Optimal Organization of Financial Intermediaries

Transcription

1 Otimal Organization of Financial Intermediaries Siros Bougheas Tianxi Wang Setember 2014 Abstract This aer rovides a unified framework for endogenizing two distinct organizational structures for financial intermediation. In one structure, called Bank, the intermediary is financed by issuing debt contracts to investors, and thus resembles commercial banks. In the other structure, called Fund, the intermediary is financed by issuing equity contracts to investors, thus resembling rivate-equity funds. The aer considers the advantage of the Bank structure relative to the Fund structure. It finds that in the former incentives can be rovided in a less costly way, but the latter is more robust to negative shocks on the asset side. Our model redicts that relative to banks, rivate equity funds are more involved in the running of the firms that they finance, contribute more to the success of these firms, and rovide funds to higher-risk, higher-return firms. JEL Classification: D86, G00 1 Introduction In economic environments where transaction costs, informational asymmetries and incomlete markets inhibit direct relationshis between borrowers and lenders, financial intermediaries rovide indirect ways for bringing the two arties together. U to a very large extent this intermediation role is erformed by banks. A defining characteristic of banks is that on their liability side they raise funds mainly by offering fix obligations to investors deositors. In the last twenty years, we have seen a raid growth of an alternative class of financial intermediaries, namely, rivate equity funds, that, unlike banks, raise School of Economics, University of Nottingham, University Park, Nottingham ng7 2RD, UK; siros.bouhjeas@nottingham.ac.uk, tel.no: Deartment of Economics, University of Essex, Colchester, CO4 3SQ, UK. wangt@essex.ac.uk. Fax:

2 funds by offering equity claims to their investors who are known as limited artners see Mertrick and Yasuda, Some tyes of rivate equity funds finance, like banks, a variety of new investments for firms unable to access directly the caital markets. For examle, venture caital secializes in financing young, innovative firms, growth caital finances exansion activities of relatively mature firms, and mezzanine caital offers investors referred equity to finance activities of small firms that are unable to raise suffi cient funds in the caital market. 1 The volume of caital managed by rivate equity funds has risen from $5 billion in 1980 to $100 billion in 1994 to about $1 trillion in The co-existence of two distinct organization structures for financial intermediation raises the following questions. What are the relative advantages of each structure? Which are the tyes of firms more likely to seek funding from each structure? We address these questions, in a unified framework where deending on the values of arameters, the otimal equilibrium contractual arrangement in equilibrium corresonds to one of these two structures. In our model, an intermediary that bridges entrereneurs and many small investors rovides a service that can otentially increase the robability of success of the rojects that it finances. Examles of this tye of services include consultation, marketing, and controlling entrereneurial moral hazard. The rovision of this service, however, is unobservable to the investors. As a result, the intermediary is liable to a moral hazard roblem. So far, our model is similar to Holmström and Tirole The innovation of our aer is that, after the funds have been invested, the rojects are subject to a shock, oserved only by the intermediary, that divides rojects into two tyes: A tye h roject can benefit from the intermediary s service while a tye l roject cannot. Using a mechanism design aroach we solve for the otimal contracts on both sides of the intermediary s balance sheet. We find that the equilibrium organization structure of financial intermediation can take one of only two tyes, deending on the nature of securities they issue to investors. It is either debt in which case we will refer to the organization structure as Bank, or it is equity in which case we will refer to the organization structure as Fund. The trade-off between Bank and Fund is that while Bank has the advantage of roviding incentives 1 We are mainly concerned with intermediaries that finance new rojects so we will ignore rivate equity funds secializing in leverage buyouts that is in the acquisition of established firms and other tyes of intermediaries that invest in financial assets such as hedge funds and mutual funds. 2 The first coule of figures were taken from Fenn, Liang and Prowse 1995 while the last figure is reorted in Metrick and Yasuda To ut these figures in ersective, the total loans and leases granted to businesses and households by U.S. commercial banks form 1/10/2012 till 30/9/2012 according to FDIC was aroximately $7 trillion. 2

