Multiple-Project Financing with Informed Trading

Transcription

1 The ournal of Entrereneurial Finance Volume 6 ssue ring 0 rticle December 0 Multile-Project Financing with nformed Trading alvatore Cantale MD nternational Dmitry Lukin New Economic chool Follow this and additional works at: htts://digitalcommons.eerdine.edu/jef Recommended Citation Cantale alvatore and Lukin Dmitry (0) "Multile-Project Financing with nformed Trading" The ournal of Entrereneurial Finance: Vol. 6: ss vailable at: htts://digitalcommons.eerdine.edu/jef/vol6/iss/ This rticle is brought to you for free and oen access by the Graziadio chool of Business and Management at Peerdine Digital Commons. t has been acceted for inclusion in The ournal of Entrereneurial Finance by an authorized editor of Peerdine Digital Commons. For more information lease contact josias.bartram@eerdine.edu anna.seth@eerdine.edu.

2 The ournal of Entrereneurial Finance Volume 6 Number ring 0-8 Coyright 0 cademy of Entrereneurial Finance nc. ll rights reserved. N: Multile-Project Financing with nformed Trading * alvatore Cantale MD nternational Dmitry Lukin New Economic chool bstract The aer resents an adverse selection-based exlanation of the fact that some entrereneurs choose to finance multile rojects together by issuing a single security and other entrereneurs decide to finance each roject searately. We consider the financing roblem of an entrereneur who has access to two investment rojects and needs to raise external financing to undertake these rojects in the resence of asymmetric information. The entrereneur has rivate information about the quality of the rojects and can choose either to finance the rojects together by issuing a single security or to finance the rojects searately by issuing two securities each backed by the cash flows from the corresonding rojects. We show that the choice of financing deends on the structure of information available to outside investors. f there are two tyes of informed traders and each tye knows the true value of a different roject the entrereneur will always choose to finance rojects searately. However if there is only one tye of informed trader in the market and she has information about the true value of both rojects then the entrereneur may in some circumstances resort to joint financing. * The authors would like to thank ames Brau (the editor) rturo Bris Paolo Fulghieri George Nishiotis Pierre Hillion Theo Vermaelen and audiences at NED MD Tulane University and at the 0 cademy of Entrereneurial Finance Meetings (Los ngeles) for very helful comments. ll errors are ours. alvatore Cantale (contacting author) is at MD nternational Chemin de Bellerive 3 CH - 00 Lausanne witzerland. Phone: ; salvatore.cantale@imd.ch. Dmitry Lukin is at the New Economic chool 47 Nakhimovskii Prosekt uite 7 Moscow 748 Russia.

3 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0). ntroduction Consider an entrereneur who wishes to undertake two investment rojects and because of caital constrains needs to raise the funds in the external financial markets. The value of the rojects that he wishes to finance deends on the entrereneur's quality and the entrereneur's quality is rivate information. Nevertheless financial markets can form exectations about the average quality of entrereneurs and will rice the securities accordingly. s a consequence a good quality entrereneur whom we will define more recisely later on in the aer may discover that the market misrices the securities he issues and he will suffer from dilution. n this economy some traders may choose to become informed for a cost and receive a signal about the true value of the rojects. s a result of informed trading the rice system will become more efficient artially (or fully) revealing the true quality of the entrereneur. Under these conditions the entrereneur will choose his financing strategy under which the rices reveal more information. However to maximize his ex-ante exected wealth should the entrereneur issue only one security backed u by the two investment rojects? Or should the entrereneur issue two securities each security backed u by the cash flows of each roject? This aer resents an asymmetric-information-based exlanation of the fact that some entrereneurs choose to finance multile rojects by issuing a single security (what we refer to as "joint financing") while other entrereneurs decide to finance each roject searately ("searate financing"). We investigate a binary version of the Kyle (985) model with cometitive informed traders and we show that the choice of financing (joint vs. searate) deends on the structure of information available to outside investors. f otentially-informed traders have access to two signals and each signal reveals the quality of only one roject that the entrereneur has we show that the entrereneur will always choose to finance the rojects searately. Under searate financing informed traders trade in the security whose value is very sensitive to their information. s a consequence of this informed trading the rice system becomes more informative and the true value of each roject gets embedded in the stock rice. f instead the entrereneur finances the rojects jointly by issuing a single security the value of the security issued turns out to be less sensitive to the information of both tyes of informed traders. Consequently informed traders' rofits decrease and the number of informed traders that the model endogenously determines decreases. We show as a result that the rice system reveals less information about the quality of the issuer and the ex-ante wealth of the good-quality entrereneur is reduced. For these reasons the issuer will always refer to finance rojects searately. However if otentially-informed traders have access to only one signal and the signal is informative regarding the quality of the entrereneur (that is the signal is informative about the quality of each roject) we show that in some circumstances the good-quality entrereneur (referred as the tye-h entrereneur) may resort to joint financing. This is one of the main contributions of the aer and the intuition can be exlained as follows. Under searate financing if informed traders know the true value of both rojects and exactly one roject turns out to be of bad quality (we refer to this entrereneur as the mixed tye or the tye-m entrereneur) then informed traders will concentrate their activity on the one good roject easing the task of the market maker to rice the security at fair value. However if informed

