Buying High and Selling Low: Stock Repurchases and Persistent Asymmetric Information

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1 RFS Advance Acce publihed February 9, 06 Buying High and Selling Low: Stock Repurchae and Peritent Aymmetric Information Philip Bond Univerity of Wahington Hongda Zhong London School of Economic Share price generally fall when a firm announce a eaoned equity offering SEO). A tandard explanation i that an SEO communicate negative information to invetor. We how that if repeated capital market tranaction are poible, thi ame aymmetry of information between firm and invetor implie that ome firm alo repurchae hare in equilibrium. A ubet of thee firm directly profit from repurchae, while other firm repurchae in order to improve the term of a ubequent SEO. The poibility of repurchae reduce both SEO and invetment. Overall, our analyi highlight the importance of analyzing SEO and repurchae in a unified framework. JEL G4, G3, G35) Received June 8, 04; accepted September 4, 05 by Editor David Hirhleifer. Share price generally fall in repone to a firm announcement of a eaoned equity offering SEO). The tandard explanation for thi empirical regularity i that a firm ha information that invetor lack, and an SEO reveal to invetor that the firm information i negative ee, in particular, Myer and Majluf 984). In equilibrium firm with negative information iue equity and accept the negative hare price repone becaue the SEO provide funding for a profitable invetment. In contrat, firm with poitive information prefer to pa up the invetment rather than iue equity at a low price. Downloaded from by guet on June, 06 We are epecially grateful to David Hirhleifer and two anonymou referee for very contructive uggetion. We thank Brendan Daley, David Dick, Diego Garcia, Paolo Fulghieri, Ohad Kadan, Robert McDonald, Giorgia Piacentino, Raj Singh, Gunter Strobl, and eminar audience at Boton Univerity, the Univerity of Colorado, Georgia State Univerity, the Univerity of Minneota, the Univerity of Notre Dame, the Touloue School of Economic, Wahington Univerity in St Loui, the Pari Summer Macro-Finance Workhop, the Pacific Northwet Finance Conference, the Jackon Hole Finance Group Conference, the Finance Theory Group Conference, the Financial Intermediation Reearch Society, the Wetern Finance Aociation, and the Oxford Financial Intermediation Theory Conference for ome very helpful comment. Any error are our own. Send correpondence to Philip Bond, Foter School of Buine, Univerity of Wahington, PACCAR Hall, Seattle, WA apbond@uw.edu. See Aquith and Mullin 986), along with a large ubequent literature, ummarized in Eckbo et al. 007). The Author 06. Publihed by Oxford Univerity Pre on behalf of The Society for Financial Studie. All right reerved. For Permiion, pleae journal.permiion@oup.com. doi:0.093/rf/hhw005

2 The Review of Financial Studie / v 0 n 0 06 But if a firm really doe have uperior information relative to it invetor, a firm deciion problem i more complicated than imply deciding whether or not to undertake an SEO. In particular, a firm with poitive information potentially ha the incentive to repurchae hare, both to A) directly profit from the repurchae tranaction, and alo to B) communicate poitive information to invetor, and thereby improve the term of a ubequent SEO. However, mot exiting SEO model are tatic, which eliminate both incentive. For motive A), thi follow from the no-trade theorem Milgrom and Stokey 98): invetor can infer that a repurchae offer come from a currently undervalued firm, and hence they prefer to retain their hare. Motive B) i inherently dynamic, in that it require at leat two round of equity tranaction to implement. Yet motive A) figure prominently in managerial urvey repone, while Billett and Xue 007) provide empirical evidence for B). 3 In thi paper we analyze a dynamic verion of the tandard SEO model. Our main reult i that repurchae motived by both A) and B) indeed arie in equilibrium. Moreover, thee repurchae interact with SEO. In particular, we how that the poibility of repurchae reduce the likelihood that a firm undertake an SEO. The equilibrium outcome of the tatic game, in which bad firm iue and good firm do nothing, i fragile, in the ene that in the dynamic etting thi outcome fail a tandard refinement Never diuaded once convinced, NDOC, dicued in detail below). In contrat, equilibria featuring repurchae atify NDOC. Our reult ugget that the tandard explanation of the negative pricereaction to SEO announcement i incomplete, in the ene that the equilibrium that underpin the explanation mut alo feature repurchae, a point that i abent in the tandard explanation. Nonethele, our analyi till deliver the negative price reaction to SEO announcement thi i the elling low of the title), becaue in equilibrium an SEO i a negative ignal relative to both the alternative of repurchaing and doing nothing. The primary empirical implication of our analyi are that ) ome firm repurchae and then ubequently engage in an SEO, ) in uch cae, the dollar value of the SEO exceed the dollar value of the repurchae, 3) the cumulative hare price repone to a repurchae announcement and then ubequent SEO announcement i more favorable than the cumulative repone to an SEO announcement made without a prior repurchae. All three prediction are Downloaded from by guet on June, 06 In exception, uch a Luca and McDonald 990, 998) and Henney, Livdan, and Miranda 00),afirm informational advantage only lat one period. In contrat, in our paper the information aymmetry i peritent. In paper uch a Contantinide and Grundy 989), which we dicu in detail below, firm engage in two round of tranaction, but the econd tranaction i a determinitic function of the firt. 3 Brav et al. 005) urvey manager. Conitent with motive A), a very large fraction of manager agree Table 6) that the Market price of our tock if our tock i a good invetment, relative to it true value) i an important factor. The article alo report urvey evidence conitent with motive B): a very large fraction of manager agree Table 3) that Repurchae deciion convey information about our company to invetor.