3 to the intermediary at a lower cost, Fund is more robust to negative realizations tye l of the shock. In order to understand this trade-off, consider the case where the intermediary considers financing two rojects that are known to be tye h. Then, as Laux 2001 has demonstrated, in equilibrium the intermediary makes qualitative asset transformation. The contract that the intermediary agrees with the investors is debt, leaving the intermediary nothing when only one roject succeeds. Next, consider what haens when we introduce the shock which imacts the rojects after the investments have been made. Suose that one roject is tye l and the other is tye h. Further, suose that the robability of success of either tye l rojects or tye h rojects that are not monitored is very close to zero. Under the debt contract the intermediary gets nothing even if it increases the success robability of the tye h roject through monitoring. Therefore, the intermediary has no incentives to monitor that roject. Put differently, bad news about one roject ruins any incentives to monitor any of the rojects. In contrast, suose that the intermediary is financed with equity contracts. Whenever one roject succeeds, the intermediary receives a share of the revenues from the successful roject, which offers it incentives to monitor the tye h roject thus increasing its success robability even if the other roject is destined to fail. In summary, the Bank structure rovides incentives at a lower cost, but the Fund structure is more robust to bad news. We show that this trade-off between Bank and Fund holds for a wide set of arameters and that the two organization structures are the only ones occurring in equilibrium. Our model makes the following redictions: a equity-financed intermediaries are more intensively involved than banks in monitoring the firms that they finance; b the bigger the difference that the intermediary s inut makes, the more likely it is that the intermediary is organized as a Fund, and c the likelihood of Bank financing relative to Fund financing is ositively correlated with the cost of monitoring and negatively correlated with the risk of the rojects. The above redictions are consistent with the evidence reorted by Metrick and Yasuda 2010 for rivate equity funds. In articular, rediction c imlies that rivate equity funds are more likely than banks to finance rojects with small robability of success and huge returns conditional on success which is consistent with the evidence rovided by Sahlman 1990 and Kerr, Nanda and Rhodes-Krof 2014 for venture caital. Our work is related to various strands of the financial economics literature. For single-roject financing, Innes 1990 is the first to demonstrate the otimality of debt for roviding incentives under moral hazard. Laux 2001 has demonstrated that with multile rojects cross-ledging can further enhance incentives; see also Tirole ch.4, More generally, the otimality of debt contracts in roviding in- 3

4 centives related to information roblems has been reeatedly demonstrated in the literature; see among others, Diamond 1984, Gale and Hellwig 1985, and Gorton and Pennacchi In contrast, in this aer, by introducing uncertainty about roject tyes into a setting similar to Holmström and Tirole 1997, we show that the otimal security that the intermediary issues to investors can be either debt or equity. In our model intermediaries rovide a second service, namely, they gather information about their clients. That articular role has also been addressed by Ramakrishnan and Thakor 1984 and Millon and Thakor 1985, however, in these aers intermediaries do not transfer money from investors to entrereneurs. In contrast, in our aer intermediaries learn roject tyes after the funding has taken lace. Our aer follows a well-established literature that views intermediation as a solution to the roblem of delegated monitoring. For examle, Diamond 1984 finds a role for financial intermediation in Townsend s 1990 costly-state verification framework by showing that suffi cient diversification reduces delegations costs to zero. 3 In Calomiris and Kahn 1991 the incentives to monitor are rovided by the ability of deositors to withdraw their deosits at will. The monitoring service that intermediaries rovide in our model is similar to that in Holmström and Tirole The aim of all these aers has been to identify the advantages of bank loans over direct finance while our main concern is to comare the solutions to the delegated monitoring roblem rovided by alternative organization structures for financial intermediaries. Lastly, our aer is also related to the fast growing theoretical literature on rivate equity that mainly secializes on the organizational structure of venture caital. 4 Although our model is too abstract to account for the many comlex arrangements associated with these methods of finance such as stage financing and the decision to go ublic that demand a dynamic framework; see Gomers, 1995, it rovides a unified framework that sheds lights on rivate equity funds in a broad ersective by letting them comete on a level laying field against another main form of financial intermediation, namely, banks. Further, our model suggests that some features of venture caital, like the funding of 3 Since Diamod s 1984 many other authors have analyzed the delegating monitoring roblem with the costly-state verification framework e.g. see Williamson, 1986; Krasa and Villamil, 1992; Winton, 1995; Cerasi and Daltung, 2000; Hellwig, As we indicated above leverage buy-outs are not directly related to this study given that they are concerned with the re-organization of firms. See Cuny and Talmor 2007 for a review of the rivate equity theoretical literature. 4