4 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) traders learn that the entrereneur has two good rojects they will sread their trading across the two securities. This trading searation imlies that the rice system will incororate less information and the searation may force the good-quality entrereneur to issue securities that in equilibrium will be more undervalued (with resect to the tye-m entrereneur with only one good roject). Notice that in this situation searate financing still increases the informativeness of the rice system but the increase benefits only the tye-m entrereneur. When the cost of information roduction is low the equilibrium amount of informed trading is so high that the mixed tye is revealed in the market and informed traders do not make any rofit when only one roject is of good quality. The ex-ante rofits and consequently the equilibrium number of informed traders are adversely affected by the full revelation of the mixed tye. This information sillover effect increases the equilibrium degree of under-ricing of the tye-h entrereneur so that in equilibrium he may refer joint financing. Our aer is related to some of the vast literature on security design. Fulghieri and Lukin (00) develo a model in which a good quality firm needs to raise caital under asymmetric information and adverse selection. They show that the firm refers to issue a more information sensitive security (namely equity) rather than issue a security with low sensitivity to rivate information (debt). By issuing equity the firm encourages outside investors to roduce rivate information about the roject's value. By trading on this information these secialized informed investors reveal their information to the market. This aer is however different from Fulghieri and Lukin (00) in several resects. They consider the roblem of designing a security (debt vs. equity) backed by a roject. We consider the roblem of choosing the number of rojects backing a security. Habib et al. (997) argue that to finance rojects searately is always the referable choice. n the context of a rational exectations model á la Grossman and tiglitz (980) they show that when several divisions of a firm are sun off into several firms the rice system becomes more informative because it reduces the uncertainty that risk-averse uninformed investors have about the value of each single division. s a consequence their exected demand for shares increases thus increasing firm value. Habib et al.'s results deend crucially on the assumtions on the change in liquidity trading because the amount of liquidity trading lays an imortant role in determining equilibrium rices. The difference between their model and our model is that for Habib et al. resorting to searate financing increases both the informativeness of the rice system and the exected utility of informed traders thus driving u the rice. By contrast in our model this latter effect may not materialize when informed traders get a signal on the value of both rojects. f the sillover effects are large enough the rice system becomes more informative only for the tye-m issuer. s a consequence the degree of adverse selection and the resulting dilution for high quality firms increases. When this situation occurs the entrereneur refers joint financing. Chowdhry et al. (00) use a model of security design based on the rincile of information aggregation and show that firms issue different securities to different grous of investors. Each Notice that in a model with risk-averse agents an increase in exected rices doesn't necessarily corresond to an increase in exected utility. ee Marin and Rahi (000) and the so-called Hirshleifer Effect. More informative rices worsen risk-sharing oortunities for risk-averse agents thus lowering their exected utility.

5 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) firm issues securities that are highly correlated with the rivate information of the investor to whom the securities are marketed. n this resect Chowdhry et al.'s aer is similar to ours since we also show that when there are different tyes of investors each tye being informed about one articular roject it is always otimal for the entrereneur to finance rojects searately and to issue different securities. Our aer is however different in two main resects. First we consider an economy with a different information structure with resect to theirs and we show how this difference has a rofound imact on the results of the model. econd the number of informed traders (that in turn determines the degree of information roduction) is endogenous in our model. DeMarzo (005) considers first a roblem of an informed intermediary willing to sell multile assets in the resence of adverse selection and always referring to sell assets searately rather than as a ool in the context of a signalling model; then he also shows that an originator who is uninformed about the true value of the assets will choose to resort to joint financing (to say it in the sirit of the resent aer) because ooling will mitigate the underricing roblem similar to the one described by Rock (986). On the same lines but in a different setting Nanda and Narayanan (999) resent a signalling model in which an undervalued firm slits into comonent businesses in order to obtain cheaer financing. They assume that the market can observe the aggregate cash flows of the firm but not the divisional ones. f the informativeness of cash flows from different divisions is different the firm may be undervalued in the market and willing to signal its true value by raising caital through a costly divestiture. Our model is different - and hence comlementary with resect to these models because the information structure is different. We assume that though insiders of the firm have rivate information about the quality of the firm some investors in the market have more recise signals. ubrahmanyam (99) and Gorton and Pennacchi (993) show that issuing baskets of securities can decrease the losses of liquidity traders caused by informed traders. Baskets of securities have lower volatility than do individual securities. Hence the ability of informed traders to rofit from their rivate information is diminished. n contrast with their aers in our model the entrereneur decides the financing strategy. That is the decision is suly driven. n their model this decision is demand driven. dditionally our model is also related to the vast literature on venture caital. Most of the theoretical literature on venture caital considers the financing and incentive roblems facing an entrereneur trying to finance a single roject. Notable excetions include Kanniainen and Keuschnigg (003) Bernile et al. (007) Fulghieri and evilir (009) nderst et al. (007) and nderst and Müller (003). Kanniainen and Keuschnigg (003) and in a similar sirit Bernile et al. (007) consider an entrereneur with multile identical risky rojects and determine the relation between the venture caital ortfolio structure and the effort level. Fulghieri and evilir (009) consider the incentive of a venture-caital firm to concentrate its attention on one or two ventures. nderst et al. (007) show that the deth of the entrereneur's financial ockets may hel resolve his financing roblems. The common thread of these aers is that the authors investigate the san of a venture caital ortfolio or as in nderst et al. (007) investigate the role of the venture caitalist who is cash constrained in an economy where the san of the venture-caital ortfolio is fixed. n this aer we fix the number of rojects and we investigate 3

