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The Society for Financial Studies

IPO Market TimingAuthor(s): Aydoan AltiSource: The Review of Financial Studies, Vol. 18, No. 3 (Autumn, 2005), pp. 1105-1138Published by: Oxford University Press. Sponsor: The Society for Financial Studies.

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IPO MarketTimingAydoganAltlUniversity of Texas at AustinI develop a model of information spillovers in initial public offerings (IPOs). Theoutcomes of pioneers' IPOs reflect participating investors' private information oncommon valuation factors. This makes the pricingof subsequent ssuesrelativelyeasierand attracts more firms to the IPO market. I show that IPO market timing by thefollowers emergesas an equilibriumclustering pattern.High offer pricerealizations forpioneers'IPOs better reflect investors'privateinformation and triggera largernumberof subsequentIPOsthan low offer pricerealizationsdo. This asymmetry n the spillovereffect is more pronounced earlyon in a hot market.The model providesan explanationfor recentempiricalfindings that illustrate the high sensitivityof going public decisionto IPO market conditions.

Clustering of initial public offerings (IPOs) is a well-documented phe-nomenon. Starting with Ibbotson and Jaffe (1975), several studies haveshown that IPOs tend to cluster both in time and in industries.1 Whatcauses these hot and cold market cycles is less clear, however. While theIPO clustering could potentially be due to clustering of real investmentopportunities, empirical findings suggest that this link is weak. Most IPOfirms do not have urgent funding needs [Pagano, Panetta, and Zingales(1998)]; instead, firms' equity-issue decisions seem to be driven mainlyby market timing attempts [Baker and Wurgler (2002)]. Furthermore,hot versus cold market IPO firms do not appear to differ in theirgrowth prospects or future operating performance [Helwege and Liang(2002)].Recent empirical researchhas focused on information spillovers as themain driver of the hot market phenomenon. The idea is that informationgenerated in valuing a set of pioneers makes the valuation of followerseasier and hence triggers more IPOs. The evidence for the spillovereffect is strong. Lowry and Schwert (2002) and Benveniste, Ljungqvist,Wilhelm, and Yu (2003) find that IPO volume is highly sensitive to theoutcomes of recent and contemporaneous offerings. Specifically, if theA previousversionof this articlewas circulatedunder the title"ClusteringPatterns n Initial PublicOfferings,"which is also the second chapterof my dissertationat CarnegieMellon University.I would like to thank RickGreen for valuable discussions that have initiated this research. I am also grateful to Andres Almazan,ThomasChemmanur,Gian LucaClementi,BurtonHollifield,EricHughson,VojislavMaksimovic,ChristineParlour, Pegaret Pichler, Uday Rajan, Bryan Routledge, SheridanTitman, Jaime Zender, an anonymousreferee,and seminarparticipantsat several universities or their helpfulcomments. All remainingerrorsaremine. Address correspondenceto Aydogin Alti, Department of Finance, University of Texas at Austin,Austin, Texas 78712, or e-mail:[email protected].

1 For example, see Ritter (1984) and Ibbotson, Sindelar, and Ritter (1988, 1994).? The Author 2005. Publishedby OxfordUniversityPress. All rightsreserved.For Permissions,pleaseemail:[email protected]:10.1093/rfs/hhi022 Advance AccesspublicationMay 25, 2005


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offer prices of IPOs in a given month exceed initial expectations, the IPOvolume in the subsequent months increasesdramatically.2If, on the otherhand, the offer prices turn out to be lower than expected, the IPO marketdries out. In short, firms attempt to time the IPO market. The properinterpretation of these findings is difficult, however, as the theoreticaldynamics of information spillovers remains largely unexplored. Ourunderstanding of how information is incorporated into offer pricesmainly comes from book-building models where the pricing of a singleIPO is analyzed in isolation [Benvenisteand Spindt (1989) and Benvenisteand Wilhelm (1990)]. Little is known about how the IPO price formationprocess is likely to take place when the outcome of this process is antici-pated to have a spillover effect and trigger further IPOs.This article develops a model of IPO clustering that highlights theendogeneity of information spillovers. I consider an environment whereinvestors who participate in IPOs are asymmetrically informed about avaluation factor that applies to a number of firms. Since offer pricesare setbased on investors' indications of interest, the outcome of an IPO reflectsinformation that was previously private.This reduces the valuation uncer-tainty for subsequent issuers and induces further IPOs. The main result ofthe analysis is that IPO market timing obtains as an equilibriumoutcome.High offer price realizations facilitate a stronger spillover effect andtriggermore subsequentIPOs than low pricerealizations do. The intuitionfor this result is quite simple but novel. A high offer price realizationnecessarily reveals some good news on fundamentals, as no rationalinvestor would willingly overpay. But a low price realization may ariseeither when there is bad news or when informed investors with good newsdo not indicate interest in the offering. The model illustrates one reasonfor such lack of participation by the informed-an investor may shy awayfrom bidding aggressively in the early IPOs in order to retain his informa-tional advantage for subsequent offerings. More generally, informedinvestors may fail to participate in an IPO for other, exogenous reasonsas well, such as the timely availability of cash resources. Due to theuncertainty about the presence of informed bidding, the degree of infor-mational asymmetryremainsrelatively high following a low price realiza-tion. Thus fewer firms, those with more urgent capital needs, chose to gopublic upon observing low price outcomes. High prices reveal moreprivate information, and thus reduce informational asymmetry to agreater extent, triggering a larger number of IPOs. The result that IPOmarket valuations, rather than their immediate financing needs, drivefirms' decisions to go public is in line with the empiricalevidence.

Initial expectations are measured by the price range that is indicated in the IPO prospectus at the time offiling. Measures of subsequent months' IPO volume are the numbers of initial filings, completed offer-ings, and withdrawn offerings.

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The model setup captures conditions at the beginning of a potential hotmarket. A set of private firms consider going public. These firms do nothave investment opportunities that require immediate funding, but theyexpect to discover profitable projects with positive probability in thefuture. Firms lack funds to finance these potential projects, and theonly source of external financing is issuing equity. New issues are soldto institutional investors, who are asymmetrically informed about avaluation factor that is common across firms. Therefore, informed inves-tors earn information rents in the IPOs in which they participate, and thisconstitutes a cost to the issuers. Each firm weighs this cost of issuingequity against its need for external financing and chooses when to gopublic, if at all.First, a set of pioneers go public. This set, determinedendogenously inequilibrium, consists of those firms with the highest project discoveryprobabilities.Observingthe outcome of pioneers' IPOs reducesthe degreeof informational asymmetry among investors, since the offer prices arefunctions of investors' bids, which, in turn, are functions of their informa-tion. Subsequentto the pioneers'IPOs, remainingprivatefirms (followers)choose whether to go public immediately or wait until they discover pro-jects. Waitinghas an option-likevalue because a projectmay not necessarilybe discoveredin the future,in which case issuing equity, which is costly, canbe avoided. The value of going publicimmediatelystems from the tempora-rily reduced informational asymmetry. Since market conditions changeover time, the asymmetry of information among investors is likely to berelatively high in the future, suggestinga high futureissue cost. Facing thistrade-off,those followers with relativelyhigh project discovery probabilitiesdecide to go public immediately in order to take advantage of reducedinformation rents. Even firms with small chances of discovering projectsmay decide to go public within this cluster if the outcome of the pioneers'IPOs sufficientlyreduces the informational asymmetry.If one assumes an exogenous spillover effect, that is, that the outcomeof the pioneers' IPOs reveals all private information, then all followers gopublic subsequently regardlessof whether the pioneers get a high or a lowoffer price. This is because of the fact that investors cannot earn any rentsonce information becomes symmetric; therefore, a follower's cost ofgoing public becomes zero. However, the spillover effect is not, in fact,exogenous. It obtains endogenously, since informed investors anticipatethe subsequent clustering of IPOs and act strategically in the pioneers'offerings. Specifically, an investor with good news has an incentive toconceal his information early on to keep it private and use it profitablyonce some of the followers decide to go public. The investor can accom-plish this by bidding low and hence effectively staying out in the pioneers'IPOs. Clustering requires,however, that some of the private informationof investors is incorporated into the pioneers' offer prices. If an informed

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investor were to always bid low regardless of his signal, the offer pricewould not reflect any private information. But in the absence of anyinformation spillover, the followers would have no incentive to go public;thus, there would be no clustering, which is the very reason for theinformed investors to conceal their information.The tension between the tendency of informed investors to concealinformation on the one hand and the necessity of information spil-lovers for a clustering to take place on the other determines theequilibrium outcome. In equilibrium, an investor with good news isindifferent between bidding aggressively in the pioneers' IPOs (bidhigh) and concealing his information (bid low) and does both withpositive probability. This creates an asymmetry in the informationcontent of the offer price realization. A high price reveals goodnews; a low price, however, may obtain either when informed inves-tors have bad news or when they are concealing good news. The mainresult of the article follows from this asymmetry. The high offer pricerealization triggers more new IPOs than the low price realizationdoes, as the high price is more informative and therefore reduces theinformational asymmetry to a greater extent.After illustratingthe main idea in a two-period setup, I extend the modelto incorporate multiple periods. The dynamic analysis shows that thesensitivityof IPOvolume to market conditions is veryhigh at the beginningof the hot market. As the hot market progresses, this sensitivity declines.The model also provides implications about issuers' investment and cashholding policies. Firm quality in terms of investmentopportunitiesdeterio-rates in time. The late followers in a hot market are firms with little growthpotential;thus these firms end up sittingon the cash they raise for extendedperiods of time. The declinein qualityis more pronouncedwhen firms havebetter investmentopportunitieson average.In this case, the pioneersare ofvery high and the late followers are of very low quality. The likelihood ofholding onto IPO proceedsis especially high for those firmswhose IPOs aretriggered by high valuation outcomes.While the main focus of this article s the IPO market,the analysisappliesto otherforms of corporatefinancingactivityas well.For example,the modelcan easily be reinterpretedas a descriptionof the mergersand acquisitions(M&A) market: ssuersin the model are similarto mergertargets,informedinvestors to bidding firms, and projectsto merger synergies.The resultingpredictionsare in linewiththeempiricalevidenceon mergers.Similar o IPOs,mergerscluster in time and in industries[Mitchelland Mulherin(1996) andAndrade, Mitchell,and Stafford(2001)]; urthermore,mergerwavescoincidewith high market valuations [Rhodes-Kropf,Robinson, and Viswanathan(2003)].An implication of the model in this context is that late mergersin awave should create less synergisticvalue. Hot markets for seasoned equityor bond issues constitute otherpotential applicationsof the model. Whether