5 high-risk and high-return firms, may be artly accounted for by considerations realted to agency costs. We organize the aer as follows. In section 2, we describe the model and in Section 3 we solve it and resent the main results. In addition, to the derivation of equilibrium intermediation mechanisms we also comare them with alternative direct mechamisms. In section 4, we consider the robustness of our results to a an increase in the number of rojects thus introducing the ossibility of diversification, and b a more general contracting environment, and we also discuss some emirical redictions of our model. In Section 5 we offer some concluding comments. All roofs can be found in the Aendix. 2 The Model There are four dates: 0, 1, 2 and 3. There is a single good that can be stored or invested or consumed. There are two tyes of risk neutral agents: entrereneurs and investors. There are two entrereneurs E1 and E2 each endowed with a roject that requires an investment of 1 unit at date 0. There is a large number of investors each having a very small endowment of the good. Their aggregate endowment is larger than 2. The cometitive net interest rate is equal to 0, the net return to storage. Each roject can either succeed or fail. At date 3, when a roject succeeds, it returns R, while when it fails, it returns nothing. The robability of success of a roject deends on a a binary shock, and b the inut of a service, which we will refer to as monitoring, and catures any hel in managing, marketing, and identifying otential consumers. Any of the investors can otentially rovide the monitoring service. But as in Diamond 1984, to avoid cost relication, monitoring will be delegated to one single investor, whom we refer to as the monitor hereafter M. The binary shock is realized at date 1. At date 0, it is common knowledge that the shock is identically and indeendently distributed across rojects. With robability a roject is of tye h while with robability 1 its tye is l. After observing the tye of a roject, M chooses whether or not to monitor it. Monitoring does not affect the robability of success of a tye l roject which is equal to q. In contrast, for a tye h roject M can, by monitoring, increase its robability of success to q. If M decides not to monitor the robability of success is still equal to q. M incurs a fixed cost c when monitoring a roject. Investors cannot observe neither roject tyes nor M s monitoring choice. Let s q + 1 q. We assume that ex ante rojects arer effi cient but those rojects that are not monitored destroy value. Condition 1 s R > 1 + s and 1 > qr 5