6 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) the security design roblem (i.e. whether an entrereneur has to issue one or two equity securities) in a model with information roduction and adverse selection. Of all the research nderst and Müller (003) address a roblem that is most similar to ours although with many differences. They in fact study the otimal contracting between individual investors and individual roject managers (what they refer to as "decentralized financing") and between individual investors and a headquarter that runs multile rojects backed by the same security (what they refer to as "headquarter financing"). They model a multi-eriod economy in which the otimal contract offered is debt address a moral hazard roblem and exlore the relation between financing constraints and the organizational structure. We model a one-eriod economy in which we restrict our attention to equity consider the adverse selection roblem an entrereneur faces and exlore the effects of information roduction on financing. The remainder of the aer is organized as follows. n ection we describe the economy and introduce the model. n ection 3 we show that if the signal reveals the quality of the roject searate financing always dominates joint financing. n ection 4 we assume that the signal reveals the quality of the entrereneur and we show that arameter restrictions exist such that searate financing could be otimal. n ection 5 we discuss the results and conclude the aer. n the endix we include the discussion of a model without information roduction and a result of financing when the signal reveals the entrereneur's quality and markets are integrated.. The Model Consider an economy that lasts for one eriod and the choices available to an entrereneur who wishes to undertake two investment rojects and being caital constrained needs to raise the funds in the external financial markets.. Players ctions and Events We assume that all agents in the economy are risk neutral and the riskless interest rate is normalized to 0. gents in this economy are entrereneurs market makers and outside investors (investors who trade on information and liquidity traders). t t 0 an entrereneur has access to two different investment rojects that are indexed resectively by i. Project i requires an investment of i dollars at time t 0 and has a value v ~ i at time t. Without loss of generality we assume that. The realization of v ~ i can be either v or 0. f v~ i v then the roject is of good quality. f the roject yields 0 ayoff it is of bad quality. Outside investors and market makers have a common riorrobability distribution over the quality of both rojects according to which the rojects are indeendently and identically distributed with the robability of a roject being of good quality given by. The NPV of each roject is ositive: Ev~ ~ E v v. Entrereneurs have rivate information about the quality of the rojects. Namely they observe a 4

7 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) random variable V ~ ~ that is the sum of the values of roject and : V v~. v~ Therefore we can view V ~ as the entrereneur's tye in the sense that it shows the ability of the entrereneur to find rofitable investment oortunities. n this sense a higher value for V ~ imlies better entrereneurial quality. Hence we model three tyes of entrereneurs denoted by h m and l. ~ Tye-h entrereneurs observe that V v and learn that both rojects are good; tye-m ~ entrereneurs observe that V v and learn that one roject is good and the other is bad but they do not know which roject is bad and which roject is good; finally tye-l entrereneurs learn ~ from V 0 that both rojects are bad. The entrereneur is cash-constrained and needs to raise funds in the financial markets. The set of securities the entrereneur can issue is restricted to equity that he can sell in the form of an PO. Given that the entrereneur has access to two investment rojects and the set of securities is restricted to equity the entrereneur has two financing strategies available. First he can raise the required funds by issuing one security backed by the cash flows from both rojects. econd the entrereneur may decide to finance the rojects searately. n this case each roject will belong to a different comany and the entrereneur will raise the funds to finance roject i by issuing equity of comany i. From now on we will refer to equity of comany i as security i. The entrereneur will choose the financing strategy that maximizes his exected wealth. There are two tyes of outside investors: liquidity traders and informed traders. Liquidity traders exert an exogenous dollar demand that is a random variable. n the case of joint financing the entrereneur issues a single security and we denote liquidity traders' demand for this security by u ~. n the case of searate financing we denote liquidity traders' dollar demand for security i by u ~ i. We imose the following set of assumtions on liquidity traders' demand. ssumtions. The dollar demands from liquidity traders u ~ and u ~ are uniformly distribute resectively in U ; and U 0;a i ;. Liquidity traders' demands ~u and ~u are indeendent; 3. 0 a a a. These assumtions simly make the model tractable and allow us to obtain closed-form exressions for the variables of interest. nterestingly and one of the modeling novelties of the aer we do not imose any restrictions on the amount of noise trading in the case of joint financing relative to the amount of noise trading under searate financing (that is we do not need i This restriction on the information structure of insiders rules out artially ooling equilibria when the entrereneur with only one good roject deviates and raises the funds necessary to finance only the good roject. 5