3 Buying high and elling low conitent with the empirical finding of Billett and Xue 007). Additional empirical implication are that 4) ome firm repurchae in order to profit from the repurchae tranaction, and 5) repurchaing firm have good invetment opportunitie and are credit contrained. A noted, 4) i conitent with urvey repone, and a dicued in Section 6.3, 5) ha ome upport in exiting empirical tudie. The intuition for our reult that an equilibrium mut feature repurchae i a follow. On the one hand, if invetor belief following a repurchae offer are that a firm i bad, then good firm certainly profit from repurchae, ince the price they pay i low. On the other hand, if invetor belief following a repurchae offer are good, then any firm intereted in undertaking an SEO can benefit by firt repurchaing, o a to improve invetor belief. So in either cae, repurchae arie in equilibrium. Before proceeding, it i worth noting that in practice firm may repurchae their own tock either via tender offer or via open market repurchae program. Our formal model correpond both to open market repurchae program in which firm actually act a announced, and to Dutch-auction tender offer in which the price paid to invetor depend on the level of invetor interet. In the United State, open market repurchae are the dominant form of repurchae, and mot of the empirical evidence that we cite deal with thi cae. A perhap urpriing feature of open market repurchae in the United State i that firm are not legally bound to follow their announced program. Nonethele, Stephen and Weibach 998) find that 74 to 8 percent of the hare targeted at the time of the original announcement are ubequently repurchaed, and Oded 009) document a mean completion rate of 9%. Moreover, many event tudie document a ignificant abnormal return of %- 4% in hare price in repone to an announcement of hare repurchae e.g., Ikenberry, Lakonihok, and Vermaelen 995; Peyer and Vermaelen 009), uggeting that announcement are not pure cheap talk. 4 There i a large exiting literature on the information content of firm capital tructure deciion. The idea that firm repurchae their tock to ignal they are good can be traced back to the old intuition that retaining equity i a ueful ignal Leland and Pyle 977). Similarly, Example of Brennan and Krau 987) ha a good firm imultaneouly repurchaing debt and iuing equity. The debt repurchae allow the firm to ignal that it i good. A large literature tudie ignaling in tatic payout model. Although many of thee model are written in term of dividend payout rather than repurchae, the economic effect would apply imilarly to repurchae, and o we dicu both together. Downloaded from by guet on June, 06 4 Related to thi dicuion, in an early tudy of repurchae, Barclay and Smith 988) find evidence that the announcement of a repurchae program i followed by an increaed bid-ak pread, which they interpret a an increae in advere election, which they in turn interpret a invetor being unure about whether or not they are trading againt the firm. However, ubequent reearch ha not generally upported thi original finding ee the dicuion in Grullon and Ikenberry 000)). 3

4 The Review of Financial Studie / v 0 n 0 06 In one branch of thi literature e.g., Bhattacharya 979; Vermaelen 984; Miller and Rock 985), good firm pay out cah to how that they have high cah flow. Bad firm do not mimic becaue they have low cah flow, and o paying out cah neceitate either cotly external financing or ditort invetment. 5 An important aumption in thi branch of the literature i that a firm objective exogenouly) include the interim hare price, becaue, for example, a ubet of hareholder need to ell at an interim date. A econd branch of the literature e.g., John and William 985; Ambarih, John, and William 987; William 988) directly aume that pay out are cotly: in particular, dividend are tax inefficient. 6 Firm then iue equity to finance an invetment. Good firm pay out, while bad firm do not. Becaue of thi eparation, good firm are able to raie the fund they need for invetment in a le dilutive way. Bad firm do not mimic good firm becaue they would pay the ame cot inefficient cah pay out), but benefit le becaue dilution i le cotly to them than it i to good firm. In both thee et of paper, the economic function of pay out i that they detroy value. In our analyi, repurchae detroy value for bad firm, but in contrat to pay out in the above paper, they create value for good firm. Conequently, our model tie together the ue of repurchae a a ignal by ome firm a a prelude to hare iuance and invetment) with the ability of other firm to profitably engage in repurchae. In thi ene, repurchae in our model differ both from money burning Daniel and Titman 995) and wateful advertiement Milgrom and Robert 986), but intead contitute a wealth tranfer between different firm. Moreover, a novel prediction of our model i that both good and bad firm repurchae, but intermediate firm may not repurchae. Contantinide and Grundy 989) and Chowdhry and Nanda 994) both highlight a central characteritic of repurchae, namely, that they are more expenive when invetor belief about the firm are more poitive. Importantly, thi i the oppoite of the cae for hare iue. In Contantinide and Grundy 989), thi feature of repurchae allow a fully eparating efficient equilibrium to exit under ome circumtance: firm commit to pend exce cah from a fundraiing tage on repurchae, and thi mean that the more management inflate the perceived value of the claim [iued at the fundraiing tage], the more capital it raie and the more hare it mut repurchae from the outider at the inflated price. In Chowdhry and Nanda 994), thi ame force mean that low value firm do not repurchae, becaue by a parameter Downloaded from by guet on June, 06 5 Bhattacharya 979) and Miller and Rock 985) are written in term of dividend, while Vermaelen 984) i written in term of repurchae. Ofer and Thakor 987) decribe a model with imilar ingredient in which firm can both iue dividend and repurchae hare, where both action are cotly, and characterize which form of payout firm prefer. We conider the robutne of our analyi to multidimenional ignaling in Section 8. 6 Ambarih, John, and William 987) and William 988) both allow for repurchae. In both paper, and in contrat to our paper, there i a ingle date at which both repurchae and iue occur, and o there i no poibility of a firm repurchaing at one date to improve the term of iue at a ubequent date. 4