6 Entrereneurs need to obtain funds from investors to finance their rojects. There are large numbers of investors and monitors and therefore they are rice-takers leaving entrereneurs as the residual claim holders. In this section, we assume M to be a financial intermediary bridging investors and the entrereneurs, as Diamond 1984 does. Therefore, entrereneurs issue contracts to M, who in turn issues contracts to investors. However, as Wang 2012 has argued, it might be feasible for M to rovide the service only and entrereneurs to obtain funds directly from investors. Later we will consider the advantages and disadvantages of financial intermediation relative to direct finance. All arties are rotected by limited liability. The timing of the model is as follows. At date 0, E1 and E2 sign contracts with the same M. Then, M issues securities and sells them to investors thus raising funds to finance the two rojects. At date 1, M learns the tyes of both rojects. This information is rivate and not verifiable, however, each entrereneur learns the tye of her own roject. At date 2, M decides whether or not to monitor each roject. Lastly, at date 3, each roject either succeeds or fails and ayments are made according to the terms of the contracts signed. 2.1 Organization Structures of Financial Intermediation For the moment, we assume that a contract signed between one of the entrereneurs and M can deend only on the outcome of that entrereneur s rojects. Later, we will consider how our results are affected when we relax this restriction by allowing for multilateral contracting between the two entrereneurs and M. Then, given that there are only two ossible outcomes, the only tye of contract that each entrereneur can agree with M is one that secifies what M will receive when the roject succeeds. We are going to restrict attention to symmetric equilibria where the two entrereneurs choose cooeratively the identical contracts that they offer to M. 5 Thus, on the asset side of M, contracts are reresented by a ositive number, m, denoting the ayment to M from an entrereneur whose roject has been successful. Next, we turn our attention on the liability side of M s balance sheet. Given that roject returns are indeendent there are four ossible states of the world. Thus, on the liability side the contract is a rofile {r ij }, where i, j = 1, 0 reresents the success 1 or failure 0 of each roject. Limited liability 5 The symmetric Nash equilibrium contract that each entrereneur offers to M is identical to the contract that corresonds to our co-oerative solution. Clearly, there exists a continuum of other non-symmetric Nash equilibria that we ignore where one entrereneur, conditional on success, ays M less and the other ays M more. 6

7 and symmetry imly that r 00 = 0, r 01 = r 10 r 1 m R and r 11 = r 2 2m. 6 Following Innes 1990 we will ay secial attention to contracts that satisfy the following ayoff monotonicity condition MC: Condition 2 MC: r 2 r 1. Innes 1990 motivates the introduction of this constraint by the ossibility that borrowers in our case M can ad their revenues and thus avoiding the higher reayments. Of articular interest are organization structures whose liabilities take the form of either equity or debt. Definition 1 The financial intermediary is organized as a Fund F if its liability contract is equity: r 2 = 2r 1. The equity of the fund is sold at rice 2m r er share. Investors offer two units of their endowments for r m shares of the fund and M holds the rest of shares. Definition 2 The financial intermediary is organized as a Bank B if its liability contract is debt: either r 1 = m and m r 2 < 2m or r 1 = r 2 m The arrangement is a standard debt contract with face value r 2. When the intermediary is organized as a Bank it makes qualitative asset transformation given that the assets held by investors cannot be issued directly by a single entrereneur. We will demonstrate that in any equilibrium that satisfies MC only these two arrangements are ossible. 3 Equilibrium Organization of Financial Intermediation The objective of entrereneurs, as residual claimers, is to minimize the cost of external finance. The first decision that the two entrereneurs need to take is whether to offer incentives to M to monitor only when the both rojects are tye h or to ensure that M monitors a roject whenever its tye is h regardless the other roject s tye. After comaring the two cases, the entrereneurs decide what contract to offer to M. 6 Limited liability of the monitor imlies that r 1 m and r 2 2m, while limited liability for the entrereneur imlies that m R. 7

8 3.1 Case 1: M Monitors Only When Both Projects Are Tye h Suose that the two entrereneurs would like M to monitor only when both rojects are tye h. Then, each roject s ex ante robability of success is equal to 2 q q z. The robability that both rojects are tye h is equal to 2 and the robability of success of all rojects that are not monitored is equal to q. The two entrereneurs choose m so that a M has an incentive to monitor only when both rojects are good, and b the investors articiation constraint is satisfied. Thus, the roblem that two entrereneurs solve is given by Problem 1 min m subject to: IC1: 1 qm r 1 + q 2 2m r 2 2c q1 qm r 1 + q1 qm r 1 + qq2m r 2 c IC2: 1 qm r 1 + q 2 2m r 2 2c 1 qm r 1 + q 2 2m r 2 IC3: 1 qm r 1 + q 2 2m r 2 q1 qm r 1 + q1 qm r 1 + qq2m r 2 c PC1: [ 2 q1 q q1 q]2r 1 + [ 2 q q 2 ]r 2 2 r 1 m R and r 2 2m IC1 and IC2 are the incentive comatibility constraints that ensure that when both rojects are tye h M has an incentive to monitor both of them. On the left-hand side of the weak inequalities in each of these two constraints we have M s exected ayoff from monitoring both rojects when their tye is h. In that case, each roject succeeds with robability q. Thus, with robability q 2 both rojects succeed, M gets 2m from the two entrereneurs, and returns r 2 to investors, which imlies a ayoff for M of 2m r 2. Furthermore, with robability q1 q, only one roject succeeds and then M s ayoff equals m r 1. The right-hand side of IC1 is M s exected ayoff when she only monitors one roject. Then one of the rojects succeeds with robability q while the other roject succeeds with robability q. Similarly, the right-hand side of IC2 is equal to M s ayoff when she does not monitor any of the rojects IC3 is the incentive comatibility constraint that ensures that when only one roject is tye h M refers not to monitor at all. On the left-hand side of the weak inequality we have M s ayoff when she does not monitor the tye h roject in which case the robability of success of each roject equals q. On the right hand-side of the weak inequality we have the same exression as those on the right-hand 8