8 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) any restriction on the arameter ). Kyle-style models as the literature generally use do not allow to obtain results on multile-roject financing that are robust to changes in the relative amount of informed trading and use restrictive assumtions about the amount of liquidity traders for each financing strategy. The assumtion commonly used in the literature is that the variance of liquidity demand is the same. n the resent model the amount of liquidity traders in the case of joint financing can be greater or smaller than the amount of liquidity trading under searate financing. The results are comletely indeendent of this assumtion. nformed traders are atomistic act as rice takers and have access to the information-roduction technology. Each otentially informed trader is endowed with c i dollars. Before trading takes lace but after the entrereneur announces his financing choice each otentially informed trader decides whether to become informed at a cost c. he can then send the remaining dollar by buying a fraction of a single security in the case of joint financing or fractions of each security in the case of searate financing. Cometitive market makers have a rior on the amount of informed traders. They observe the sum of total dollar demands from liquidity and informed traders and use Bayes' rule to udate their exectations regarding the quality of the securities they market. They therefore set rices equal to exected values conditional on the observed total order flow (denoted as throughout this aer).. The Equilibrium Concet We restrict our attention to ooling equilibria and more secifically we consider a ooling equilibrium in which tye-h entrereneur chooses the financing strategy that minimizes his dilution costs and tye-m and tye-l ool with tye-h by mimicking his financing strategy. We eliminate equilibria other than ooling by assuming that the tye-l chooses the strategy that maximizes the exected share of the rojects the issuer retains. 3 n this case tye-h cannot searate because tye-l will follow the same strategy. n equilibrium in which tye-h and tye-l ool and choose one financing strategy and tye-m searates and chooses the other financing strategy is not ossible for the same reason. Thus the entrereneur will raise an amount of funds that is exactly equal to the required investment because the tye-h entrereneur will issue securities that are undervalued in the market. n the case of joint financing the entrereneur will issue equity in the amount necessary to raise. When the entrereneur finances rojects searately he raises by selling security and raises by selling security. The entrereneur announces whether he will finance the rojects jointly issuing a single security in the amount of or he will issue two securities at the beginning of the eriod t 0. n equilibrium the market maker determines the fraction of equity that the entrereneur issues and sells to outside investors denoted as in the aer in the case of joint financing or the fraction of security i in the case of searate financing. n this economy we define an equilibrium as follows: i 3 We have assumed for simlicity that the values of both rojects are equal to 0 for the tye-l entrereneur and insiders will have zero exected wealth under any financing strategy. Therefore they are indifferent between joint and searate financing. 6

9 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) Definition n equilibrium is given by a measure of informed traders an amount and an informed traders' break-even condition such that the following three requirements are satisfied: a. Market makers' beliefs about the amount of informed traders in the market are rational that is ; b. The fraction of equity that the entrereneur needs to sell in order to raise the required amount of financing is given by where is the total order flow submitted E v to the market makers; c. The ex-ante exected rofits of each informed trader are zero. Deending on the informativeness of the signal both market makers and informed traders will lay different strategies and the game they lay will lead to different equilibria. n the following section we assume that two tyes of otentially-informed traders exist. The first tye can learn the true value of the first roject and only of the first roject at a cost c. The second tye can learn the true value of the second roject and only of the second roject at a cost c. n other words when this situation occurs the signal reveals the quality of the roject. n ection 4 we assume that only one signal is available for otentially-informed traders and this signal reveals erfectly the quality of the entrereneur: if an informed trader acquires the signal she learns the true value of both rojects. We show that the results of the model change significantly when a otentially informed trader can observe the true value of both rojects. Finally we must notice that in the current economy but in the absence of information roduction the choice of financing becomes irrelevant and the entrereneur is indifferent between searate and joint financing. This result that we derive more formally in the endix imlies that the different conclusions that we reach in what follows regarding the choice of financing can be attributed solely to the effects of information roduction. 3. The ignal Reveals the Quality of the Project n this section we assume that a trader can send c dollars and becomes informed about the quality of one roject. More recisely a trader of tye can send c dollars and receives a signal that is informative about the first roject. trader of tye can acquire a signal about the second roject at a cost c. Without loss of generality we assume that c c c. Both signals are erfectly informative: after acquiring the information an informed trader of tye i knows the true value of roject i. Let si gb be a signal about the quality of roject i received by a trader of tye i. f s i g the signal is good and v ~ i v at t. f s i b then the signal is bad and v~ i 0 at t. n this case the signal reveals the quality of the roject but not the quality of the entrereneur. n what follows we first derive equilibria for the different choices of financing. Then we comare these equilibria and choose the one that maximizes the ex-ante exected wealth of the tye-h entrereneur. 3. earate Financing Under searate financing the entrereneur offers two securities for sale each backed by the cash 7