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ahot marketoccursowing o informationpillovers shypothesizednthisarticledependson theunderlyingnformational tructuren eachapplica-tion. The resultsare morelikelyto explainIPO hot marketsor waves ofmergerswhere argetsareprivate irms,as inbothcasesthecompletion f adeal revealsa substantialamount of private nformation.The spillovereffectmay be weaker or acquisitionsof publicly radedfirms,seasonedequity ssues,orbond ssues, ince hesecondarymarket outinely eneratesinformation boutthe firms nvolved n thesetransactions.To the best of my knowledge, his articlepresents he first model ofclusteringof IPOs in which the dynamicsof information pilloversandIPOmarket imingariseendogenously.A few otherarticleshaveanalyzeddifferentaspectsof IPOclusteringakingas givenanexogenousspillovereffect. Maksimovicand Pichler(2001)examinehow the decision to gopublic interactswith productmarketcompetition.In theirmodel, thepioneers' POs reveal nformation hat can inducefurtherentryinto theindustry.Therefore,pioneersface a trade-offbetweenobtainingpublicfinancingearlyandrevealing heirtechnology o potentialnewentrants.Unlike thecurrentarticle,however, heirmodel assumesexogenousreve-lation of information itherbythepioneers' POsorbysecondarymarkettradingbefore the followersmake theirdecisions.Similarly,Benveniste,Busaba,and Wilhelm 2002)presenta modelwherethe pioneer's POisassumed o revealnewsaboutindustry-widerowthopportunities.Theyfocus on how the follower free-rideson such news and the potentialcoordination oleof aninvestmentbank nminimizingheadverse ffectsof this free-rider roblem.Hoffmann-Burchardi2001)developsa similarmodelof free-riding ehaviorbut considers he case where heasymmetryof informationis between entrepreneurs nd investors.Her analysisrelatesthe likelihoodof clustering o the riskaversionof entrepreneurs.Finally, Subrahmanyamnd Titman(1999) explore he link between hedecisionto go publicand the informational fficiencyof publicequitymarkets.Theypointto thepositiveexternalityn informationproductionwhenthereis a largernumberof publicly radedfirms and suggestthatthisexternality an lead to a clusteringof IPOsin emerging conomies.This articlealso relatesto the literatureon IPO priceformationpro-cess. Startingwith Rock (1986)and Benvenisteand Spindt(1989),thislineof researchhasemphasizedhecostsof goingpublicthat arisewheninvestorspossessprivate nformation bout ssuers'value[BenvenistendWilhelm(1990),Maksimovicand Pichler(2002),Shermanand Titman(2002),and Biais,Bossaerts,and Rochet(2002)].Thesearticlesconsiderthepricingof a singleIPO in isolationandtypicallyanalyze hedesignofoptimal book-buildingmechanisms hat minimize informedinvestors'informationrents.In contrast,the objectiveof the currentarticle is todevelopa benchmark nalysisof information pillovershat arisewithinasequenceof IPOs.

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The trade-off an informed investor faces between being aggressiveversus concealing information has been discussed in the market micro-structure literature before, most notably by Foster and Viswanathan(1994, 1996). In these analyses, the informed agent trades in a singlesecurity through time and tends to reveal less information early on. Thecurrent article focuses on the equilibrium response of issuers to informedinvestors' strategies; hence the IPO cluster, i.e., the opportunity set ofinformed investors, evolves endogenously.The remainderof the articleis organizedas follows. Section 1presentsthemodel. Section 2 examines the benchmark case with no information spil-lovers. Section 3 characterizes the equilibriumwith information spilloversin the two-period setup. Section 4 extends the analysis to multiple periods.Section 5 discusses the empiricalimplications. Section 6 concludes.

1. The Model1.1 The firmsI assume universal risk neutrality and a risk-free rate of zero throughout.I consider a continuum of firms with a total measure of one (the distribu-tion of firms is explained in greater detail below). Firms live for twoperiods, year 1 and year 2. Each firmj has assets in place that generatea final net payoff of Xjat the end of year 2. This payoff is determined bythe realizations of year-1 and year-2 factors, thereforeXj= Xlj + X2j.Foreach year i E {1,2}, either Xij= o ("good news") or XiA 0 ("badnews"),where each outcome has equal probability. Suppressing the j subscript,I assume that X1is perfectlycorrelated across firms. Also, X2for any firmis independent of X1.3

In addition to their existing assets, firms have future investmentoppor-tunities. Specifically,firmj expects to discovera projectwith probability ojin year 2. The project, if discovered,costs I at the beginning of year 2 andpays F at the end of year 2. Therefore, if a firm with a project invests itstotal final payoff will be X + F; otherwise the payoff will be X.4 The firmsare indexed by their project discovery probabilities.The measure of firmswith discovery probabilityco or less is denoted by G(o)),coE [0,1].I assumethat the distribution G has no atoms; that is, G is continuous on [0,1].1.2 FinancingFirms have no cash in hand in either year 1 or year 2. The only way forthem to raise external funds is to go public and sell equity. Initially, each

3 The second year factor X2 may or may not be correlated across firms.4 The projects have positive NPV, i.e., F > I. Furthermore, it is assumed that the NPV is large enough sothat a firm always prefers the costly IPO to letting the project expire. The costs of the IPO, due toasymmetric information among investors, are characterized below.

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firm has one outstandingshare owned by an entrepreneur.f a firmdecides to go public, the entrepreneurells her share (i.e., the wholefirm) to outside investors through the equity issue game describedbelow. Out of the proceeds V, the entrepreneur epositsI within thefirmandconsumes he restof the proceedsV- 1.51.3 Investors nd nformationTwoclassesof investors,nformedanduninformed, articipate s buyersin IPOs.Thereare N > 1uninformednvestors. n addition, hereareMiinformed nvestorswho observe he realizationof Xiat the beginningofyeari. The numberof informednvestors s random n eachyear.Specifi-cally, Mi = k with probabilityp (1 p)k- 1,wherek E {1,2,...} andp < 1.6Notice thatp parameterizeshe degreeof competitionamonginformedinvestors.The expectednumberof informed nvestorsequals lip, whichis decreasingn p. For technicalreasonsdiscussedbelow,I assumethatp>1/8.An informed nvestordoes not know whetherhe is the only informedinvestor or if there are other ones. The uninformed nvestorsand theentrepreneurs ave access only to public information.7At the end ofyear i, the realizationof Xi becomespublicinformation.Hence,privateinformation s short-lived.To simplify he discussion, t is assumed hatyear-1investorsand year-2investorsare not the same. Within a year,however,the set of investorsremainthe same.Also, whethera specificinvestor is informed is not publiclyknown;otherwisethe asymmetricinformationconcernstriviallycould be avoidedby sellingIPO sharesonly to theuninformednvestors.

This structure of asymmetricinformation is similar to those inBenveniste and Wilhelm (1990) and Sherman and Titman (2002).The informedinvestorsin the model correspond o large institutions.The informationaladvantageof these investorsis likely to stem fromthe researchthey conduct on issuing firms,as well as their ability tobetter interpretand quantifythe informationthey learn duringroadshow presentations.The uninformedinvestorscan be thought of asretail investorsand small institutionswho have access only to publicinformation.5 In an earlier version of the article it was assumed that the entrepreneursells only a fraction of the firm toraise I, and the results were identical to those reported here.6 Conditional on k, the informed investors are drawn from a continuum that represents the pool ofpotentially informed investors.7 As in several therstudies hat focuson theasymmetryf informationmong nvestors, abstract romthe potentialasymmetry f informationbetween he betterinformed ssuersand the investors orsimplicity. ee Allen and Faulhaber1989),Grinblatt ndHwang 1989),andChemmanur1993)formodelswhere ssuersarebetter nformed han nvestors.

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1.4 Equity issue gameThe equity issue game is a second price auction. Each investor, whetherinformed or uninformed, bids a price for the issuing firm. The investorwith the highest bid wins and pays the second highest bid. In case of ties,that is, when J> 1 investors bid the highest price V, each of theseinvestors gets 1/J of the issue at the price V. After the auction, the sellingprice is announced, and the equity issue game ends.8'91.5 Timingof eventsThe timing of events within year 1 is as follows. First, informed inves-tor(s) learn X1. Afterwards, there are up to T periods in which firms cango public. Specifically, in the first period, those firms that decide to gopublic, if any, do so simultaneously by selling their shares in an aggre-gated second price auction. With probability /3,the second period follows,in which the remaining private firms again have the chance to go public.With probability 1 - /, year 1 ends and X1 is revealed. Similarly, giventhat period t < Tis concluded, period t + 1 follows with probability 3, oryear 1 ends with probability 1 - 3. If period T is reached, following thepotential IPOs in this period, year 1 ends and X1 is revealed.The timing of events in year 2 is similar, except that in year 2, onlythose firms that did not go public in year 1 and then have discoveredprojectsgo public. ? First, informed investor(s) learn X2.Then the issuingfirms hold their IPOs. For simplicity, I assume that there is no sequen-cing of IPOs in year 2. Finally, X2 is revealed and consumption takesplace.The hot market dynamics in year 1 are governed by the parameter pair(T, 3). Year 1 is characterizedby the uncertainty surrounding X1. Oncethis uncertainty is resolved, a new period with new uncertainties, year 2,starts. In this context, T can be interpreted as the upper bound on thelength of the time period in which the uncertainty about X1 dominatesfirms' valuations. This time period can turn out to be shorter and is morelikely to be so for smaller values of /. Thus, 3 captures the likelihood ofan extended period of IPO clustering. In order to illustrate the main idea,I first focus on the simplest case with T = 2 and 3 = 1in Sections 2 and 3.To gain further insights about hot-market dynamics, Section 4 thenextends the analysis to allow for T > 2 and 3 < 1.