9 side of the weak inequality in IC1, showing M s net exected ayoff when she monitors the tye h roject. Lastly, the solution must also satisfy the articiation constraint of the investors. At date 0, with robability 2 both rojects are tye h, M monitors both of them, and each roject succeeds with robability q; with robability 1 2 at least one roject is tye h, M does not monitor any roject, and each roject succeeds with robability q. Thus, the robability that only one roject succeeds is equal to 2[ 2 q1 q q1 q], while the robability that both rojects succeed is equal to 2 q q 2. Then, the right-hand side of PC1 shows the exected ayoff of investors when M monitors only when both rojects are tye h, in which case she monitors both rojects. Proosition 1 Suose that the two entrereneurs would like M to monitor only when both rojects are of tye h and let c c q q. Then, i Finance is feasible if and only if c min zr 1, R 1 z. ii If finance is feasible then a if c z the otimal contract is given by b if c > z Proof. See the Aendix. r 1 = m Z = 1 + z z q + q c ; r 2 = 2 2c z r 1, z q + q z the otimal contract is given by r 1 = 1 z ; r 2 = 0; m Z = 1 q q z + c. Given that the two entrereneurs would like M to monitor only when both rojects are tye h otimality requires that M s ayoff is minimized when only one roject succeeds and concentrated on that state when both rojects succeed. Given m Z, the asset asside of M s balance sheet, this leads to a liability contract that takes away M s revenue in states when only one roject succeeds, namely r 1 = m Z. Then, r 2 is inned down by the investors articiation constraint. This tye of contract is called live or die and was originally derived by Innes In case a the ayoff to investors is constrained by the limited liability of M. The term 7 See also Tirole.133, z < 1 catures the cross-ledging effect 9

10 see Tirole, 2006,.159. For = 1, the term reduces to q, which is the same as in Laux 2001 and Tirole The comlexity here is due to the uncertainty at date 0 about the tye of each of the two rojects. Introducing this uncertainty is imortant for our work since, as we will show in the following section, it allows for multile financial intermediation organization structures. When c 2 < z the liability contract is debt with face value r z 2 and the intermediary defaults when at least one roject fails, otherwise, MC is violated. This is because when c is suffi ciently high, which in turn imlies that r 1 is high, the investors articiation constraint requires that we set a value for r 2 that is lower than r 1, in which case MC is not satisfied. In case b the contract is constrained by the condition that the ayoff of investors cannot be negative and the contract always violates MC. The following roosition characterizes the otimal contract for the case when MC must be satisfied. Proosition 2 Suose that the two entrereneurs would like M to monitor only when both rojects are tye h and let c c q q i Finance is feasible if and only if c min ii If finance is feasible then a if c. In addition, suose that contacts must satisfy MC. Then, zr 1, R 2. the otimal contract is given by r 1 = m Z = 1 + z z q + q c ; r 2 = 2 2c z r 1, z q + q z b if c > the otimal contract is given by 2 r 2 = r 1 = 2 z ; m Z 2 q + q = c +. 2 z As the liability contract of M is debt with face value r 2, M is organized as a Bank. Proof. See the Aendix. When c > defaults only when both rojects fail. MC is binding and the liability contract now changes to debt. The intermediary Figure 1 shows the otimal contract in the c, R lane, where α B 2, 10