5 Buying high and elling low aumption) invetor belief are alway uch that the price i too high. A uch, in Chowdhry and Nanda 994) model firm ditribute cah via repurchae only when invetor information i negative relative to the firm information, and via dividend otherwie. Our paper complement the analyi of thee author by howing that, perhap urpriingly, the poitive relation between repurchae price and invetor belief mean that ome equilibrium repurchae mut occur. 7 The reaon i that good firm will repurchae unle invetor belief aociate repurchae offer with very good firm; but even in thi cae, repurchae remain attractive, ince by repurchaing today a firm change invetor belief and hence improve the term of a ubequent hare iue ee Subection 4.). Oded 005) demontrate how a good firm can ignal it type via a repurchae program that give it the option, but not the obligation, to repurchae at a future date. A firm repurchae hare from current invetor who are hit by a liquidity hock: hence, the no-trade theorem doe not apply, and a repurchae program give the firm a valuable repurchae option, which by itelf increae the current hare price. However, the firm current invetor undertand they will uffer by trading againt the firm, and thi generate countervailing downward preure on the current hare price. But the repurchae option i more valuable to good firm, becaue by an important aumption they are rikier, a well a higher in value than bad firm. Hence, there i an equilibrium in which good firm announce a repurchae program, but bad firm do not mimic, becaue they would pay the ame cot downward preure on today hare price) but gain a le valuable option. In contrat to our paper, Oded 005) doe not conider repurchae a a prelude to equity iuance. The above dicuion focue on paper that tudy repurchae in the context of aymmetric information between a firm and it invetor. Naturally, there are other factor that affect the incidence of repurchae perhap mot notably, the differential tax treatment of repurchae and dividend payment. Another example i Huang and Thakor 03) uggetion that repurchae are ueful becaue they reduce diagreement among a firm hareholder. Grullon and Ikenberry 000) offer a good urvey of the literature on repurchaing. In many microtructure model e.g., Kyle 985) an informed trader buy and ell hare in many period. Cloet to our paper are the mall number of paper in which an informed trader trade in oppoite direction in different period, for example, buy in early period and then ell in later period ee Kyle and Viwanathan 008 and the reference therein). However, the economic motivation for thi dynamic trategy i very different from in our paper: in thee prior paper, the informed trader buy early in order to extract more money from Downloaded from by guet on June, 06 7 Note that the timing of equilibrium repurchae i very different in our model from that of Contantinide and Grundy 989). In our model, a firm firt repurchae, and then ubequently may iue equity to fund an invetment. In Contantinide and Grundy, a firm intead firt iue a ecurity to raie funding, with a commitment to dibure exce cah via repurchae. 5

6 The Review of Financial Studie / v 0 n 0 06 the noie/liquidity trader he ell to later. In contrat, in our paper the informed trader the firm) alway ell at a fair price. The firm that make trading profit in our etting are very good firm who buy undervalued hare in early round. The ource of thee profit i the loe experienced by wore firm who alo buy in early round. A relatively mall literature tudie dynamic model of trade under aymmetric information without noie/liquidity trader. Noldeke and van Damme 990) and Swinkel 999) tudy a labor market model in which education act a a ignal. Fuch and Skrzypacz 03) tudy trade of a ingle indiviible aet that i more highly valued by buyer than the eller. They focu on whether more trading opportunitie increae or reduce welfare. Kremer and Skrzypacz 007) and Daley and Green 0) tudy a imilar model in which information arrive over time. In contrat to thee paper, in our model both ale and repurchae are poible; trade i in diviible hare; and the gain from trade arie from the poibility of financing a profitable invetment. Perhap cloet to the current paper are Morellec and Schurhoff 0) and Strebulaev, Zhu, and Zryumov 04). Both paper tudy dynamic model in which a firm with long-lived private information chooe a date to raie outide financing and invet. In both paper, iue and invetment are tied together by aumption), and the combination of repurchae with ubequent equity iue which i our main focu i not examined. Intead, the main reult of both paper concern the timing of invetment. A contemporaneou paper by Ordonez, Perez-Reyna, and Yogo 03) tudie a dynamic model of debt iuance. In a model with moral hazard in place of advere election, DeMarzo and Uroevic 006) tudy the dynamic of a large hareholder elling off hi take in a firm.. Example Firm have cah and the opportunity to invet.5 at date in a project that ubequently yield.9. Hence, firm need to raie additional fund of 0.5 in order to invet. Firm can either repurchae buy) or iue ell) hare at date and. All uncertainty i reolved at date 3, and firm act to maximize their date 3 hare price. The initial number of hare i normalized to. Firm aet-in-place a are uniformly ditributed over [6,]. If date tranaction are exogenouly ruled out and tranaction are only poible at date, thi etting i imply a verion of Myer and Majluf 984) with a continuum of firm type. We firt decribe an equilibrium of thi benchmark. 8 Firm a 7.4 raie fund 0.5 by iuing 0.5 hare at a 8. price P MM =8. and then invet. Firm a>7.4 do nothing. To ee that the Downloaded from by guet on June, 06 8 The equilibrium decribed entail firm either raiing jut enough outide financing to fund the invetment or doing nothing. Other equilibria exit in which iuing firm raie trictly more fund than required. However, all equilibria of the benchmark are characterized by a cutoff firm type uch that firm below thi cutoff iue and invet, while firm above thi cutoff do nothing ee Propoition ). 6

7 Buying high and elling low Figure Equilibrium of the example decribed in the main text price P MM i fair, note the expected value of a conditional on a 7.4 i 6.7 and that P MM olve P MM = P MM Given the iue price P MM, the date 3 hare price of firm a =7.4 i 8.4 if it doe nothing and i =8.4 if it iue and invet. Hence, firm a< trictly prefer to iue and invet, while firm a>7.4 find iue too dilutive and trictly prefer to do nothing. Our paper focu i the cae in which tranaction are poible at both date and. In thi cae, the following i a perfect Bayeian equilibrium PBE), illutrated in Figure : At date, firm with aet-in-place in either [6.75,7.07] or [0.55,] pend cah to repurchae.55 hare at a price P =.55. The remaining firm do nothing. At date, firm with aet-in-place below 6.75 raie fund 0.5 by iuing hare at a price P D =7.77, and invet. Firm with aet-in place in [6.75,7.07] raie fund.5 by iuing.5 hare at a price 8.00 P RI =8.00, and invet. The remaining firm do nothing. We verify thi i an equilibrium. Firt, conditional on firm behaving thi way, the repurchae and iue price are fair, a follow. The date iue-afterrepurchae price P RI =8.00 i fair, ince it olve P RI E[a a [6.75,7.07]]+.9 = P RI Downloaded from by guet on June, 06 7