8The results are robust to whether further information, such as the realized allocation, is announced.9 I do not model an active secondary market;investors hold shares for their final (i.e., end of year 2) payoff.Notice, however, that the model is consistent with the existence of a secondary market. Since all agentsare risk neutral, the no-trade theorem applies and there will not be any trading activity when thesecondary market opens.10In this model, the only reason to go public is to raise funds for investment. In year 2, those firms that didnot discover projects do not need financing, so they choose to remain private and avoid the costly equityissue.

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X2 s revealed,Informednvestor(s) Informednvestor(s) consumptionobserveX, X, is revealed observeX2 takesplace(Some) ollowers iscoverP-auction F-auction projects;ssueequityf needed

year1 year2Figure 1Timing of events

When T = 2, a firm may choose to be apioneer, that is, it may go publicin the first period of year 1. Alternatively, the firm may choose to be afollower, that is, it may wait until the pioneers' offering is concluded andthen make its decision. Given the outcome of the pioneers' offering, afollower may then choose to go public in the second period of year 1, orremain private until year 2. I refer to the first and the second offerings ofyear 1 as the P-auction and the F-auction, respectively.Figure 1 summarizes the timing of events. The beginning of year 1corresponds to the end of a previous cold market. One can imagine year1 as a period of increased commonality across firms' valuations, provid-ing the conditions for information spillovers and a new hot market.Year 2 represents the distant future. While a firm has no projects tofinance in year 1, such a project may be discovered with positive prob-ability in the future. Therefore year 2 is not necessarily the same calen-dar period for all firms; rather, it should be interpreted as a firm-specificand possibly random point in time at which the firm learns about itsinvestment opportunities.

2. The Benchmark Case: No InformationSpilloversAs a benchmark, I first characterize the decision to go public and theoutcome of the resulting IPO in the case where there is only one firm.Consider the bidding strategiesof investors in an IPO. Let VHbe the bidsubmitted by an informed investor who has received good news Xi = a,and let VL be the bid submitted by an informed investor who hasreceived bad news Xi= 0. The bid of an uninformed investor is denotedby Vu. For notational convenience, let C(co)=cF+ (1 - (o)I+ a/2.11

The number f periodswithinyear1is irrelevantn thissection, ince here s onlyonefirm n theIPOmarket ndhence hereareno informationpillovers crossperiods.

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Proposition 1. In the singlefirm case:(i) Whenafirm withprojectdiscovery robability ogoes public nyear1,

VH = C() + , VL = VU = C(). (1)(ii) Whena firm (having discovered a project) goes public in year 2,

VH=FX + a, VL Vu F +X1. (2)(iii) In both cases above, the informationalasymmetry amonginvestors

is resolvedafter the outcome of the IPO is announced.All proofs are in Appendix B unless they appear in the text. Parts (i)and (ii) of Proposition 1 describe the equilibriumbids of investors. Whenthe informed investor(s) have bad news, the realized auction price is VL,which is the full information value of the firm given bad news. Similarly,when there are at least two informed investors and the news is good, theauction price is VH,which is the value of the firm given good news. It iswhen there is only one informed investor with good news that asymmetricinformation imposes a cost to the issuer. Specifically, the informed inves-tor wins the whole issue at the price VL, but the value of the firmconditional on good news is VL+ a. Therefore, going public is costly;the ex ante expected rent earned by informed investors constitutes a costto the issuing firm.Notice that in the single firm case where there is no role for informationspillovers, an informed investor plays a revealingstrategy in equilibrium,in the sense that when he has good news, he bids high. Consequently,information becomes symmetric among investors once the outcome of theIPO is announced. The high price realization VH reveals good news.Given the low price realization VL,on the other hand, an uninformedinvestor can infer from his allocation what the news is. If he gets noshares, there must be one high bid, and hence the news is good; whereas ifhe gets a positive allocation, the informed bid(s) are low, and hence thenews is bad. Therefore, in the case of a single IPO with no informationspillovers, both the high and the low price realizations of an IPO resolvethe informational asymmetryamong investors. The implication is that if afollower were to exist, it would go public after a pioneer's IPO, regard-less of whether the pioneer gets a high or low price, as symmetricinformation would imply a zero issue cost. Of course, the equilibriumdescribed in Proposition 1 holds only for the case where there are nosuch followers. This result-that high versus low prices are equally infor-mative if no clustering is anticipated-provides a benchmark. The nextsection will demonstrate that when clustering is anticipated by informedinvestors, the resulting offer price realizations differ in their informationcontent.

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Consider he IPOtimingdecisionof the firm.Recall that as of year 1,the firm'syear-2projectdiscoveryprobabilitys ow< 1.Proposition 2. Withno information spillovers, a firm nevergoes public inyear 1. It goes public in year 2 only if it discovers a project.

Going public is costly becauseprivatelyinformed investors extractrentsin an IPO. A firmchooses the timingof its IPO to minimize hiscost. Waitinguntil year 2 has an option value, since if no projectisdiscovered, he firm will avoid the costly IPO in year2. Therefore, hefirmhas a strictpreferenceo wait and issuein year2 onlyif a project sdiscovered.Thisresultsets thebenchmarkorIPOtiming:whenthereareno information pillovers,here s no roomforIPOmarket iming;a firmgoes public only if it needs immediate inancing.12

3. Informationpilloverswith a CommonValuationFactorNow I turn to the case where firm values are driven by a commonfactor. Consider the benchmarkequilibriumdescribed n Proposition1. Suppose, for now, that equations in (1) describe the equilibriumstrategiesof investorsin the P-auctiongiven a set of pioneers goingpublic.Then, by part (iii) of Proposition1, investorsbecomesymme-trically nformedafter the P-auctionpriceis announced.Now considerthe subsequent PO decision of a follower.The cost of going publicinyear 1 is zero, as informationhas becomesymmetricamonginvestors,and hence the entrepreneurwill get the fair value for her firm. Incontrast,the cost of waitinguntil year 2 is positive,becausein year 2informed nvestorswill receivesignalsabout X2,and a new asymmetryof informationwill arise before a potential year-2 IPO. Comparingthe costs of the two alternatives, hen, the follower decidesto go publicin year 1 subsequent o the P-auction.This illustrateshow the informa-tion spilloverfrom the pioneers'IPOs can triggerthe IPOs of otherfirms.How does an informed nvestorbidin theP-auction n anticipationofthis spillovereffect?In particular,do the strategiesdescribed n Propo-sition 1 still constitute an equilibrium?Suppose that the measure ofpioneersis Zp.Therefore the measure of followers is 1-Zp. Considerthe optimalbiddingstrategyof an informed nvestor with good news,

12Thebenchmarkalueof the results n thissection houldbeemphasized.Clearlydifferent atternsmayemerge n anothermodel with no information pillovers.For example, he IPOoutcomemay onlyreduce,but not completelyeliminate, he informational symmetry, r a firm with no immediatefinancingneedsmay nevertheless hoose to go public if the degreeof asymmetricnformationstemporarilyow forexogenous easons.Theverysimplebenchmarkhe currentmodeldelivers s ratherintended o make the illustration f the informationpillover ffectsdevelopedn the next sectionastransparents possible.

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say investor 1, given that other investors bid as in (1). By biddingVH, investor 1 secures an expected profit of psaZpfrom the P-auction,where

PsPo P2 (3)kp(l _ p)k-k=l

is the probability that investor 1 is the only informed investor.'3 However,by bidding VH, investor 1 reveals his private information and cannotmake any profits in the F-auction. Suppose investor 1 deviates to VL.Now his P-auction profit is cut to (psazp)l(N + 1), because when he winswith a low bid he shares the issue with N uninformed investors. But bybidding VL,investor 1 conceals his information and makes uninformedinvestors believe that he has bad news (provided that there is no otherinformed investor to reveal the good news). If a follower goes publicsubsequently, uninformed investors will bid the expected value of thefirm given their belief that information has become symmetric,but inves-tor 1 knows that the true value of the firm exceeds this bid by a, theamount he has concealed. Therefore, investor 1 can obtain a profit of ctper follower in the F-auction by submitting an appropriate winning bid(recall that he will pay the second highest bid). Since the public alsobelieves that information has become symmetric, all the followers gopublic in the F-auction. Hence, the expected F-auction profit of investor1 when he conceals his information is psa(l - Zp).The total payoff fromdeviating is

psZP +PS(l - z,), (4)which exceeds psaZpwhen zp< (N + 1)/(2N + 1). It follows that witha relatively small group of firms choosing to be pioneers, investor 1would profitably deviate to bidding VL in the P-auction, and there-fore the strategy profile (1) would not be an equilibrium of theP-auction.The above discussion illustrates an important feature of the model:an informed investor with good news tends to conceal his informationearly on when he anticipates a wave of IPOs in the near future. In theanalysis below, we will see that such strategic use of private informa-tion is the main factor shaping the equilibrium. The subgame perfectequilibrium is analyzed in three parts. First, the equilibrium of theP-auction is obtained, given conjectures about the F-auction. Thesecond part characterizes the issue decisions of the followers given the

13Investor 1 calculates this probability conditional on the fact that he is informed.