11 Figure 1: The otimal contract if M monitors only when both rojects are tye h To the left of the kinked bold line the combinations of low roject returns R and high agency costs c imly that finance is not feasible. Above the kink, that is for suffi ciently high agency costs, the contract design is further restricted by MC. Ignoring the MC constraint, the otimal contract requires that r 2 < r 1 which violates monotonicity. Notice that even if monitoring costs are equal to zero unless R 1 z investors cannot break even. 3.2 Case 2: M Always Monitors When A Project Is tye h Now, consider the case when the two entrereneurs would like M to monitor a roject whenever it is tye h. In this case, each roject s ex ante success ossibility is equal to s. Now, they solve the following roblem: Problem 2 min m subject to: IC1, IC2, IC4: q1 qm r 1 + q1 qm r 1 + qq2m r 2 c 1 qm r 1 + q 2 2m r 2 PC2: s 1 s 2r sr 2 2 r 1 m R and r 2 2m The incentive comatibility constraints IC1 and IC2 are common to both roblems, given that once more the two entrereneurs would like M to monitor both rojects when both are tye h. However, in this new roblem the two entrereneurs would like M to monitor whenever a roject is tye h, indeendently of the tye of the other roject, and, therefore, IC4 is obtained from IC3 by reversing 11

12 the direction of the weak inequality. The articiation constraint is also similar to that of Problem 1; the only difference is that a roject s ex ante robability of success is now higher s > z. Proosition 3 Suose that M monitors every tye h roject and let c i If q q < 1+ then finance is feasible if and only if c min finance is feasible a if c b if c > s1 s s1 s the otimal contract is given by r 1 = m S = 1 s + s c ; r 2 = 2 1 s c. s q the otimal contract is given by r 1 = 1 s 1 s ; r 2 = 0; m s = c + 1 s 1 s. c q q. Then, s R 1 s, R 1 s1 s. When ii If q q 1+ then finance is feasible if and only if c R 1 s. When finance is feasible the otimal contract is given by r 1 = r 2 2 = 1 s ; m S = c + 1 s. As the liability contract of M is equity, M is organized as a Fund. c Proof. See the Aendix. In art i of Proosition 3, MC is not necessarily satisfied. More secifically, for art i-a when 2 s 2 s < s1 s the liability contract is debt with face value r 2 and the intermediary defaults when at least one roject fails, otherwise, MC is violated. For art i-b the contract is constrained by the condition that the ayoff of investors cannot be negative and the contract always violates MC. The following roosition characterizes the otimal contract for the case when MC must be satisfied. Proosition 4 Suose that M monitors every tye h roject and let c c q q. In addition, suose that contacts must satisfy MC. Then, i If q q < 1+ then finance is feasible if and only if c min s R 1 s, R 21 q 2 s. When 2 s finance is feasible 12

