The proof of this part of the theorem is trivial once we note that thecascade proceeds are certain, while pre-marketing proceeds are state contingent.



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402 Journal of Financial and Quantitative AnalysisProof of Theorem 5:The proof of the theorem builds on the proof of Theorem 2. The level ofunderpricing is determined by the incentive compatibility constraint (8),

H-l H-lE^t^i K+i] iv,h+\ > X>;h=0 h=0

Oh-PU- 1H + 2 qL,h>

which, using (11') to substitute for qLthand the fact that tt^+i = (H/(2(h + l)))7r^to substitute for Tr'hn the LHS, can be written as

(A-5) 2\H

' h=lH-lh=0 8h~Pl

+ 1H + 2(Q + S0h)-hqu,h

H-h

Maximizing (10') is equivalent to minimizing Ylh=o ^hWh - P?h\>which ap-pears on the LHS of (A-5). Minimizing this expression requires minimizingthe RHS of (A-5), satisfying the condition with equality and, at the same time,maximizing qu,h- Minimizing the RHS of (A-5) can be achieved by settingQ + s?h- hqv,h = 0 when possible (i.e., by setting qUih = (Q + S?h)/h when h>Q)and by setting P?h = 0h and minimizing Q + s?h- hqUth (by setting s?h= 0 andqu,h = 1) when h < Q.The allocation strategy outlined above grants priority to investors with Usignals and, hence, is consistent with maximizing qUth. In fact, qu,h is set to themaximum of one share when h < Q. When h> Q, qu,h can be increased furtherby setting s?h- min[(h ? Q), s] > 0. This will both maximize qu^ from Q/h to(Q+S?h)/h and insure that Q+s?h - hqUfh = 0, in the states h=Q,...,H. (Note that,because the maximum possible allocation to an investor is one share, choosing s?hsuch that s > s?h > h ? Q will not increase qUth and, hence, will only increaseQ + s?h hqUfh and the RHS of (A-5).)To solve for the minimized level of underpricing, we denote [Oh ? P?h]byvh, substitute the solution outlined above in (A-5), and satisfy the condition withequality. This gives the following,

(A-6, ?m{Q*so - ?(^)f>;(?^),h=Q x v ;/ h=0 x 7which appears in the theorem.Proof of Theorem 6:

Expression (A-6) can conveniently be written as

h=n h=n x v 7/ h=o xh=Q h=QQ-hH-h

where v'his the new level of underpricing per share for the original offer sharesand v'l is the underpricing per share for the additional shares, assuming for the



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Benveniste and Busaba 403moment that these two sets of shares can be underpriced differently. Because theRHSs of (A-4) and (A-6) are identical, the LHSs should be equal. Therefore,1. if (as it should be) v'h = vjf = vh V h, then it should be that averageunderpricing per share in the presence of the option to adjust issue size, v, is lessthan that without the option, u (to show this, we let uh = u and vh = v V h, such that(A-4) and (A-6) hold; then, QYHqW + E^hSp = G?f=e*W showingclearly that v should be less than u);2. if the underwriter sets v'h= uh V h, then it should be that v^ = 0V/i (thismeans that the additional shares are selling for Ohat the margin, with total addedproceeds ofs?h6h in each state).

ReferencesBack,K., andJ.Zender."Auctions f Divisible Goods: On the Rationale or theTreasuryExperiment."Reviewof FinancialStudies,6 (1993), 733-764.Beatty, R., and J. Ritter. "InvestmentBanking,Reputation,and the Underpricingof InitialPublicOfferings."Journalof FinancialEconomics,15 (1986), 213-232.Benveniste,L., andW. Busaba. "PriceDiscoveryandthe OptionValuein Going Public."WorkingPaper,Boston College (1995).Benveniste, L.; W. Busaba;andW. Wilhelm. "PriceStabilizationas a BondingMechanism n NewEquityIssues." Journalof FinancialEconomics,42 (1996), 223-255.Benveniste, L., andP Spindt."How InvestmentBankersDetermine he Offer Priceand Allocation ofNew Issues."Journalof FinancialEconomics,24 (1989), 343-361.Benveniste,L., andW.Wilhelm. "AComparativeAnalysisof IPO ProceedsunderAlternativeRegu?latory Regimes."Journalof FinancialEconomics,28 (1990), 173-207.Chalk,A., andJ.Peavy. "InitialPublicOfferings:DailyReturns,OfferingTypes,andthe PriceEffect."FinancialAnalystsJournal,43 (1987), 65 -69.Chowdhry,B., and A. Sherman. "International ifferences in OversubscriptionndUnderpricing fIPOs."Journalof CorporateFinance,2 (1996), 359-381.Hanley,K. W. "TheUnderpricing f InitialPublicOfferingsand hePartialAdjustmentPhenomenon."Journalof FinancialEconomics,34 (1993), 231-250.Hansen, R.; B. Fuller;and V.Janjigian."TheOver-allotmentOptionandEquityFinancingFloatationCosts: An EmpiricalInvestigation."FinancialManagement,16 (1987), 24-32.Koh,F., and T.Walter."A DirectTest of Rock'sModelofthe Pricingof UnseasonedIssues." Journalof FinancialEconomics,23 (1989), 252-272.Loughran,X; J. Ritter;andK. Rydqvist. "InitialPublicOfferings:Internationalnsights."Pacific-BasinFinanceJournal,2 (1994), 165-199.Michaely,R., and W. Shaw. "ThePricingof Initial PublicOfferings:Testsof Adverse-SelectionandSignalingTheories."Reviewof FinancialStudies,1 (1994), 279-319.Ritter,J. "The Costs of GoingPublic."Journalof FinancialEconomics,19 (1987), 269-281.Rock,K. "WhyNew Issues areUnderpriced"Journalof FinancialEconomics,15 (1986), 187- 212.Schultz, P., and M. Zaman. "Aftermarket upportand Underpricingof Initial Public Offerings."Journalof FinancialEconomics,35 (1994), 199-220.Spatt,C, and S. Srivastava."PreplayCommunication,ParticipationRestrictions,andEfficiencyinInitialPublicOfferings."Reviewof FinancialStudies,A(1991), 709-726.Wang,J., and J. Zender."AuctioningDivisible Goods."WorkingPaper,Univ. of Utah(1996).Welch,I. "SequentialSales,Learning,and Cascades."Journalof Finance,Al (1992), 695-733.

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