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outcome of the P-auction.Finally,the equilibrium ets of pioneersandfollowersare determined.3.1 The P-auctionSupposethat the measureof pioneers s zp.Also, supposethat the mea-sureof followers hatdecide o go public n theF-auctionafterobservinga low pricerealization n the P-auction s zf.14 Considerthe followingconjectures bouttheequilibriumtrategies f investors n the P-auction.An informed nvestorwith bad news bids VL.An uninformednvestorbids VP>VLP.n informed nvestorwithgood newsplaysa mixedstrat-egy by bidding VPwith probabilityq and bidding VH>Vj with prob-ability 1 - q. Notice that under this conjecture,a good-news nformedinvestor tends to conceal his informationby imitating a bad-newsinformed nvestorwithpositiveprobability.At one extreme,whenq = 0,such mitationdoesnot takeplace;at the otherextreme, = 1,a good-newsinformed nvestoralways mitates. nthissection,I characterizeheequili-briumvaluesof q, VL,VP,and VH,given he investors' xpectations boutthesubsequentF-auction.

Consider VP first. Since uninformed nvestorsdo not observeanyprivatesignals about firm value, they compete away rents and makezeroexpectedprofitsin equilibrium.ThereforeVPis the persharepriceat which an uninformed nvestorbreakseven:

2(C(o)- VP)+ 2 (p( l -) )k qk(C(c) + - V) (5)If the news is bad, whichhappenswith probability1/2, informed nves-tor(s)bidlow. In thiscase,each uninformednvestorgets 1/Nof theissue;hencethe firstterm n (5).Notice that when the news is good [thesecondtermin (5)], the only time uninformed nvestorswin shares s whentheinformed nvestor(s)bid low, whichhappenswithprobabilityqkif therearek informed nvestors.Solvingfor the infinitesumin (5) and rearran-ginggives VP as a functionof q:

V(q) = q+C(w)(1-q+2pq ) (6)1 - q + 2pqLet usconjecturehat VP = C(co)+ x.Considerhe decisionproblem fan informednvestorwithgood news,say, investor1, giventhe strategiesof other nvestors.By biddingVH, nvestor1 securesanexpectedpayoffof

14 The analysis below will show that in equilibrium, all of the followers, that is, a measure of 1 - zp,will gopublic in the F-auction if the P-auction price realization is high. The high and the low prices of theP-auction will also be characterized below.

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reH(q) = ps(q)[C(wC) + a - V (q)]zp, (7)where

kp( p)k- lqk-Ps(q) k= P (8)Z~ p(1 -)k1 _ - p(8)k=l

is the conditional probabilitythat investor 1 wins the P-auction making apositive profit (which happens either when there is no other informedinvestor, or when there are other informed investors but they all bid low).The termin brackets n (7) is the perpioneerprofitobtainedin thesecases.15Notice that investor l's F-auction profit is zero when he bids Vj in theP-auction. This is because by bidding VH,investor 1 reveals to the unin-formed investors that he has good news, and therefore loses his informa-tional advantage. For example, if the P-auction price turns out to be VH,uninformedinvestors infer that there are at least two high bids. If, on theother hand, the price realization is Vu/(q),investor 1 wins the whole issue,and the uninformed nvestors,from their allocationof zero shares, nfer thatthe winner has good news. In either case, the uninformedinvestors learninvestor l's signal,and therefore n the subsequentF-auction investor 1 hasthe same public information as the uninformed. Thus, regardlessof themeasureof follower firms going public, investor 1 cannot make any profitsin the F-auction if he bids VH in the P-auction.Using (6), (7) simplifiesto

re,q) - (9)H(q) = (1 - q + pq)(1 - q + 2pq)Considernow the expected payoff of investor 1 when he bids VP in theP-auction.His P-auctionprofit s nowzero,sinceVL is lessthantheuninformedbid VP q). Butby concealinghisinformation,nvestor1can nowhopeto make

profits n the subsequentF-auction.Thisexpectedprofitis given byeL - PsaZf (10)

The detailsof the derivationof (10)aredelegatedto Lemma B.1 in AppendixB which characterizesheequilibriumof the F-auction,but the briefintuitionis as follows. By bidding V[, investor 1 conceals his private informationfrom other investors. The effect of this informationon firm value is a perfollower;therefore,the aggregateeffect, given that a measurezf of followers15 If there are other informed investors who also bid high, the profit of investor 1 is zero, since Vpequals thefirm value given good news.

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will go public in the F-auction, is zfa. Investor 1 will realize this amountas his profit by bidding high in the F-auction, and only in those states ofthe world where the second highest bid is less than his bid. This is the casewhen investor 1 is the only informed investor, which has a probability ofps as given by (3).ThepayofffrombiddingVHweaklyexceeds hepayofffrom V[ ifandonlyif

Y(q) = (1 - q +pq)(1 - q + 2pq) < Zp (11)ZfLet

_ 1 ifp 24(1-p)(2p-1) >3(12)

y ,min ( f ifp > 2(qE[0,1] if p >Also, let q*(zp,zf)denote the equilibrium value of q given zp and zf.Proposition 3 summarizes the analysis in this section.

Proposition 3 (The P-auction Equilibrium). Suppose that the measure ofpioneers is zp and the measure of followers that decide to go public afterobserving Vu is Zf:

(i) If Zp/zf > Y, informed investors with good news never concealtheir information,that is, q*(Zp,Zf) 0.(ii) If Y < Zp/Zf < Y, informed nvestors withgood news conceal theirinformationwithprobabilityq*(Zp,zf), whereq*(zp,zf) olves Y(q)=ZpIzf.(iii) If Zp/Zf < Y, informed investors with good news always concealtheir information,that is, q*(zp,zf)= 1.(iv) In all three cases above, uninformed nvestors bid VU(q*(zp,zf)).Informed investors with bad news bid some VL 2/3, there are two solutions in the (0, 1)interval. Therefore, there may be two equilibria of the P-auction given zpand Zf. However, this does notnecessarily imply multiple equilibria for the overall game, since zpand zf are in fact endogenous quantitiesto be determined as part of the equilibrium.

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or else the price Vu(q) is dictatedby the bids of the uninformed.The lowbid V represents he strategyto stay out of the auction, that is, an investorwho submits VLeneverexpectsto win. Consequently, he bid VLis indetermi-nate;all thatmatters is that VL < VP(q) to ensurestayingout of the auction.Given this, I refer to V s th hs he highprice andV(q) as the lowprice of theP-auctionin the rest of the discussion.

Proposition 3 illustrates a quite intuitive result. When the future IPOvolume Zfis expected to be small relative to the current volume Zp,aninformed investor does not tend to conceal his information; rather, hemakes aggressiveuse of it in the pioneers'IPO. But if a big wave of IPOs isexpected,an informed investoris betteroff savinghis information for futureuse. Byconcealingthegood news,an informed investorforgoes profitsin thepioneers' IPO, but in return prevents the leakage of his information andhence secures his informationally advantagedposition for the coming waveof IPOs. Notice the asymmetry in such strategic behavior. An informedinvestor with good news gains from saving his information for futureuse,but an informed investor with bad news does not. This is because of thenatural asymmetry built into one-sided auctions. By overbidding, aninformedinvestorwith bad news would lose money in the P-auction. More-over, such a move would only make the uninformed investors more aggres-sive in the F-auction, since they would mistakenlybelieve that the winninginvestor has good news.Therefore,overbidding n theearlyauction does notprovide an informational advantage to the informed investor that can beexploited in the future offerings when he has received bad news. The nextsectionwill show that this asymmetry n the incentivesof informedinvestorswho receive good versus bad news has important implications for theinformation content of the outcome of the pioneers'IPO.3.2 The IPO decisions of followersThis sectioncharacterizes he IPO decision of a follower,giventheoutcome ofthe P-auction. Suppose that in equilibrium,an informed investor with goodnews concealshis informationwithprobabilityq in the P-auction. Considerafollowerfirm with a projectdiscoveryprobabilityof o. If the follower choosesto waituntilyear2, withprobability1- co t willnot discovera projectand willnot need to go public.Withprobabilityco, t willdiscovera projectandwillgopublicin year2 to raisefinancing.The cost of thispotential year-2IPO is thesameasinthebenchmarkcase,whichispa /2 (seetheproofof Proposition2 inAppendixB).Theprobabilityof ayear-2IPO is o;hence,theyear-1expectedissue cost of the follower when it chooses to wait is

CWait POC (13)The follower compares this cost to the expected issue cost of going publicin the F-auction, that is, immediately after observing the outcome of the

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P-auction.Thereare two possibleoutcomes:eithertheP-auctionprice sthe high price VH, or it is the low price VPu(q).First considerthe highprice VH. This priceobtainsonly whenat least two informed nvestorsbid high. Thus the informationasymmetry s resolvedupon observingVH. Then theyear-1 ssue cost of thefollower s zero,since its shareswillget their fair price from the now symmetrically nformed investors.Consequently,upon observingVH,the followergoes public regardlessof o.Next,considerhelow priceVu/(q).Observinghispricerealization,hefollowernfers hat nformationmaystillbeasymmetricmongnvestors. orexample,t maybe the casethatthere s no highbid Vf, andtherefore heuninformednvestors annot ell whether here s badnewsor theinformedinvestor(s)avestrategicallyoncealedoodnews.17NowtheIPOdecision fthe followers not trivial;heexpectedssuecost of goingpublic nyear1ispositive.Thiscost isgivenby

Clssue(q)= pq

1+ E p(1_p)k (qk+ k(1-q)qk-)- k=l (14)pq( - q + pq)2 =C.(1 - q +pq)2 +p(l - (1 - p)q2)

Recall that only an informed nvestorwho has concealedgood newscanextract entsn theF-auction ndwilldosoonly f thereareno other nformedinvestors.Theterm nbracketsn (14)is theprobabilityf this eventcondi-tional on havingobserved he low P-auctionpriceVP(q).LemmaB.1 inAppendixB showsthat in this state of the world,the investorwho hasconcealedhis informationwinsthe F-auctionandextractsa rentof a perfollowergoing public.Therefore,we get the expectedssue cost (14)for afollower onditional nhavingobservedVu(q).In (14), Csue(O) = 0 and Clssue(1) = pa/2. Intuitively, if informedinvestors never conceal their information q = 0), the outcome of theP-auctionalwaysresolves heasymmetry f information, nd thefollowercan go public subsequently t zero cost. Therefore,f q = 0, all followerswill go public after the P-auction.At the other extreme,if informed

17 It is important to emphasize that the asymmetry in the information content of high versus low pricerealizations is not an artifact of employing second price auctions in the analysis. For example, in thebenchmark case where a single IPO is considered, both the high and the low price realizations resolve theinformational asymmetry between the informed and the uninformed investors. The low price becomesless informative than the high price only when the informed investors strategicallyconceal their informa-tion in anticipation of clustering. One can also show, at a cost of complicating the algebra, that the sameresults hold with first price auctions; that is, that the low price realization becomes less informative whena subsequent clustering of IPOs is anticipated.