13 a if c 2 s 2 s the otimal contract is given by r 1 = m S = 1 s + s c ; r 2 = 2 1 s c. s q b if c > 2 s 2 s the otimal contract is given by r 1 = 2 r 2 = 2 s 2 ; s m s = 21 q c + 2 s 2. s As the liability contract of M is debt, M is organized as a Bank. ii If q q 1+ then finance is feasible if and only if c R 1 s. When finance is feasible the otimal contract is given by r 1 = r 2 2 = 1 s ; m S = c + 1 s. As the liability contract of M is equity, M is organized as a Fund. Proof. See the Aendix. The intuition behind the switch in the liability contract stated in Proositions 3 and 4 is as follows. First, on the asset side, M s revenue, conditional on the number of successful rojects, is given by 0, m, 2m. The ayment to M is equal to the difference between this revenue and his liability obligation, 0, r 1, r 2, which is given by 0, m r 1, 2m r 2. Therefore, the design of the liability contract matters for M s incentives to monitor. Second, in the resent case the entrereneurs want M to monitor an h-tye roject even if the other roject is a l-tye, which succeeds with robability q. This requires that M is aid even if only one rject is successful. The lower is q, the higher the ayment to M must be when only one roject succeeds. For examle, if q = 0, namely, if the l-tye roject never has a chance to succeed, M has an incentive to monitor the other h-tye roject only if she receives a ayment in those states when only one roject succeeds i.e. m r 1 > 0. This consideration has a negative effect on r 1 and a ositive effect on r 2 in order to make the investors break even, and thus we get the equity contract. Therefore, the lower is q, the more likely is that the the equity contract is otimal. This exlains why the switch between debt and equity contracts for the resent case deends on the ratio q/q. 13

14 This also exlains why in the revious case, where the entrereneurs want M to monitor an h-tye roject only if the other one is also an h-tye, this switch is not there: the other roject succeeds with a relatively greater robability, q, and thus the concern that drives the equity contract does not arise. 3.3 Equilibrium Organization Structure The equilibrium structure of financial intermediation is decided by the two entrereneurs since they have all the bargaining ower. For q q 1+ the otimal intermediation structure, if it exists, is always Bank. For q q > 1+ and when both intermediation structures are feasible, we need to comare Proosition 2 with Proosition 4. In case 1, with robability 2 both rojects are tye h and thus M monitors both of them, which imlies exected rofits qr m Z for each entrereneur given that each roject succeeds with robability q. With robability 1 2 at least one roject is bad and M monitors does not monitor at all. Then, each roject succeeds with robability q, which imlies that each entrereneur s utility is given by qr m Z. Therefore, in case 1 each entrereneur s exected utility is equal to V Z = 2 qr m Z qr m Z = z R m Z. Similarly, in case 2, each entrereneur s exected utility is equal to V S = qr m S + 1 qr m S = s R m S. By comaring the exressions for the two exected utilities and restricting attention to arameter configurations such that at least one organization structure is feasible we arrive at the following result: Theorem 1 Equilibrium Organization Structure: 1 Suose that q q 1+. The equilibrium structure is Bank. 2 Suose that q q > 1+. Then, a if qq > s z 2 q + q then i Fund is the only feasible organization structure if c R 1 s and s z q + q + qq s qq > R; ii Bank is the only feasible organization structure if c min R 2 q + q 2 z, q + q z R 1 and s z q + q + qq s qq R; iii when both Bank and Fund are feasible Bank dominates Fund if s z q + q + qq min c, c + s z q + q qq > R, s z 2 z 14

15 otherwise, Fund dominates Bank. b If qq s z 2 q + q then the equilibrium structure is Fund; either it is the only feasible organization structure or it dominates Bank. Proof. See the Aendix. Figure 2 shows for the case qq > s z [2 q + q] and for each air c, R whether finance is feasible and, if so, the equilibrium financial intermediation structure. Figure 2: The equilibrium structure for Theorem 2a We can better understand the trade-off between the two organization structures by comaring M s corresonding exected ayoffs. We concentrate our discussion on the case q q > 1+ where a trade-off between the two structures exists. We know that in both cases investors break even. M s exected ayoffs are given by U B = 22 q q 2 is straightforward to show that U B < U F. 8 c q q under Bank and U F = 2sc q q under Fund. It The intuition behind this inequality is that the cost of roviding incentives to M is lower under Bank. The otimality of debt contracts in the resence of moral hazard is well known in the literature e.g. Innes,1990; Laux, 2001; Tirole, This is a consequence of the maximum incentive rincile, which says that the agent shall receive a ositive ayment only when all the informative signals dislay the values indicating she has chosen high effort. 9 Therefore, M 8 { } { sign U F U B} = sign q + 1 q 2[2 q q 2 ] q + q { sign 1 q 2 q 2 } + qq = which is clearly ositive. 9 See Laffont and Martimont 2003 and Bolton and Dwatriont