10 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) flows from each roject. Each security is sold in the corresonding market. We assume that markets are segmented that is market makers in one market cannot observe the total order flow in the other market. n what follows we derive the equilibrium in one market. The equilibrium in the second market will be identical First Market The dollar demand of liquidity traders in the first market is uniformly distributed on density function given as follows (we omit subscrits for notational simlicity): g u a u 0 a 0 u 0 a [ 0 a] with () t the beginning of the eriod a measure of informed traders decides to become informed. nformed traders are atomistic and act as rice takers. f the signal is good they will buy one dollar worth of the security and the total dollar demand from informed traders will be. f the signal is bad they do not submit any order. 4 The demand of liquidity traders u is realized at the same time. nformed and liquidity traders submit their orders simultaneously to market makers. Market makers observe the total order flow u and use Bayes' rule to udate their robability of the roject being good setting the rice for the security equal to the conditional exectation of the cash flows of the roject. M Let reresent market makers' beliefs about the equilibrium amount of informed traders in the market. Given uniformly distributed liquidity demand Bayesian udating takes a simle form. f M the total order flow is less than then market makers learn that the demand from informed traders was zero and hence the roject is bad. n this case the issue fails. f the total order flow M is greater than but less than a then the osterior robability of the roject being good is g u equal to the rior robability (from Bayes' rule: v~ ( ) Pr v ). f g( u ) ( ) g( u) the total order flow is greater than a market makers correctly infer that there is ositive amount of informed trading in the market and the roject is good. n equilibrium market makers' beliefs M are rational. That is. The roortion of equity the firm has to sell is then given by: Ev v v a a () 4 hortselling is not ermitted for informed and liquidity traders. Only market makers are allowed to short sell the security in order to absorb net order flow and avoid rationing. 8

11 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) This amount is therefore iecewise constant. When the total order flow is low enough there is no udating even if the roject is good. However when the realization of the total order flow is high enough market makers correctly infer that the roject is good (full revelation) and the rice of the equity is set equal to its true value. Given the ricing rule () the ex-ante exected rofits of each informed trader are given by: E u v c (3) We can rewrite the last exression as: vv vv Pru a ( )Pr Pru a Pru a u a c c v v c (4) where the first equality comes from the fact that the second term in arenthesis is zero. When liquidity demand is high enough the issuer's tye is revealed and informed traders do not make any rofits. ince the robability that the roject's tye is not revealed is equal to Pr( u a ) we can derive the equilibrium amount of informed traders by equating (4) to zero: a c 0 a (5) 3... Exected Wealth of the Entrereneur The residual fraction of equity that the entrereneur with the good roject retains deends on the realization of the demand of liquidity traders. f this amount is low no udating occurs on the robability of the roject being good and the issuer suffers from dilution. f the realization of the liquidity demand is high enough the tye of the roject is fully revealed (as being good) to the market and the entrereneur sells the security for its true value. We can exress the ex-ante exected wealth of the issuer of the good roject as: U G v v Pr u a v Pru a a v a (6) Using the zero rofit condition in (5) and simlifying we obtain that the exected wealth of the 9

12 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) entrereneur in one market conditional on the roject being good is given by: U G v c (7) The exected wealth of the entrereneur in (7) consists of two terms. The first term v is the full information value of the roject. ntuitively ositive-informed trading occurs only when the value of the roject is equal to v. Hence the entrereneur is able to obtain the full information value of the roject while bearing some costs. The second term the cost borne by the issuer is the er dollar cost of information roduction multilied by the size of the issue and adjusted for the robability that informed traders can use this information to make rofits Both Markets n the second market the exected wealth of the entrereneur who has a good roject is given by the same exression (7). The tye-h entrereneur has two rojects that are both of good quality. Hence in the case of searate financing we have roven the following lemma: Lemma When the entrereneur finances the rojects searately the equilibrium ex-ante h exected wealth of the tye-h entrereneur is given by: U U h G c U v (8) That is the equilibrium ex-ante exected wealth of the entrereneur of the tye-h is equal to the NPV of the two rojects minus the dilution costs (which are equal to c / ). 3. oint Financing n the case of joint financing the two rojects are ooled together and the value of the security that the entrereneur sells is given by: V v v v with robability v with robability v with robability 0 with robability (9) The entrereneur has to raise the amount necessary to finance both rojects that is. n the revious case (searate financing) a certain number of informed traders were informed about the true value of the securities in each market. But the information they had was homogeneous among traders in that market. n the market for the first security for examle all informed traders had the same information regarding the first security and no trader had suerior information about the ayoff of the second roject. The situation is different in the case of joint 0