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investors always conceal their information (q = 1), the outcome of the P-auction does not reveal any information at all. But with no informationspillovers from the P-auction, the issue decision of a follower is identicalto the decision in the benchmark case. From Proposition 2, a followerstrictly prefers to wait until year 2 rather than paying the high issue costof pa/2 in year 1. Hence, if q = 1, no follower goes public subsequent tothe P-auction. In the intermediate cases q E (0,1), a follower compares(13) to (14) to make its decision. Let

2q(1 - q + pq)2co =(q) _ (15)(1 - q +pq)2+p(l - (1 -p)q2)

denote the cutoff projectdiscovery probabilitycoat which (13)equals(14).18Firms with co> c*(q) decide to go public in year 1, as waitingis more costlythan issuing immediatelyfor thesefirms. Firmswith c < o*(q),on the otherhand, choose to wait, as they are less likely to discoverprojectsin the futureand consequentlytheirwaiting options are more valuable.3.3 EquilibriumLet qe, oe, zp, and zf denote the equilibrium quantities. First, notice thatqe = 0 is not an equilibrium outcome. At qe = 0, the issue cost in theP-auction is the same as in the benchmark case. Recall from Proposition 2that in this case, firmsprefer waiting to going public.Thereforezp = 0, thatis, all firms choose to be followers. Now, suppose that one firmdeviates anddecidesto be a pioneer. Sinceqe = 0, the publicbelieves that the outcome ofthe P-auction will resolve the asymmetry of information. Hence allfollowers will subsequentlygo public in the F-auction, that is, z~ = 1. Butthen, case (iii) of Proposition 3 applies: Zp/z = 0, which impliesq*(zp,z) = 1, contradicting the firms' belief that qe = 0. In other words,when informed investors are anticipated to reveal their information com-pletely in the P-auction, firms are better off waiting. But this createsincentives for investors to conceal their information should some firms gopublic in the P-auction, breakingthe sustainabilityof the belief qe = 0.

Similarly,qe = 1is not an equilibriumoutcome. At qe 1, the issue costin the P-auction is zero. Intuitively, if informed investors never reveal anyinformation, the uninformed do not face a winner's curse problem, andthus they are willing to pay the ex ante expected value of the firm. At zerocost, all firms decide to go public in the P-auction, that is, zp = 1 andz~ = 0. But then, part (i) of Proposition 3 applies: Zp/z = oo, whichimplies q*(zp,z) = 0, contradicting the firms' belief that qe 1. Inother words, when informed investors are anticipated to conceal theirinformation completely, the information rents become zero, inducing all

18Forp > 1/8, (15) is guaranteed to be a probability, that is, ac*(q) E [0, 1] for any q E [0,1].

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firms to go public early. But with no firms remaining private, investors'incentivesto conceal their information is eliminated,breakingthe sustain-abilityof the belief qe = 1.The intermediatecase qeE (0,1) correspondsto part (ii) of Proposition 3,which requiresY>P > Y > 0. It follows that with qec (0,1), both zpand zfare positive. Let Cpand Cfdenote the expectedissue costs in the P-auctionand the F-auction, respectively,where the expectations are taken beforeeither auction takes place. For Zp o be positive, it must be the case that Cp< Cf,otherwise no firmwould preferto be a pioneer. For zf to be positive,it must be the case that Cf < Cp;otherwise those firms that make up zfwould be better off joining the pioneers. Therefore,

Cp_ ( kp(1 -p) qk(-q) [C() + -V (q)] p Cf (16)P V u() 2 Cf.k=lAbove, the left-hand side is the expected issue cost in the P-auction. Theterm in parentheses is the probability that one informed bidder with goodnews bids high and others, if there are any, bid low in the P-auction. Inthese states of the world, the winner of the P-auction extracts the rent inthe bracketed term. The right-hand side is the expected issue cost of theF-auction. Only an investor who has concealed good news can make aprofit in the F-auction and only in those cases when there are no otherinformed investors. The probabilityof this event is pq/2, and the investor'sprofit is a. Substitutingfrom (6), solving for the infinite sum, and rearran-ging, (16) can be written as

1 - q - q(1 - q +pq)(1 - q + 2pq) = 0. (17)Some algebraic manipulation shows that there exists a unique qe E (0,1)that solves (17).19Given this value of qe, the other equilibriumquantitiesare determined easily as follows:

2e 2qe(l -qe + pqe)2(1 - qe +pqe)2 +p(l - (1 -p)(qe)2)

z;+ z= - G(_we), (18)= (1 qe pqe)(1 _ qe + 2pqe)zf

'9 Specifically, let f(q) be the function on the left hand side of (17). The existence of a solution qe E(0,1) tofl(q)= 0 is guaranteed by the facts thatfl0) > 0,f(1) < 0, and thatfis continuous. Also,f'(q) < 0 for anyq E (0,1) such thatf(q) = 0. Therefore there can be at most one solution toflq)- 0 in the (0,1) interval,that is, qe is unique.

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The first line of (18) restates (15); it gives the equilibrium cutoffproject discovery probability (e such that firms with o < Ce choose toremain private after observing the low price realization in the P-auction.Therefore all of these firmsare followers. The remainingfirmswith o > oe,which have a measure of 1 - G(ce), go public eitherin the P-auction or theF-auction, hence the second line of (18). Whether an individualfirm in thisset chooses to be a pioneer or a follower is indeterminate,since by (17), thefirm is indifferentbetweenthe two auctions. However, the equilibriumratioof pioneers to followers within the set of firms {o > oe is determinate,givenby the thirdline of (18). This simplyrestates Y(q)= zplzf(frompart(ii)of Proposition 3), which must be satisfied for informed investors to beindifferentbetween the high and the low bids in the P-auction. In equili-brium, the total measure of followers is z; + G(we). All of these followersgo public in the F-auction if the P-auction price realization is high, sincethen the asymmetryof information is resolved. However, only those withco> (Oe, that is, a measure of z, choose to go public if the P-auction pricerealizationis low. Thus, we obtain the main result of the article:

Proposition 4. In equilibrium,the IPO volumefollowing the high pricerealization of the P-auction is higher than the IPO volume ollowing thelowprice realization.In deciding when to go public, each firm attempts to minimize theinformation rents investors are expected to extract. In contrast, investorsdesire to trade on their information when such rents are maximal. Thetension between these two timing objectives shapes the equilibrium.If theset of pioneers is very small relative to the followers, investors are better

off concealing their information early on. This makes the pricing of apioneer's IPO less sensitive to private information, alleviating the win-ner's curse problem for the uninformed and hence reducing the cost ofgoing public. At the same time, it becomes less attractivefor a firm to waitand free-ride on the information spillover, as the pioneers' IPOs areexpected to reveal scant information. For both reasons, the pioneer setattracts more firms, and the follower set shrinks. At the other extremewith a very large set of pioneers, investors have no reason to conceal theirinformation, as few followers remain to be exploited in the future. Withpioneers' IPO outcomes expected to reflect plenty of information, firms'free-riding incentives become stronger. As a result, the set of followersexpand at the expense of pioneers. Equilibriumobtains when the spillovereffect is just strong enough to make an issuer indifferent between the twoIPO dates. While both dates attract issuers in equilibrium, the preferencefor waiting is strict for some of the followers, namely those with relativelylow project discovery probabilities. These firms go public subsequentlyonly if the pioneers' offer prices turn out to be high. The result is the

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asymmetricresponseof the IPO volume to offer prices described nProposition4.Recall that the expectednumberof informed nvestors s lip. There-fore lower values of p correspond o a morecompetitive nformationalenvironment.

Proposition (Comparativetatics forp). Asp decreases,(i) qe increases.

(ii) Zp/f decreases.An investor oncealshis information arlyon so that he canprofit romit in the next round of IPOs. His abilityto do so cruciallydependsonwhether hereareother nformed nvestorsn themarket.All elseequal,adecreasenp makes t more ikelythatother nformednvestors xist,andhence reduces he per-follower rofitthe investorexpects o makein theF-auction. This has two equilibrium mplications.First, the reducedinformationrent of the F-auction tilts firms toward being followers.Since some firms have to be pioneers n equilibrium, e mustchangein

sucha wayas to restore he relativeattractiveness f beinga pioneer.Thishappensvia an increase n qe, whichreduces he information ontent oftheoutcomeof the P-auctionand thus increases he relative ost of goingpublic ora follower.Second, heprofitability f theF-auctionrelative othe P-auctionmust be restored n order to keep the informed nvestorsindifferentbetweenbiddinghigh and low. The decrease n pioneer-to-follower ratio facilitates his by shiftingsome of the informationrentsfrom the P-auction o the F-auction.