8 The Review of Financial Studie / v 0 n 0 06 The date direct iue price P D =7.77 i fair, ince it olve P D E[a a [6,6.75]]+.9 = P D The date repurchae price i fair, ince conditional on date repurchae, there RI i a probability =0.8 that the date price i P =8.00 and a 0.55 E[a a [0.55,]] probability =0.8 that it i =.34, and o the expected date price i.55. Second, firm repond optimally to the tated repurchae and iue price. If a firm repurchae and then iue, it ha =.35 hare outtanding at date 3. If a firm iue directly, it ha =.35 hare outtanding at 7.77 date 3. Hence, the date 3 hare price of a firm with aet-in-place a under both thee alternative i.9+a.35, and the date 3 hare price from repurchaing at date and then doing nothing i a =.09a,.55 and the date 3 hare price from doing nothing at both date i imply +a. Out of thee three alternative, firm with aet-in-place below 7.07 obtain the highet payoff from either repurchaing and then inveting, or directly iuing and inveting; they are indifferent between the two option. Firm with aetin-place between 7.07 and 0.55 obtain the highet payoff from doing nothing. Finally, firm with aet-in-place above 0.55 obtain the highet payoff from repurchaing at date and then doing nothing. 9 Dicuion: Firm with aet-in-place a>0.55 repurchae hare for trictly le than their true value, a +, and o make trictly poitive profit. The reaon invetor accept the lower price i that thee firm pool with wore firm namely, firm with a between 6.75 and 7.07). But thi raie the quetion of why thee wore firm are prepared to repurchae. They do o to improve the term at which they can ubequently iue. If intead they attempt to iue equity directly, they obtain a wore price: pecifically, they iue hare at a price 7.77 rather than A in the title of our paper, thee firm buy high and ell low. Downloaded from by guet on June, 06 9 We have etablihed that firm act optimally when their choice et i limited to the four equilibrium trategie. Thi till leave open the poibility that a firm could profitably deviate to ome other trategy. Off-equilibrium belief that deter uch deviation are pecified in the proof of Propoition 3. 8

9 Buying high and elling low The intermediate interval of firm with between 7.07 and 0.55 find iue too dilutive, a in Myer and Majluf 984), and alo find repurchae too expenive. Firm with a>0.55 trictly profit from their repurchae tranaction, even though thee tranaction fail to create any value. The ultimate ource of thee profit i that the inveting firm with a 7.07 pay a premium to raie capital. By thi, we mean that if firm a 7.07 could all credibly pool and iue directly, the iue price P would atify P = ), that i, P =7.94, and o the P payoff of each firm a<7.07 would be.9+a =.9+a, which i higher than they.3 get in the above equilibrium. A related obervation i that the equilibrium of the Myer and Majluf 984) etting, where repurchae i impoible, entail invetment by firm with aetin-place between 6 and a cutoff level trictly above The reaon more invetment occur in thi cae i that low a firm are able to iue without ubidizing the profitable repurchae of high a firm. Thi raie the quetion of whether low a firm are able to avoid the croubidy even when repurchae are poible. The anwer i that they cannot, at leat not in any equilibrium atifying NDOC ee Propoition 4). The reaon i that, in any equilibrium, high a firm make trictly poitive profit. Thi property arie becaue firm with a cloe to the maximum value of make trictly poitive profit unle invetor require a price cloe to 3 to ell their tock to a repurchaing firm, or in other word, invetor interpret a repurchae offer a coming from a firm with a high a. But equilibrium zero profit for high a firm are inconitent with uch belief, becaue high a firm could then profitably deviate to repurchae at date, triggering very poitive belief, and then iue at a very favorable price at date ince the belief inherited from date are very poitive).. Model and Preliminary Reult Our model i eentially the ame a that of Myer and Majluf 984). The only ubtantive difference i that wherea Myer and Majluf 984) conider a firm interaction with the equity market at jut one date, we conider two poible date. A we will how, thi additional feature generate equilibrium hare repurchae. There are four date, t =0,,,3; an all-equity firm, overeen by a manager; and at each of date and, a large number of rik-neutral invetor who trade the firm tock. We normalize the date-0 number of hare to. At date 0, the manager of the firm privately learn the value of the firm exiting aet aet-in-place ). Write a for the expected value of thee exiting aet, where a [ a,a ], and the ditribution of a i given by meaure μ. We aume the ditribution of a ha full upport on [ a,a ] and admit a bounded and continuou denity function, denoted by f. In addition to aet a, the firm ha cah or other marketable ecuritie) with a value S. Downloaded from by guet on June, 06 9

10 The Review of Financial Studie / v 0 n 0 06 At the end of date, the firm ha an opportunity to undertake a new project. In Section 7, we extend the model to allow for a choice of invetment timing, with the firm able to invet at either date or date.) The project require an initial invetment I and generate an expected cah flow I +b. For implicity, we aume that b i common knowledge; in other word, we focu on a verion of the Myer and Majluf 984) environment in which aymmetric information i about aet-in-place, not invetment opportunitie. Throughout, we aume I>S, o that the firm need to raie external financing to finance the invetment I. We make the following extremely mild aumption on the relation between b and the denity function f of aet value: Aumption. of a. The denity f equal /b at at mot countably many value The aumption i atified generically. It i ued only in the proof of equilibrium exitence Propoition 3 and 4). At date t =,, the firm can iue new equity and/or repurchae exiting equity. Equity iue and repurchae take place a follow. The manager offer to buy or ell a fixed dollar amount t of hare, where t >0 correpond to hare repurchae and t <0 correpond to hare iue. Invetor repond by offering a quantity of hare in exchange. In other word, if t >0 each invetor offer a number of hare he will urrender in exchange for t, and if t <0, each invetor offer a number of hare he will accept in return for paying the firm t. At t =, there i a mall probability α 0 that the firm i exogenouly unable to execute a capital market tranaction. Concretely, the need to make deciion about other matter may exhaut a firm deciion-making capacity, or random factor may reult in a firm board failing to reach the conenu needed to authorize capital market tranaction. 0 The poibility of α>0 i required only for part b) of Propoition 4, which etablihe the exitence of an equilibrium atifying NDOC. Even here, the reult hold for arbitrarily mall value of α>0. We term a firm that i exogenouly unable to acce capital market at date a inactive, and any other firm a active regardle of whether the firm actually take a date action). Note that both a and I +b are expected value, o our model allow for very volatile cah flow. In particular, we aume that there i enough cah-flow volatility that it i impoible for firm to iue rik-free debt. In general, the choice between riky debt and equity under aymmetric information Downloaded from by guet on June, 06 0 Board approval i required for both SEO and repurchae program. One could alo analyze a verion of the model with a ymmetric aumption at date, that i, at each of date and, there i a probability α that a firm i exogenouly unable to execute a capital market tranaction. Adding thi poibility at date ha no impact on our reult, but add unneceary complexity to the analyi. 0