13 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) financing: the entrereneur issues only one security and its ayoff deends on the values of both rojects. n such a case two tyes of informed traders will be trading in equilibrium and both tyes have less than erfect information about the true value of the security. Let and be the equilibrium numbers of informed traders of each tye. n the endix we rove the following: Result The number of informed traders of the first tye is equal to the number of informed traders of the second tye. That is. The demand of liquidity traders is uniformly distributed on [ 0 ]. Market makers given their rational beliefs will observe the total order flow and udate their exectations about the value of the cash flows. Consider Figure. Deending on the total order flow no udating full revelation or artial revelation of the entrereneur's tye will occur. Figure From Figure we can see that we have five different regions for the total order flow u. f 0 then market makers infer that both rojects are bad and the issue fails. f then market makers infer that both rojects cannot be good and use Bayes' rule to calculate their exectations regarding the cash flows: 5 E V v v f then no udating occurs market makers do not learn any information and the 5 Notice that in this case the firm can be either of tye-m or tye-l. Without loss of generality we assume that the issue fails.

14 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) ~ * v conditional exected value is equal to their rior i.e.: E V. f then the market makers infer that both rojects cannot be bad and the conditional exected value is given by EV ~ * v. Finally if the total order flow falls in the region between and we have full revelation that both rojects are of good tye and the conditional exected value will be equal to the true value of the cash flows: that is v. Each tye's informed traders' rofits will deend on the realization of the order flow. The order flow will in turn deend on the quality of the rojects. f both rojects are good then informed traders of both tyes will be trading in the market. f for examle only roject is good then only informed traders who bought a signal about the first roject will be resent in the market. Consider the ex-ante exected rofits of an informed trader who decides to urchase a signal about the value of the first roject. With robability she will receive a good signal and will submit a buying order. Her rofits are then given by: v v Pru v v u Pr v v ( ) u Pr v v ( ) Pr u c (0) The intuition behind (0) goes as follows. The first two terms reresent the er dollar rofits when both rojects are good. The robability that this condition will be realized is. The total order flow is then equal to u and can fall in regions V and V of Figure. The first term is the er dollar rofit when falls in the third region; the second term is the rofit when falls in the fourth region. When the total order flow falls in the fifth region the tye is fully revealed and the rofits of an informed trader are zero. imilarly the third and the fourth terms of (0) give the er dollar rofits when the first roject is good but the second roject is bad. The total order flow is then u and can fall in regions and V of Figure. n region the issue is cancelled. The third and the fourth terms reresent the rofits when the total order flow falls in regions and V resectively. ubstituting the values of the robabilities and simlifying the terms we can write the zero rofit condition for the informed trader as:

15 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) c 0 () From the above zero rofit condition it follows that the equilibrium amount of informed traders is equal to: c () Consequently the exected wealth of the tye-h entrereneur is given by: U h v v ( ) v (3) The first term corresonds to the wealth of the tye-h entrereneur when the total order flow is not informative; the second term to the case when there is artial revelation; and the third term to the case when the tye is fully revealed to the market. Plugging the exression for () into (3) we obtain the following lemma. Lemma The exected wealth of the tye-h entrereneur under joint financing is given by: from U h v c( ) 3 (4) Notice that as in the case of searate financing the exected wealth of the tye-h entrereneur 3 consists of two terms. However now the first term v is less than the full information value v because ositive informed trading occurs not only when the issuer is of tye-h but also when the issuer is of tye-m. That is the rice system is less informative. The cost borne by the entrereneur is again the cost of information roduction er dollar of trade c multilied by the size of the issue ; however the robability adjustment is now equal to. 3.3 Choice of Financing When the ignal Reveals the Quality of the Project We are therefore ready to state our first result: Proosition f there are two tyes of informed traders in the market and each tye is informed about the true quality of only one roject then the entrereneur will always finance the rojects searately. Proof. We need to rove that the tye-h entrereneur will suffer from less dilution when he finances the rojects searately. That is we need to show that the exected wealth is greater 3