4. DynamicAnalysisTheanalysisso far has illustrated heendogenous ormationof informa-tion spillovers n a simple two-periodsetup.To examine the dynamicpatterns n the spillovereffect,I now turn to the generalcase with T > 2and/3 < 1.In the model,hot marketsoccurduringperiodswhen firmvalues arerelativelyhighlycorrelated.Various macroeconomicand technologicalshocks outside the model contributeto the emergenceas well as theeventualdemise of suchperiods.For example,a hot marketmay cometo an unexpectedend when the economy is hit by a downturn thatadverselyaffectsthe firms'current ash flows andmakestheirvaluationmore sensitiveto idiosyncratic utureprospects.The parameter3 cap-turesthisuncertaintyn the lengthof the hot period.When 3 = 1,a firmknows that it has exactly T chances to go publicduringthe clusteringperiod.In themorerealisticcase/3< 1,eachperiodt < T is followedby

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eitheranother period t + 1, or a shock that ends the hot market,where thetwo events have probabilities 3 and 1 - 3, respectively.The 3 shock makes a firm's timing problem more involved and inter-esting. Recall that when 3 = 1, each firm j with coj> (e is indifferentbetween being a pioneer and a follower in equilibrium. In contrast, thetiming preferences are strict for all firms except a measure-zero set when3 < 1. To understand why this is so, consider a firm I that is indifferentbetween going public in the current period t and waiting for anotherperiod. Firm I's cost of waiting is a probability-weighted average of theissue costs in various future paths. In some of these paths, the 3 shock isrealized and the hot market ends, leaving the firm with the expected issuecost of going public in year 2, which is increasing in col.Now consideranother firmj with coj> col.For both firms, the issue cost of period t isthe same as it does not depend on co.However, the cost of waiting forfirmj is higher, since in those future paths where the hot market ends,firmj will experiencea largeryear-2 expected issue cost. It follows that allfirmsj with (oj> colstrictly prefer going public in the current period t towaiting. Since the equilibriumexhibits the same property for all periods,the model with 3 < 1 puts more structure on the IPO timing problem of afirm.

Formally, the equilibrium is characterized by vectors q = (ql,..., qT),0e = (1o,..., coT) such that

(i) An informed investor with good news plays a revealingstrategyinperiod T. qT = 0;(ii) After t - 1 periods with low price realizations, an informed inves-tor with good news bids low with probability qt and high withprobability 1 - q in period t;(iii) Firms with project discovery probabilities o E [col, 1] go public inthe first period;(iv) Firms with coe [cot,cot_ 1) go public in period t if period t - 1priceis low;

(v) Firms with o e [0, Wot_ ) go public in period t if period t - 1 priceis high.The structure of the dynamic equilibrium is similar to the two-periodequilibrium of Section 3. Investors play a revealing strategy in period T,as it is their last chance to use their information. In previous periods,however, they are likely to conceal their information. After observing theoutcome of period t - 1, and providedthat the marketproceedsto period t,remainingprivate firms decide whether to go public immediatelyor wait.If period t - 1 price realization is high, the asymmetry of informationis resolved and all remaining firms go public in period t. If the pricerealizationis low, only some firms, those with project discoveryprobabil-ities above the threshold (ot go public.

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The systemof equationscharacterizinghe equilibriumare formallystated in AppendixA. While similar to the equilibrium onditions inSection3, theseequationsconstitutea morecomplicated ystemdue tothe largernumberof periods nvolved.As a result,I analyze hedynamicequilibriumnumerically.For the base case analysis,I assume that theprojectdiscoveryprobabilities f firmsare distributed niformlyn [0,1],that is, G(co)= o. I pick T = 10, 3 = 0.95, and p = .4 for the remainingbase caseparameters.Table1summarizeshe results.Noticethatqtdecreasesn t anddoes soat anincreasing ate.Investors end to revealvery ittle nformationntheearlyperiods,as the pool of privatefirmsis largeand the incentivetoconceal nformations strong.As morefirmsproceedwith theirofferings,fewerpotentialIPO firmsremain.Accordingly, nvestorsstartbiddingmoreaggressivelyn laterperiods.The IPO volumeis verylow in the firstperiod;only those firms withvery good investmentopportunities(co> 0.966) go public. The lastcolumnin Table 1 reportsthe probability hat good news still remainsprivateinformationat the end of periodt, conditionalon the marketlastingat least t periods.Not surprisingly,he degreeof informationalasymmetrys quite highearlyon. As a result, ow pricerealizationsarefollowedbylittle IPOactivity ntheearlyperiods.Recallthat aftera highpricerealization, ll remainingirmsgo public.Therefore, PO volume shighlysensitive o marketconditionsat the beginningof a hot market.This is illustratedn the fourthcolumnof Table1,whichreports he ratioof theIPOvolume ollowinga highpriceoutcome o thevolume ollowinga low price.For instance,a high pricein the firstperiod triggersabout23timesasmanysubsequentPOsasa lowpricedoes.Intime, nformation

Table 1Base case equilibriumt qt co, VolHIVolL Pr(H concealed)1 0.893 0.966 - 0.7702 0.878 0.923 22.69 0.5933 0.863 0.871 17.91 0.4564 0.846 0.810 14.19 0.3495 0.823 0.738 11.21 0.2636 0.793 0.654 8.78 0.1937 0.748 0.557 6.75 0.1348 0.670 0.446 5.03 0.0849 0.509 0.320 3.53 0.04010 0.000 0.176 2.23 0.000Base case parameter values are T = 10, 3 = .95, and p = .4. Firms' project discovery probabilities areuniformly distributed in [0,1].The second and third columns above report qtand co,for each round t. Thefourth column displays the ratio of the IPO volume following a high price realization to the volumefollowing a low price realization. The last column is the ex ante probability that good news remainprivateinformation at the end of round t conditional on round t being reached.

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gets relativelyless asymmetric,as it becomes less likely that investors areholding back good news. Therefore in the late part of a clustering period,IPO volume respondsless sharplyto the outcomes of recentofferings.To examine the effects of increased competition among informedinvestors, I now replicate the above analysis for p = .2, keeping otherparameter values as in the base case. The resulting equilibrium is sum-marized in Table 2. A comparison of Table 2 to Table 1 shows thatProposition 5 generalizes to the multi-period setting. For all t, qt ishigher when p is lower. In words, an investor is more likely to holdback information when he faces more competition. Of course, this byitself would not necessarily imply less information revelation, as theexpected number of informed investors is not constant across the twotables. However, the last column of Table 2 shows that the degree ofinformational asymmetry indeed remains higher when there is morecompetition among informed investors. This results in a thinner IPOmarket that attracts only those firms with relatively good investmentopportunities (column three). It follows that with more competition,IPO volume is more sensitive to recent outcomes at every period (col-umn four).At first look, these are counter-intuitive results. Why would morecompetition hamper information spillovers and reduce the IPO volume?After all, competition should lead to lower information rents, and ifanything, encourage going public. Issue costs are indeed lower withmore competition, yet this is true for hot and cold markets alike (i.e.,not only for year 1, but also for year 2). Hence, a more competitivemarket structure does not necessarily favor more clustering. We haveseen in the previous section that all else being equal, firms' free-ridingincentives become stronger under increased competition. Restoring equi-librium then requires a weakening of the spillover effect so that not allfirms choose to wait and free-ride.The by-product of this adjustmentis ahot market where less information is revealed and fewer firms go public.

Table 2Increasedcompetitionamong informed nvestors:p = .2t qt ot V/olI VolL Pr(H concealed)1 0.959 0.989 - 0.8242 0.951 0.975 69.49 0.6743 0.941 0.956 52.38 0.5474 0.928 0.932 39.13 0.4385 0.909 0.900 28.84 0.3446 0.882 0.856 20.85 0.2607 0.837 0.798 14.65 0.1878 0.758 0.717 9.86 0.1209 0.584 0.601 6.19 0.05810 0.000 0.426 3.43 0.000

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Table3 summarizesheimpactof reducing3.Concealinggoodnewsisa less attractive trategyn thiscase,sincethehotmarket s more ikelytoend without giving the investoranotherchanceto trade.As a result,investorsmakerelativelymoreaggressiveuse of their information.Thishas an asymmetricffecton the IPOvolume n theearlyversus atepartsof clustering.The earlyperiodsattract fewerfirmsrelativeto the basecase,as theincreasedpresenceof informed nvestorsamplifiesssuecosts.At the sametime,eachperiodendsup revealingmore informationdue tomore aggressive nformedbidding. Eventually,enough information srevealed o dominatethe effect of increased nformedparticipation, olate periodsattractmoreissuersrelative o the basecase. Similarly, hesensitivity f IPOvolumeto pastoutcomes s higherat the startof the hotmarket,but lowerat the end.The growth potentialof a firm is capturedby its projectdiscoveryprobabilityco in the model. The numericalanalysisso far presentedcases where the distribution of firms with respect to co is uniform.Table4 illustratesheequilibrium hen irmshaverelatively oorergrowthprospects. pecifically,G(co) 1-(1 - c)3 in Table4;therefore hedensityfunctiong(co)= 3(1 - c)2 puts moreweighton smallprojectdiscoveryprobabilitieselative o the uniformdistribution. incethe typical irmislesslikely o needfinancingn thiscase,it requiresmore nformationo berevealedbeforegoing public.Therefore ewer firmsgo publicin everyperiodrelative o the base case. Investorsaremorelikelyto saveinform-ation for futureuse,as thepool of potential ssuersremainsargerat anygiven ime.Thesensitivity f IPOvolume o recentpriceoutcomesshigherthroughouthe hot market. n termsof projectdiscoveryprobabilities,hepioneers hat startthe hot marketare of lowerqualityrelative o thebasecase. This is true for early followersas well. However,the very latefollowersarein fact of higherquality compareperiod10in Tables1 and4). In otherwords, hequalityof issuersdeterioratesmoreslowlyas thehotmarketprogresses.