11 Buying high and elling low i nonobviou; ee Fulghieri, Garcia, and Hackbarth 04) for a recent characterization. In Section 8 we dicu the robutne of our analyi to allowing for other ecuritie.) At date 3, the true value of the firm i realized, including the invetment return, and the firm i liquidated. Write P 3 for the date-3 liquidation hare price, and write P and P for the tranaction price of the hare at date t =,. Becaue the number of invetor trading at each of date and i large, competition among invetor implie that the date t hare price i P t =E[P 3 date t information, including firm offer t ]. ) The manager objective i to maximize the date 3 hare price, namely, P 3 = S +a +b invetment, ) P P where invetment i the indicator function aociated with whether the firm undertake the new project, and the denominator reflect the number of hare outtanding at date 3. Note that in the cae that only hare iue are poible, the manager objective function coincide with the one pecified in Myer and Majluf 984), which i to maximize the utility of exiting paive ) hareholder. In our etting, where repurchae are poible, the manager objective function can be interpreted a maximizing the value of paive hareholder, who neither ell nor purchae the firm tock at date and. Alternatively, the manager objective can be motivated by auming that the manager himelf ha an equity take in the firm and i retricted from trading the firm hare on hi own account. For ue throughout, oberve that ) and ), together with the fact that the firm invet whenever it ha ufficient fund, imply that the date price conditional on and i P, )= S +E[a, ]+b S I P. 3) Downloaded from by guet on June, 06 Note that if the manager alo put weight on a high date hare price, thi would further increae the manager incentive to repurchae equity. On the other hand, it i important for our analyi that the manager doe not fully internalize the welfare of date 0 hareholder who ell at date : in particular, our analyi require that if a manager i able to repurchae hare at le than their true value, then he doe o. A dicued in the text, one jutification i that the manager eek to maximize the value of hi own equity take. A econd jutification i that when a firm repurchae it own tock, it may not be it exiting hareholder who ell hare to the firm; intead, the firm repurchae offer may be filled by hort-eller of the firm tock. Attaching zero welfare weight to hort-eller i analogou to the Myer and Majluf 984) aumption of attaching zero welfare weight to new purchaer of the firm hare. A eparate but related iue i whether a firm hareholder could improve firm value by contracting with the firm manager, a uggeted by Dybvig and Zender 99). For example, a Corollary demontrate, before the value of aet a i realized, a firm hareholder would ideally like to prohibit a firm from repurchaing it hare. However, and parallel to Peron 994) repone to Dybvig and Zender, uch a commitment i vulnerable to renegotiation becaue once a i realized high a firm can generate value for their hareholder by repurchaing.

12 The Review of Financial Studie / v 0 n 0 06 Iterating, ) and 3), together with the law of iterated expectation, imply that the date price conditional on and the unconditional date 0 price are, repectively, P )=S +E [ a +b S I ], 4) P 0 =E[P 3 ]=S +E[a]+b [fraction of firm that invet]. 5) From 3) and 4), the payoff of firm a from, ) i ) P = S +a+b S I S+E S +E[a, ]+b S I S +a+b S I [a+b S I ]) ) S +E[a, ]+b S I ). 6) We characterize the perfect Bayeian equilibria PBE) of thi game. We retrict attention to pure trategy equilibria in which all invetor hold the ame belief off-equilibrium. We focu on equilibria in which all firm play a bet repone a oppoed to equilibria in which almot all firm play a bet repone). 3 Finally, we tate a imple monotonicity reult, which we ue repeatedly: Lemma. If a and a are either both active firm or both inactive firm, and conduct capital tranaction ) ), and,, repectively, with S > S, then a <a. In other word, better firm raie fewer fund acro date and. An immediate corollary of Lemma i a follow. Corollary. In any equilibrium, there exit cutoff a,a i [ a,a ] uch that all active repectively, inactive) firm a<a repectively, a<a i ) invet and all active firm a>a repectively, inactive firm a>a i ) do not invet. 3. One-Period Benchmark Before proceeding to our main analyi, we characterize the equilibrium of the benchmark model in which firm can only iue or repurchae hare at date, with the date iue/repurchae deciion exogenouly et to 0. The main concluion of thi ection i that the Myer and Majluf 984) concluion hold: only the lowet a firm iue and invet, and repurchae play no meaningful Downloaded from by guet on June, 06 3 Given a perfect Bayeian equilibrium in which almot all firm play a bet repone, one can eaily contruct an equilibrium in which all firm play a bet repone by witching the action of the meaure zero et of firm who originally did not play a bet repone. Becaue only a meaure zero et of firm are witched, the original et of belief remain valid.