16 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) under searate financing than under joint financing. Using Lemma and the definition of given in () we simlify and get: U v h (5) From () we have that: c (6) Then using (5) and (6) we obtain: U h c v c v v U h where the first inequality comes from (6) and the last equality comes from Lemma. When we have two tyes of informed traders in the market each informed about the quality of one roject financing rojects searately is a dominating strategy. Pooling rojects together reduces the value of information for each tye of informed traders and the number of informed traders decreases. Notice in fact that by comaring (5) and () we see that the condition a holds. That is the relative amount of informed trading is greater in the case of searate financing than in the case of joint financing. Or equivalently the rice system is more informative in the case of searate financing for a given amount of informed trading. When fewer informed traders trade on their information the rice system becomes less informative and the degree of adverse selection in the market increases reducing the exected wealth of the entrereneur. Therefore the entrereneur will always finance the rojects searately. 4 The ignal Reveals the Quality of the Entrereneur We have assumed so far that two signals are available: one about the first roject and the other about the second roject. n this section we assume that there is only one signal available to otentially-informed traders and this signal reveals erfectly the entrereneur's quality. n other words if an informed trader acquires the signal she learns the true value of both rojects. More formally the set of available signals consists of one erfectly revealing signal s s s where s g b. f s g i i then roject i is good; if s i b then roject i is bad. otentiallyinformed trader can ay a cost and observes the signal g g g b b g bb. t turns out that the results of the model change drastically when the structure of available signals is 4 c c s (7)

17 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) different. 4. oint Financing t is more intuitive to consider first the case when the entrereneur announces that he will finance both rojects by issuing a single security. The ayoff structure to this joint firm is given by (9). Let be the number of informed traders in equilibrium. The strategy of each informed trader will now deends on both s and s. f both rojects are good that is s ( g; g) then the informed trader will buy one dollar worth of security. f both rojects are bad that is s ( b b) then the informed trader will not trade. Her decision whether to trade or not when one roject is good and the other is bad i.e. g b b g will deend on the value of the arameters of the model. We will roceed in the following order. First we solve the model for the case when informed traders do not buy the security when they learn that g b b g and then for the case when they do trade when cases will indeed be the equilibria of the model.. Then we state under what arameter values these Let us first assume that informed traders do not trade when only one roject is good. That is let us assume that each informed trader uses the following equilibrium strategy: buy one dollar worth of the security when both rojects are good and do not trade otherwise. Given this informed traders' strategy market makers will udate their exectations about the value of the cash flows in the following way. f the total order flow is less than then both rojects cannot be good and the issue fails. f the signal is not informative and the osterior exected value for the value of the firm is equal to its rior: that is ~ EV v. f the total order flow is greater than then both rojects are good and the ~ exected value of the firm is given by E V v The zero rofits condition of the informed traders is given by: s g b b g s. s Pru c 0 (8) nformed traders will trade only when both rojects are good and will earn ositive rofits only when the total order flow is below. The ex-ante exected wealth of the tye-h entrereneur is given by: U h v Pr u (v ) Pru Using (8) to exress Pru and substituting it into (9) we find that if in equilibrium informed traders trade only when both rojects are good then the ex-ante exected wealth of the tye-h entrereneur in the case of joint financing is given by: 5 (9)

18 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) c v U h (0) Note that the result is almost identical to the case of searate financing in the revious section. The only difference is that the cost is divided by instead of because the ex-ante robability of submitting an order for an informed trader is now. Let us now consider the case when informed traders also submit buying orders when only one roject is good. n this case informed traders will not trade only if both signals are bad. fter adjusting the market makers' ricing rule and following a similar logic as in the revious case it is straightforward to rove that if in equilibrium informed traders do not trade only when both rojects are bad then ex-ante exected wealth of the tye-h entrereneur in the case of joint financing is given by: c U h v () The first term in arenthesis is greater than the first term in (0) reflecting that ositive informed trading reveals less information. The second term is less than because the robability of U h h ositive informed trading is higher. Note that = when c. This value turns out to be the threshold such that for all values of c below this value a ositive-informed trading equilibrium occurs only when the issuer is of tye-h and for all values of c above this threshold we find a ositive-informed trading equilibrium when the issuer is either tye-h or tye-m. To rove the following lemma we have only to check that informed traders' strategies are indeed otimal given market makers' beliefs. Lemma 3 f there is a ositive amount of informed traders in equilibrium then for all values of c such that c informed traders trade only when both rojects are good and the ex-ante exected wealth of the tye-h entrereneur in the case of joint financing is given by: c U c v U h () and for all values of c such that c informed traders do not trade only when both rojects are bad and the ex-ante exected wealth of the tye-h entrereneur in the case of joint financing is given by: U h v c (3) 6