Table 3Reduced likelihood of an extended hot market: , = .90t qr eo)tol VolVoL Pr(H concealed)1 0.845 0.972 - 0.6862 0.812 0.934 25.33 0.4673 0.784 0.883 18.38 0.3184 0.751 0.818 13.57 0.2135 0.715 0.737 10.11 0.1406 0.674 0.639 7.53 0.0887 0.626 0.523 5.51 0.0538 0.561 0.389 3.88 0.0299 0.439 0.234 2.52 0.01210 0.000 0.058 1.33 0.000

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Table 4Fewer firms with high growth potential: G(0))= 1 -(1 - ))3t qt ot G(co) VolHIVolL Pr(H concealed)1 0.912 0.730 0.980 -0.8062 0.902 0.649 0.957 41.54 0.6513 0.891 0.585 0.929 34.07 0.5244 0.875 0.529 0.896 28.01 0.4175 0.854 0.477 0.857 23.01 0.3276 0.823 0.426 0.811 18.84 0.2477 0.775 0.377 0.758 15.30 0.1778 0.693 0.328 0.696 12.28 0.1139 0.523 0.279 0.624 9.67 0.05510 0.000 0.228 0.540 7.42 0.000

5. Empirical ImplicationsAs discussed in the introduction, Lowry and Schwert (2002) andBenveniste, Ljungqvist, Wilhelm, and Yu (2003) find that firms attemptto time IPO market conditions. Unexpectedly high offer prices arefollowed by dramatic increases in the numbers of initial filings andcompleted offerings, whereas low prices lead to an increase in withdrawalrates. These findings are consistent with a number of explanations. Forexample, if macroeconomic or sector-wide expectations about the profit-ability of investment are time-varying, increasing expectations wouldcause positive price revisions for pioneers' IPOs, and at the same time,would trigger IPOs of other firms whose financing needs have just risen.As indicated above, however, the link between the clustering of financingactivities and real investment is weak in the data. Alternatively, as Bakerand Wurgler (2002) suggest, issuers may be timing investor sentiment.Positive price revisions of pioneers may simply signal high investorsentiment and attract more firms to the IPO market.

This article offers an alternative explanation for IPO market timingthat emphasizes the role of information spillovers. Anecdotal as well asempirical evidence suggests that IPO offer prices are highly sensitive toinstitutional demand; underwritersgather the input of key investors inpricing new issues and award these investors with favorable allocationsand prices in return.20In going through this process a potential issuerbenefits from observing the outcomes of recent IPOs, as these outcomesreflect investors' demand. The strength of this spillover effect is likely to

20 Aggarwal, Prabhala,and Puri (2002) find that institutional investors are awarded with more shares whenthey indicate demand for issues priced at the upper end of the filing range, which are also expected toappreciate more in the secondary market. More direct evidence comes from Cornelli and Goldreich(2001, 2003), who use detailed data on investors' indications of interest. They show that although thenumberof bids is usually large, only a small fraction of these bids provide information in setting the offerprice. Moreover, the investors who submit these largerand more informative bids are awarded with moreshares.

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be a majordeterminant n a firm's decisionto go public.The centralpredictionof this article s that higherofferpriceoutcomes betterfacil-itate the spillovereffect,that is, theyaremoreinformativeabout inves-tors' demand for new issues. In other words, it is the informationcontent,not the level, of high IPO offer prices that triggerssubsequent ssueactivity.In this regard, he distinguishing mpirical mplicationsof the modelrelate to measuresof uncertaintyand informationalasymmetryamongmarketparticipants. f high priceoutcomesindeed result in less uncer-taintyand moresymmetricnformation, ubsequent aluationof both thenewlypublicfirmsandthe newofferings houldbecomerelatively asier.In particular, he secondarymarkettradingof the pioneersshouldbemoreliquid(lowerbid-askspreads,smallerprice impactof trades),andthe book-buildingprocessfor the followersshould involve less uncer-tainty (tighter filing ranges,smallerprice revisions in absolutevalue).These patternsshould be more pronouncedearlyon in a hot market,when the pool of potentialissuers s largeand the degreeof valuationuncertainty high (see Section 4).21

The model also providespredictionsabout the investmentpoliciesofhot market ssuers.Thehot market s triggeredby the IPOs of pioneers,which are firmswith good investmentopportunities.Followers,on theother hand, have weakergrowthprospects.As a result,followersaremore likely to hold onto IPO proceedsfor extendedperiodsof time.Thesepredictionshave not beenformallytestedbefore;however,somesupportingevidenceexists. For example,Van Bommeland Vermaelen(2003)show thatfirmswhoseIPOs are moreunderpricednvestat higherrates subsequent o becoming public. Since underpricing onstitutes acost to the issuingfirm,thesefirms resemble he pioneers n the model,which face relativelyhighissuecosts and possessbetter nvestmentpro-jects. More directevidencecomes fromAlti (2005),who finds that hotmarket issuersadd more of the IPO proceedsto their cash balancesrelative to their cold marketcounterparts.This finding is consistentwith the prediction hat followerstend to sit on the cash they raise,asmost of the hot market ssuersareby definition ollowers.The results n Section4 yieldfurther estable mplicationswithregardto issuers' nvestmentand cashholdingpolicies:*Issuer quality increases with the degree of competition amonginformed nvestors.Deepermarketswith greater nstitutionalnves-tor participation esult n IPOclusterswhereboth the pioneersandthe followersare less likelyto sit on the cashtheyraise.

21 Consistent with these predictions, Benveniste, Ljungqvist, Wilhelm, and Yu (2003) find that followersexperience smaller price revisions than pioneers and that this pattern is stronger in the early part of thehot market.

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* The likelihood of a change in market conditions is captured by ,in the model. Low 3 values correspond to highly volatile marketswhere information gets stale relativelyquickly. Comparing Table 3 toTable 1, pioneers and early followers are predicted to be high qualityfirms in high volatility environments. Conditional on a long cluster-ing period, however, late followers are of lower quality in the highvolatility case.

* Issuer quality deteriorates faster through time in the case of the highgrowth industries. The pioneers arehighly likely to invest, whereas thelate followers arehighly likelyto sit on the cash. Matureindustriesthatlack growth opportunities exhibit a less pronounced time-seriespattern in this regard.

6. ConclusionThis article presents a model of information spillovers in IPOs. TheIPO timing decision of a firm is driven by its concern to minimize theoffer mispricing, which obtains because of asymmetric distribution ofinformation among investors. A hot market starts when commonfactors become relatively more important determinants of firms'values. Information spillovers from pioneers' IPOs help reduce uncer-tainty on common valuation factors and make going public less costlyfor the followers. IPO market timing emerges as an equilibrium out-come in this setup. High offer price realizations for pioneers betterreflect investors' information, facilitate a stronger spillover effect, andhence trigger a larger number of subsequent IPOs. The model empha-sizes one reason for this to happen, namely, the strategic use ofinformation by long-term investors in the IPO market. More gener-ally, any factor that creates uncertainty about the presence ofinformed investors in pioneers' offerings can give rise to the sameoutcome: a high price reveals good news, but a low price only revealslack of high bids, and not necessarily bad news.The dynamic analysis shows that the jump in the IPO volume inresponse to high offer prices is more pronounced early on in a hotmarket. Issuer quality declines as the hot market progresses. Pioneersare more likely to use the IPO proceeds for investment in the nearfuture, whereas followers tend to hold onto these proceeds forextended periods of time. Further testable implications of the analysisrelate hot market dynamics to the depth of the institutional investorpresence in the IPO market and the industry characteristics of theissuers.

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AppendixA: Characterizationof the Dynamic Equilibrium(i) Indifference conditions of firms {cTl,..., o_r1}: After observing t - 1 low pricerealizations, firm wo is indifferent between going public in period t and waiting ifand only if

C^at -_ (1 -) (et + f Pk'(q,.,qti-)qtk( -qt+l)qt+ll)(ql...qtk=l (A1)k-Tissue= ( P(q,..,qt_,)k(1 -qt)q l)7(q,...qt) t {,...- 1}k=lAbove, Pk (q1,..,qt-1) is the public's posterior that there are k informed investorswith good news given t - 1 low pricerealizations. The term 71(q1,..., t)is an investor'sprofit when he wins with a high bid and pays the uninformed bid:

l(ql ,..qt) = C((t) + a - Vu ( (A2)where the uninformed bid VL(q) s calculated as in (6).(ii) Indifferencecondition of firm OT: Since T is the last period, a firm that waits in thisperiod defers its potential IPO until year 2. Accordingly, the indifferencecondition offirm (OT s obtained by setting / = 0 in (Al).

(iii) Indifference ondition of an informed nvestorwithgood news inperiodt {1... T- 1}:(a) If qtE (0,1), then

o00A EJPk(q1,-,qt1-)(qtqt+l)k 7(q ,...,qt+l)[G()t)-G({ot+I)]k=l

oo= ePk(q,...qt-)qt - r(q,.....,qt)[G(ot- )- G(cot)],t E {l,...,..- 1} (A3)_k=l

Above, Pk(ql,...,qt-1) is the investor's posterior that there are k - 1 other informedinvestors given t - 1 low price realizations.The first line of (A3) is the expected profitwhen the investor bids low in period t and plans to bid high in period t + 1 in case thehot market continues. The second line is the expected profit from bidding high inperiod t.(b) If qt = 0, then

PPi(q1.qtq l,...qt+l)[G(w,) - G(ot+ )]< P{(q,...qt-i)7r(ql,..qt)[G(wt-) - G(ot)].

This condition states that when qt = 0, the expected profit from bidding high inperiod t should be at least as large as the expected profit from deviating to a low bid.(iv) Equilibrium:The dynamic equilibriumis characterizedby qe= {ql,..., qr} and De ={col,... ()T}, which solve the recursive system of equations (Al) and (A3), with the

boundary conditions (A4) and qr = 0.