13 Buying high and elling low role. In other word, the addition of the poibility of repurchae to the Myer and Majluf 984) environment i, by itelf, inconequential. Intead, our reult further below are driven by the poibility of firm engaging in capital tranaction at multiple date. The key reaon that firm do not take advantage of repurchae in a one-period model i the no-trade theorem Milgrom and Stokey 98). Even though firm enjoy an informational advantage relative to invetor, they are unable to profit from thi advantage. 4 Propoition. i of meaure 0. In the one-period benchmark, the et of firm that repurchae Propoition etablihe that, in the one-period benchmark, a firm ability to repurchae it own tock play no meaningful role. Accordingly, the equilibria of the one-period benchmark coincide with thoe of the tandard Myer and Majluf 984) etting, a formally etablihed by the next reult. Propoition. In any equilibrium, there exit a a,ā] uch that almot all firm below a iue the ame amount and invet, while almot all other firm receive the ame payoff a doing nothing i.e., P 3 =S +a). Propoition characterize propertie an equilibrium mut poe. However, it doe not actually etablih the exitence of an equilibrium. But thi i eaily done. In particular, fix any uch that S I, and define a a the olution to a =max a [ a,ā ] S +a +b : S +a. 7) S+E[a a [a,a ]+b] There i an equilibrium in which all firm with aet below a iue and raie an amount, while firm with aet above a do nothing. Off-equilibrium path belief are uch that any other offer to iue i.e., <0 and = ) i interpreted a coming from the wort type a, and any offer to repurchae i.e., >0) i interpreted a coming from the bet type ā. Oberve that if I +a +b + I S S +a, S+E[a]+b thi benchmark model ha an equilibrium in which all firm invet. In thi cae, aymmetric information about a doe not caue any ocial lo. To focu Downloaded from by guet on June, 06 4 Bond and Eralan 00) tudy trade between differentially informed partie in a common-value etting. The no-trade theorem doe not apply becaue the eventual owner of the aet take a deciion that affect the aet final cah flow. Trade affect the information available to the party making the deciion. A imilar force allow repurchae to occur in the full model, analyzed below: trade of hare at date affect a firm ability to raie finance at date. 3

14 The Review of Financial Studie / v 0 n 0 06 on the economically intereting cae in which aymmetric information ditort invetment, for the remainder of the paper we impoe the following aumption: Aumption. α I+a+b + I S S+E[a]+b <S+a. 5 For ue below, note that Aumption implie ā>e[a]+b>a+b. 8) A final point to note about the one-period benchmark i that it poee multiple equilibria. One ource of multiplicity tem from the net iue ize,. Thi can be een from Equation 7), which determine the marginal inveting firm a : different choice of uch that S I lead to different olution a. A econd potential ource of multiplicity i that, even fixing, the inequality in 7) may hold with equality at multiple different value of a. Economically, there may be an equilibrium in which the marginal inveting firm ha a high a, leading to a favorable iue price, which enable high a firm to invet without uffering too much dilution; and another equilibrium in which the marginal firm ha a low a, leading to an unfavorable iue price, which implie that only low a firm are prepared to uffer the dilution cot aociated with invetment. The firt ource of multiplicity can be eliminated by appealing to equilibrium refinement. In particular, the only choice of that urvive D i =S I. 6 The econd ource of multiplicity can be eliminated by impoing further condition on the ditribution of a. In particular, if the following condition hold, then for any uch that S I there i a unique equilibrium of the one-period benchmark aociated with thi. Condition. E[ã ã a]+b a i trictly decreaing in a. S+E[ã ã a]+b Condition hold, for example, whenever a i ditributed uniformly. Condition i ued only in Propoition 7. Lemma. If Condition hold, then for any atifying S I, there i a unique equilibrium of the one-period benchmark. Downloaded from by guet on June, 06 5 The factor α i included on the LHS to enure that, in the full model, there i no equilibrium in which all active firm invet, even if they receive a cro-ubidy from firm that are exogenouly inactive at t =. If there are no inactive firm α =0), Aumption i imply I+a+b + I S <S+a. S+E[a]+b 6 The D refinement criterion Cho and Krep 987) require that after any deviation, the upport of off-equilibrium belief i a ubet of thoe firm that are mot likely to make uch a deviation. In brief, an equilibrium with S >I fail D becaue the off-equilibrium belief aociated with a deviation =S I that are needed to upport uch an equilibrium heavily weight firm with low a, even though firm with higher value of a gain from thi deviation for a trictly larger et of off-equilibrium belief. A full proof i available upon requet. 4

15 Buying high and elling low 4. Analyi of the Dynamic Model We now turn to the analyi of the full model, in which firm can engage in capital tranaction at multiple date. 4. Exitence of a repurchae equilibrium We firt how that there i nothing pecial about the example above. There alway exit an equilibrium in which the bet firm trictly profit from repurchaing, while wore firm repurchae their tock for more than it i worth that i, buy high to improve the term at which they can ubequently iue hare to finance the invetment. Propoition 3. For either α =0, or α >0 ufficiently mall, an equilibrium exit in which a trictly poitive ma of firm pool and repurchae at date. A trict ubet of thee firm make trictly poitive profit from the repurchae, and do nothing at date. The remaining repurchaing firm repurchae their tock for more than it i worth, and then iue enough hare to finance invetment at date. The proof of Propoition 3 i contructive. Firt, the proof contruct an equilibrium for the cae α =0. The equilibrium i either imilar to the above example; or feature all firm repurchaing at date, with a trict ubet then iuing equity to fund invetment at date. The proof then perturb the equilibrium contructed for α =0 to contruct an equilibrium for the cae of α mall but trictly poitive. 4. Neceity of repurchae A i common in game of aymmetric information, multiple equilibria exit. However, we next how that the propertie tated in Propoition 3 are poeed by any equilibrium atifying the refinement NDOC Oborne and Rubintein 990). Hence, the NDOC refinement elect preciely equilibria that feature repurchae. NDOC i a conitency condition on how belief evolve over time. Once invetor are 00% ure that the firm type belong to ome et A, NDOC tate that ubequent belief put poitive probability only on firm type within the cloure of A. Thi retriction i highly intuitive and i typically regarded a mild; ee, for example, Rubintein 985) and Groman and Perry 986), or more recently, it ue a Aumption in Ely and Valimaki 003) and a Condition R in Feinberg and Skrzypacz 005). More formally, in our context, NDOC tate that date invetor belief after oberving off-equilibrium firm action, ) mut atify the following: A) if i an equilibrium action, then date belief aign probability to the firm type lying in the cloure of the et of firm who play in equilibrium, and B) if i not an equilibrium action, and date belief aign probability to ome ubet A of firm type, date belief likewie aign probability to the cloure of the ame ubet A. Downloaded from by guet on June, 06 5