19 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) 4. earate Financing When the entrereneur announces that he will finance the two rojects searately informed traders' strategies change in the following way. f only one roject is good then she will trade in this security. f both rojects are bad she will not trade. f both rojects are good she will trade in the security where exected rofits are higher. n equilibrium the exected rofits will be the same and an informed trader will be indifferent between trading in the first or the second security so that half of the informed traders will trade in the first security and the other half will trade in the second security. 6 s a result "excessive" informed trading will occur when the entrereneur is tye-m and has only one good-quality roject and less informed trading will occur when the entrereneur is of tye-h. s we will show the tye-h entrereneur is worse off because of this information sillover effect. Note that the equilibrium strategy the informed traders use now deends on the values of both rojects. ccordingly we can reasonably assume that market makers for a security correctly anticiating the behavior of informed layers in equilibrium will observe the total order flow in the other security to learn additional information when setting the ricing rule. n this section we will start our analysis assuming that markets are segmented and the market makers cannot observe the total order flow in the other market. 7 We can write the ex-ante exected rofits of each informed trader as (we again omit subscrits for notational simlicity): Pru a ( ) Pru a c (4) where the first term reresents the trading rofits when both rojects are good and the number of informed traders in each security is and the second term reresents the trading rofits when only one roject is good and all informed traders trade in this security. Note that in the above calculations we assumed that Pr u a 0 n other words when the equilibrium amount. 6 We imlicitly assume that informed traders cannot slit their orders. The informed trader then randomizes between trading in the first and the second markets when both rojects are good. The robability of choosing each market is the same and equal to For the sake of comleteness in the endix we relax this assumtion allowing markets to be integrated and we show that. the main results of this section holds (i.e. for some arameters of the roblem the entrereneur may resort to searate financing) and. contrary to intuition the exected wealth of the tye-h entrereneur can be lower than in the case of segmented markets. 7

20 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) 8 of informed trading is low enough there is a ositive robability to earn non-zero rofits even when only one roject is good. From (4) the equivalent condition is f the cost of information roduction is lower than the above threshold then the good roject is erfectly revealed when the second roject is bad and all informed trading is concentrated in the market with the good roject. From now on we assume that and we consider only the case when informed traders do not make any rofits when the issuer is of tye-m. Under this assumtion the effect of the information sillover is of imortant magnitude and the degree of adverse selection in the case of searate financing may become so high that the issuer will refer to finance rojects jointly. f the second term of (4) disaears and the zero rofit condition becomes: (5) The exected wealth of the tye-h entrereneur from financing the first and the second roject is the same. To calculate his exected wealth we consider only one security and multily this exression by two. That is the ex-ante exected wealth of the tye-h entrereneur becomes: (6) where the third equality is obtained by substituting (5). We have therefore roved that: Lemma 4 f a ositive amount of informed trading occurs in equilibrium and the cost of information roduction is below then ex-ante exected wealth of the tye-h entrereneur in the case of searate financing is given by: (7) 4.3 The Choice of Financing Whether the entrereneur chooses searate or joint financing deends again on the difference in exected wealth.. ) ( c c c c c c c 0 ) ( Pr c a c a u Pr ) ( Pr c v a v a u v a u v U h c c v U h

21 alvatore Cantale Dmitry Lukin/The ournal of Entrereneurial Finance 6 (0) Proosition f there is ositive amount of informed trading in equilibrium the entrereneur's financing choice will deend on the information roduction costs:. When the cost of information roduction c is low enough c min c then the entrereneur is indifferent between joint and searate financing.. When the cost of information roduction c satisfies c c then the entrereneur will finance rojects jointly. Proof. Let us first consider the case when c. n this case under joint financing and the strategies layed in equilibrium informed traders trade only when both rojects are good. Using h h Lemma 4 and Lemma 5 and more recisely from () and (7) we observe that U U and the entrereneur is indifferent between joint and searate financing. Now let us consider the case when c c so that the information roduction cost is at an intermediate level. We assume ( ) here that c which is equivalent to Using (3) and (7) we can write the U U h h difference between and as: 3. h h c U U 0 (8) given that c. The intuition behind this result is simle. Under both searate and joint financing informed traders make ositive rofits only when both rojects are good. Recall in fact that under joint financing given that c ositive informed trading occurs only when both rojects are good; under searate financing when c c the tye-m issuer does not make any rofits. s a result the relative value of the demand from informed traders is the same for both financing strategies. Given market segmentation the equilibrium in each security market under searate financing is simly a scaled-down version of the equilibrium under joint financing. However when the information roduction cost is in the stated range we have two countervailing forces at lay on the relative amount of informed trading. On the one hand under the arameter restrictions the tye-h entrereneur faces less adverse selection under joint financing. ntuitively in the case of searate financing when the cost of information roduction is low enough informed traders make rofits only when both rojects are good. However when the rojects are financed jointly informed traders make rofits not only when both roject are good but also when only one roject is good. That is informed traders make rofits in more states of the world than in the case of searate financing. The ability to generate rofits in more states of the world increases the relative amount of informed trading under joint financing thus decreasing the dilution costs that cause the issue. On the other hand under joint financing ositive informed trading occurs not only when the entrereneur is of tye-h but also when he is of tye-m. Consequently the market makers cannot searate tye-h from tye-m entrereneurs even after the high realization of the total order flow reveals that there is a ositive amount of informed trading. That is the market will realize that the entrereneur is either of tye-h or of tye-m and the entrereneur of tye-h continues to be underriced. From tye-h entrereneur's oint of view the inability of the market makers to searate tyes decreases the relative imact of informed trading on the 9