AppendixB: Proofs of ResultsProof of Proposition 1. (i) If the discoveryoccurs,the payoff will be F; otherwiseshareholderswillgetI. Hence, theprojectrelatedpayoff is coF+ (1- ()I. Also, the assets in placewill generateX2 n year2, whoseyear-1expectedvalue is a/2. The sum of these two components s C(co).Notice

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that there is no asymmetric nformation about C(co) n year 1. The asymmetric nformation isabout X1. First, consider the bid by a good-news informedinvestor,say investor 1, given theequilibrium trategiesof other nvestors.If investor 1bids VH, hen either hereareotherinformedinvestors who also bid VH,or there is no other informed investor.In the firstcase, the expectedprofit fromwinninga shareis C(co)+ c - VH= 0. In the secondcase, all other investors bid VL;hence,theprofitis C(o))+ a - VL= x.Now, by bidding V< VL,nvestor1can neverwin.Biddingany Vc (VL,VH) esults n the sameexpectedprofitas withbidding VH, ince the auctionprice sthe secondhighestbid. Finally, bidding V> VHmakes investor1 winmore shareswhenthereareotherinformed nvestors,but the profit pershare n this stateof the world is zero. Comparingallthreecases, bidding VH s a best responsefor investor 1. Now consider a bad-news informedinvestor,say, investor2. His equilibriumpayoffis zero,sincethepricehepays VL qualsthe valueof the sharesC. By bidding V > VL, nvestor2 gets more shares but obtains the same payoff ofzero sincepershareprofitis zero.Therefore,bidding VLis a bestresponsefor investor2. Finally,an uninformedinvestor makes zero profits by bidding VL,since he wins sharesonly when theinformed nvestor(s)bid low. By biddingV> VL,hewouldobtain thesamepersharepayoffzero,and only win more shares.Hence, VLis a best responsefor an uninformed nvestor.

(ii) The proof in this case is identical to case (i), except that C = F + X1, since co= 1 for afirm going public in year 2, and X1,the payoff from year 1 performance,has alreadybecomepublic information.

(iii) After the auction, the realizedprice is announced. If the price is VH, all investorslearnthat the news is good. If the price is VL,but investors who bid VLdo not get any shares,theyconclude that thereis a high bid, and hence the news is good. Finally, if the priceis VLand allinvestorsget a positive allocation, they conclude that the informedinvestor(s)have bad news.Thus, information becomes symmetricafter the auction is completed.Proof of Proposition2. Since the net presentvalue (NPV) of the projectis assumed to be largeenough to always induce investment, the IPO is a zero-sum game between the issuer and theinvestors.Therefore,from the viewpointof the issuer,the objectiveof maximizingthe expectedproceeds coincides with the objective of minimizing the expected rents that accrue to theinvestors. Consider a firm with projectdiscovery probabilityco.If the firm waits until year 2,then with probability 1 - c there will not be any discovery, and the firm will not need to gopublic. In this case the expected profits of investors is zero. With probabilityco,the discoverytakes placeand the firmgoes public in year2. From Proposition 1, investorscapturerentsonlywhen thereis one informed investorand the news is good. The probabilityof this event isp/2,and the informed investor earns a profit of a in this case. Then, the year-l expected cost ofgoing public in year2 ispoa/2. If the firmgoes public in year 1, the expectedcost is again pal2.Since co < 1, the firm strictly prefers waiting until year 2 to going public in year 1.LemmaB.1 (The F-auctionEquilibrium):Supposethat the measureoffollowers that decide togo public after the P-auction is zf. Let R(XI) -= if the outcome of the P-auction has revealedgood news to the uninformed nvestors and R(XI) = 0 otherwise.

(i) The following bids constitute an equilibrium of the F-auctionfor a follower withproject discoveryprobabilityo).VF(co)= C(O) + R(XI ,I(o) C, () C((o) +) - (B1)

(ii) The aggregate F-auction profit of an informed investor with good news who hasconcealed his information in the P-auction is azf if there is no other informedinvestor and zero otherwise.Proof of Lemma B.1. (i) First, consider the uninformed bid in the first line of (B1). Anuninformed investor wins only when there is no good-news investor who has concealed his

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information.nth t d nhis asethe bidinthefirst ine of (B) breaks ven.BiddingV>V() givesthe samepershareprofitof zero; herefore,winningmoresharesby biddinghigherdoesnotincrease hepayoff.Hence,V (w))s optimal or an uninformednvestor.Next,considerabad-newsnformednvestor.With he bidin the second ine of (BI)he breaks ven.Sinceallother nvestorswill bid at least VL Co),he bad-news nvestor annothopeto bidhigherandmake a positiveprofit.Thus, VLo))is optimal or a bad-news nformednvestor.Finally,consider good-newsnformednvestorwho hasconcealedhisinformation. ince hesellingmechanism s a secondpriceauction,this investorwill choose a bid that maximizes henumberof states n whichhe wins andpays ess thanor equal o the truevalueof the firm.Since,giventhe strategyprofiles n (B1),the good-newsnvestorcan neveroverpay,he iswilling o bid as highaspossible.Then,anybid V> VU(w))s optimal.(ii)Whenthere s onlyone informed nvestorwithgoodnews and he has concealedhisinformation,heF-auctionprice s VT(wo),whereas he truevalueof the firm s VF(co)+ a.Therefore,he ncrement is theprofitof thegood-news inner. ince hemeasure f followersthatgo publicntheF-auctionszf,theaggregate-auction rofitof thegood-news innersZfa. Iftherearemultiplenformednvestors ithgoodnews, heyall bid VHFC), which qualshetruevalueof thefirmgiven hegoodnews.Hence heyallmakezeroprofitsn thiscase.

Proof of Proposition . First considera bad-newsnvestor, ay,investor2. In all threecases,his total expectedprofitis zero. If investor2 bids V > Vu, his expectedprofitisnegative,because,unlikethe uninformed,he knows that he has bad news. Also, suchaggressive iddingcanonlyinduce heuninformedo believe hat thenews s good,whichwill makethemaggressiven the F-auction seeLemmaB.1).Hence,V > Vulosesmoneyin the P-auctionandcannot increase hepayoffin the F-auction.ThenbiddingV


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P-auction and zero from the F-auction. FromP < Y < Y(l) =2p2, (B2)Zf

it follows that p2czf > azp/2. therefore bidding V V.Bidding V> V/ in turn strictly dominates bidding Vuj,since the bid VP leads to sharing theissue with the uninformed and hence reduces the P-auction profits and also earns zeroF-auction profits as it reveals the good news when investor 1 is the only informed investor.Therefore bidding some V< V^ is optimal for investor 1.

Proof of Proposition5. (i) Let qe = q(p). Taking the derivative of both sides of (17) withrespect to p and rearranging gives

(1 - q + 2pq)q3+ 2(1 - q +pq)q3()=(2 -3p)q2 - 2(1 -p)( - 2p)q3 - (B3)

The numerator of (B3) is positive. Therefore we need to show that the denominator isnegative:

1(2 - 3p)- 2(1 -p)(1 - 2p)q < (B4)q2Ifp > 1/2 (B4) is satisfied, since the two terms on the left-hand side are less than 1/2 and 1/4,respectively. Forp < 1/2, suppose that (B4) is not satisfied. Then

q >q2 > (B5)2- 3pIt follows that

< (2 -3p)- 2(1 -p)(l -2p)q(B6)2(1 - p)(l - 2p) (I _ p)2 + (1 - 2p)2 (B6)< (2 - 3p) - < 1,

2-3p (I -p) + (l - 2p)which is a contradiction since q E (0,1). Therefore (B4) is satisfied and q'(p) < 0, whichproves part (i).

(ii) From (17) and the thirdline of (18), zp/z~ = (1 - qe)/qe. By part(i), qe is decreasing np,hence zp/zi is increasingin p.

ReferencesAggarwal, R., N. R. Prabhala, and M. Puri, 2002, "Institutional Allocation in Initial Public Offerings:Empirical Evidence,"Journalof Finance, 57, 1421-1442.Allen, F., and G. Faulhaber, 1989, "Signaling by Underpricing in the IPO Market,"Journalof FinancialEconomics, 23, 303-323.Altl, A., 2005, "How Persistent Is the Impact of Market Timing on Capital Structure?,"forthcoming,Journalof Finance.Andrade, G., M. L. Mitchell, and E. Stafford, 2001, "New Evidence and Perspectives on Mergers,"Journalof Economic Perspectives, 15, 103-120.Baker, M. P., and J. Wurgler, 2002, "Market Timing and Capital Structure," Journal of Finance, 57,1-32.

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Benveniste, L. M., and P. A. Spindt, 1989, "How Investment Bankers Determine the Offer Price andAllocation of New Issues," Journalof Financial Economics, 24, 343-361.Benveniste, L. M., and W. J. Wilhelm, 1990, "AComparative Analysis of IPO Proceeds under AlternativeRegulatory Environments,"Journalof Financial Economics, 28, 173-207.Benveniste, L. M., W. Y. Busaba, and W. J. Wilhelm, 2002, "Information Externalities and the Role ofUnderwriters in Primary Equity Markets," Journalof Financial Intermediation,11, 61-86.Benveniste, L. M., A. P. Ljungqvist, W. J. Wilhelm, and X. Yu, 2003, "Evidence of InformationSpillovers in the Production of Investment Banking Services,"Journalof Finance, 58, 577-608.Biais, B., P. Bossaerts, and J.-C. Rochet, 2002, "An Optimal IPO Mechanism," Review of EconomicStudies, 69, 117-146.Chemmanur, T., 1993, "The Pricing of IPOs: A Dynamic Model with Information Production," Journalof Finance, 48, 285-304.Cornelli, F., and D. Goldreich, 2001, "Bookbuilding and Strategic Allocation," Journal of Finance, 56,2337-2370.Cornelli, F., and D. Goldreich, 2003, "Bookbuilding: How Informative Is the Order Book?," JournalofFinance, 58, 1415-1443.Foster, F. D., and S. Viswanathan, 1994, "Strategic Trading with Asymmetrically Informed Traders andLong-Lived Information," Journalof Financial and QuantitativeAnalysis, 29, 499-518.Foster, F. D., and S. Viswanathan, 1996, "Strategic Trading When Agents Forecast the Forecasts ofOth

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