16 The Review of Financial Studie / v 0 n 0 06 Propoition 4. a) Any equilibrium atifying NDOC ha the propertie tated in Propoition 3 and, in particular, feature trictly profitable repurchae at date. b) For α>0 ufficiently mall, an equilibrium atifying NDOC exit. The economic behind Part a) of Propoition 4 i a follow. Under Aumption, the bet firm do not invet in equilibrium. 7 Suppoe that, contrary to the tated reult, they do not repurchae either. Conequently, the final payoff of a high-value firm a i imply S +a. Thi implie that repurchae are unattractive for the top firm ā only if invetor charge at leat S +ā to urrender their hare; in turn, thi require invetor to believe that repurchae offer come from very good firm. But given thee belief, a low-value firm could profitably deviate from it equilibrium trategy by repurchaing at date, thereby triggering belief that it i very good, and then by NDOC) iue at a high price at date. An important implication of Propoition 4 i that the equilibrium outcome of the one-period benchmark economy i not an equilibrium outcome of the full model under NDOC. At firt ight, thi might eem urpriing: one might imagine that one could take the equilibrium of the one-period economy and then aign off-equilibrium belief to make other action, and in particular repurchae, unattractive. However, the dynamic nature of the model make thi impoible. The reaon i that, a jut illutrated, to deter repurchae, belief mut aign a large weight to a repurchaing-firm being a high type; but given thee belief, a deviating firm can iue at attractive term at date. In brief, under NDOC it i impoible to aign belief that deter both date repurchae and date iue. 4.3 Exitence of a repurchae equilibrium atifying NDOC Part b) of Propoition 4 etablihe the exitence of an equilibrium atifying NDOC. 8 Thi i the only reult in the paper that require α>0, that i, ome firm are exogenouly unable to conduct capital market tranaction at date. To undertand the main threat to equilibrium exitence, conider again the example of Section, in which α =0. In the equilibrium decribed, if a firm doe nothing at date, the NDOC retriction implie that invetor believe the firm ha a type a 0.55, regardle of the firm date action. Thi in turn mean that any firm that doe nothing at date i able to repurchae hare at date for a price of +0.55=.55 or le). In particular, firm with a>0.55 would make trictly poitive profit by doing nothing at date, and then repurchaing at date. In thi example, the act of doing nothing at date carrie a lot of ignaling power and arguably too much ignaling power. After all, it i eay to imagine Downloaded from by guet on June, 06 7 Formally, thi i etablihed in Corollary A-4 in the Appendix. 8 Madrigal, Tan, and Werlang 987) give an example of a game in which no equilibrium atifie NDOC. 6

17 Buying high and elling low that a firm doe nothing at date for ome exogenou reaon; for example, perhap it manager fail to get approval for either an iue or repurchae, or i otherwie ditracted. It i exactly thi iue that i addreed by the poibility that a firm i exogenouly inactive at date, that i, α>0. In thi cae, NDOC doe not impoe any retriction on invetor belief about firm that do nothing at date. A an aide, we note that for many parameter value we are able to etablih the exitence of an equilibrium atifying NDOC even for the cae α =0. The example fall in thi cla, becaue doing nothing at date and then repurchaing at date i not a profitable deviation if off-equilibrium belief are that a firm that doe nothing and then repurchae ha a =0.55. Note that thi belief atifie NDOC.) The reaon i that both the deviation profit and equilibrium profit for firm a>0.55 are a.55. However, thi concluion depend on the fact that, in equilibrium, firm ue all their available cah to repurchae hare. For general parameter value and the cae α =0, we have neither been able to etablih a general exitence reult, but nor have we found a counterexample to exitence. 5. Repurchae and the Incidence of Share Iue In the etting we analyze, the ame force namely, a firm uperior information about it value affect both a firm iuance and repurchae deciion. Importantly, the two deciion are linked and, a uch, mut be analyzed together. In particular, we how that the poibility of hare repurchae reduce the fraction of firm that conduct a large enough iue to finance the invetment. More formally, we compare the equilibria of the benchmark one-period model, in which hare repurchae do not arie, with the equilibria of the full model. We how the following: Propoition 5. Conider an equilibrium in which a) a poitive ma of firm engage in trictly profitable repurchae and b) any inactive firm that invet raie weakly fewer fund than any active firm that invet. There exit an equilibrium of the one-period benchmark economy in which trictly more firm invet. 9 Downloaded from by guet on June, 06 Propoition 4 etablihe that condition a) hold in any equilibrium atifying NDOC. Condition b) i vacuouly atified if there are no inactive firm α =0). It i alo trivially atified if there are inactive firm α>0), and any inactive firm that invet raie jut enough fund to invet i.e., S =I). One reaon to focu on equilibria with thi property i that in the one-period 9 In particular, under Condition, there i a unique equilibrium of the one-period benchmark that atifie D, and a greater fraction of firm invet in thi equilibrium than in any equilibrium of the full model. 7

18 The Review of Financial Studie / v 0 n 0 06 benchmark, any equilibrium in which firm raie trictly more funding than required fail D. 0 Propoition 5 etablihe that the poibility of repurchaing hare reduce hare iuance. It i worth highlighting that thi effect doe not in general tem from firm witching from hare iuance to hare repurchae. To illutrate thi point, conider again the example of Section. In the one-period benchmark, firm with a 7.4 iue. In the full model, firm with a 7.07 iue, with firm between 7.07 and 7.4 doing nothing. Intead, the reduction in iuance tem from the fact that, in equilibrium, ome high-value firm trictly profit from repurchaing their tock for le than it true value. Becaue invetor breakeven in expectation, the ultimate ource of thee profit i low-value firm who initially pool with high-value firm and repurchae, in order to reduce the cot of ubequent iue. Low-value firm loe money on the repurchae leg of thi tranaction. In the one-period benchmark, repurchae do not arie Propoition ), and low-value firm do not have to endure thi lo-making leg. Thi allow them to iue at better term, and in turn mean a greater fraction of firm find iuance and invetment) preferable to noniuance. In our model, overall ocial urplu i imply the product of b and the fraction of firm that invet. Hence, an immediate corollary of Propoition 5 i the following. Corollary. Any equilibrium atifying the condition tated in Propoition 5 ha lower ocial urplu than ome equilibrium of the one-period benchmark model. At leat ince Arrow 973), it ha been undertood that the poibility of economic agent ignaling their type by undertaking a ocially cotly action may reult in lower welfare relative to a ituation in which ignaling i prohibited or otherwie impoible. In our etting, however, repurchae carry no deadweight cot, yet welfare i till reduced. 6. Stock Price Reaction and Other Model Prediction 6. Stock price reaction A dicued in the introduction, an important implication of the benchmark one-period model i that a firm tock price fall in repone to an Downloaded from by guet on June, 06 0 Becaue our dynamic model i not a tandard ignaling game in particular, the informed party take action at two eparate date, with a repone from the uninformed party in between), trictly peaking D and other tandard refinement do not apply. Nonethele, we view the reult from the one-period benchmark a providing a good reaon to treat with coniderable upicion any equilibrium of the full model in which firm raie financing trictly in exce of I at date. If each invetor hold a diverified portfolio of hare, thi welfare meaure coincide with the Pareto welfare ranking. For a recent reult along thee line, ee Hoppe, Moldovanu, and Sela 009). 8

19 Buying high and elling low announcement of an SEO, and thi prediction i conitent with a large body of empirical reearch. Our analyi how that the ame force that deliver price drop in repone to SEO alo lead to equilibrium hare repurchae. Here, we analyze the model prediction for price reaction. Recall that, in equilibrium, a ubet of repurchaing firm loe money on the repurchae tranaction. Such firm are nonethele happy to repurchae becaue, by doing o, they improve the term of the ubequent SEO: Propoition 6. Let, ) and ), be trategie each played by a poitive ma of firm, where both allow invetment, that i, S I and S I. Suppoe that, ) i a repurchae trategy, that i, >0, while ), doe not entail repurchae, that i,, 0. Then P, ) P, ), with trict inequality if only a ubet of repurchaing firm invet, that i, Pr )<. Moreover, if <0, then P ) =P, ). The following implication i immediate. Corollary 3. The cumulative price change, P P 0, of a firm that repurchae and then iue to fund invetment i greater than the cumulative price change over the ame period of a firm that iue to fund invetment without repurchaing. Thee prediction are conitent with the empirical finding of Billett and Xue 007), who document that the price repone to an iue announcement i le negative for firm that previouly repurchaed in the preceding three year than for firm that did not. Our model alo predict negative announcement effect for hare iue. Note that thi prediction depend on the comparion of the iue price with the alternative of ) doing nothing and ) repurchaing. Comparion ) i the tandard effect tudied in exiting one-period model. Comparion ) i new to our analyi. An announcement of a direct hare iue without prior repurchae) lead to a price drop relative to an announcement of a repurchae becaue, by Propoition 6, the iue price following a repurchae i higher than the price aociated with direct iue. Our formal reult i a follow. Downloaded from by guet on June, 06 Propoition 7. Suppoe that Condition hold, Condition b) of Propoition 5 hold, and all equilibrium trategie are played by a poitive ma of firm. a) Price fall in repone to hare iue at date : if S <I then E[P, <0] P ), with trict inequality if a poitive ma of firm that play do not invet. b) Price fall in repone to hare iue at date : E[P <0]<P 0. Note that the condition tated in Propoition 7 are required only for Part b), dealing with the date price repone, and are not required for Part a), dealing 9

20 The Review of Financial Studie / v 0 n 0 06 with the date price repone. The condition are ufficient to eliminate the poibility of equilibria in which inactive firm iue at very bad term at date, in which cae date iue could conceivably generate a price increae becaue it ignal that a firm i active rather than inactive. Our model alo generate cro-ectional prediction between, on the one hand, the ize of repurchae and iue, and on the other hand, the price repone aociated with thee tranaction. Thee prediction emerge in equilibria of the model in which multiple repurchae and iue level coexit in contrat to the example, which feature jut one repurchae level). 3 A one would expect, larger repurchae are aociated with higher repurchae price. Similarly, larger iue are aociated with lower iue price. Both prediction are conitent with empirical evidence: ee, for example, Ikenberry, Lakonihok, and Vermaelen 995) orallen and Michaely 003) for evidence on repurchae, and Aquith and Mullin 986) for evidence on iue. Propoition 8. a, repurchae) Let and > >0 be equilibrium repurchae, with aociated price P and P, uch that there exit firm that repurchae repectively, ) and do not conduct any other capital tranaction at any other date. Then P P. b, iue) Let ) ) =0, and =0, be equilibrium trategie uch that S >S I. Then P ) ), >P,, that i, greater cumulative iue i aociated with lower date price Repurchae ize veru SEO ize In our model, firm that repurchae and then iue do o in order to finance an invetment that they initially lacked the reource to undertake. Conequently, a very baic prediction of our model i that when firm repurchae and then conduct an SEO, the revenue from the SEO exceed the cah ditributed via prior repurchae. Conitent with thi prediction, Billett and Xue 007) report that the median and mean ratio of repurchae to ubequent SEO i 6% and 38%, repectively. 6.3 Repurchae, financial contraint, and invetment opportunitie Our model i one in which firm A) poe profitable invetment opportunitie, but B) lack eay acce to outide financing to undertake thee invetment, and moreover, thee fact are publicly oberved. Our main reult how that, under uch circumtance, a ubet of firm repurchae. In contrat, if either aumption A) or B) doe not hold, no repurchae would occur within our model. A uch, our analyi predict that repurchae activity hould be Downloaded from by guet on June, 06 3 One can how, via numerical imulation, that uch equilibria exit. 4 It i alo poible to etablih that >, that i, greater cumulative iue i aociated with maller initial repurchae. A proof i available upon requet. 0