16 should receive a ayoff only when both rojects succeed. By introducing uncertainty about the roject s tye this aer finds a disadvantage of debt contracts. The very feature that enables them to rovide incentives at a lower cost makes them less robust to bad news. To see this, consider the extreme case where q = 0, where according to the theorem the equilibrium structure is Fund. Suose that only one roject is tye h. Under the Bank structure, as there is at most one successful roject, M s ayoff will be 0 if she monitors the tye h roject and thus she does not monitor at all. One iece of bad news is suffi cient to destroy M s incentives to monitor. In contrast, under the Fund structure M monitors the only tye h roject and receives a share of the outut. We conclude that while it is cheaer to rovide incentives by oting for the Bank structure, the alternative Fund structure is more robust to the ralization of negative shocks. 3.4 Intermediate versus Direct Finance Thus far, we have assumed that M is a financial intermediary that rovides both the monitoring service and transfers funds from investors to entrereneurs. But is it ossible that an arrangement of direct finance, where M only rovides the monitoring service, can do better? Below we show that this is never the case and moreover if contracts are restricted to be bilateral as in the case of financial intermediation, direct finance does worse. Proosition 5 Suose that the contract between an entrereneur and M can only be conditioned on that entrereneur s roject s outcome. Then M monitors a roject whenever it is tye h. This allocation can be imlemented by financial intermediation with a Fund arrangement. Proof. See the Aendix. With bilateral contracts M s ayoff is equal to 0 when both rojects fail, m when only one roject succeeds and 2m when both rojects succeed. This comensation structure generates incentives to monitor whenever a roject is of tye h. Thus, under the direct mechanism each entrereneur hires an M not necessarily the same as a director at a wage c q q and issues equity with return rate 1 s directly to investors. Clearly, the Fund is indistinguishable from direct finance. There are two comlications with the direct mechanism. Firstly, investors would be vulnerable to the ossibility that the entrereneur terminates the contract with M. In contrast, under the Fund structure by bundling the monitoring with the financing activities this ossibility does not arise. This is because while a firm can find an excuse to 16

17 fire a director, it cannot fire a creditor before it clears its debt obligations to him. Secondly, the Fund has the advantage of a more effi cient governance structure. Irresectively, of the organization structure, investors will not commit their funds unless they are convinced that entrereneurs will be monitored. Under direct finance this can only be achieved if investors oversee all entrereneurs searately to ensure that their activities are monitored. Put differently, they deend on the governance structure of each entrereneur s firm. In contrast, under the Fund structure investors can rely on the governance structure of only one firm, namely, the Fund. The following result is a direct consequence of the above roosition. Corollary 1 Consider arameter values such that, according to Theorem 1, Bank dominates Fund. Then, financial intermediation dominates direct mechanism. The advantage of the Bank structure is its ability to erform asset transformation. The only way to imlement the Bank solution through a direct mechanism is by using multilateral mechanisms. that allow for contracts between one entrereneur and M that are contingent on the outcome of the other entrereneur s roject. This imoses a stronger requirement on the information of the relevant arties. What haens with multi-lateral contracting is discussed below. 4 Discussion In this section we a examine the imlications of diversification for the choice of intermediation structure, b consider a more general contracting environment in order to consider the robustness of our solutions, and c discuss the emirical relevance of our model. 4.1 Diversification and Internal Control U to this oint, we have assumed that there are only two entrereneurs. What haens if the financial intermediary M can fully diversify its assets as the number of the entrereneurs goes to infinity? Full diversification offers the Bank structure some advantages because a under the Bank structure M s rofits are zero while under the Fund structure M earns ositive rofits, and b there is no aggregate uncertainty about the ortfolio return which cancels the advantage that Fund has. Does that consideration of full diversification destroy the trade-off between the two structures considered above? 17

18 The answer is negative if internal control roblems are associated with large enterrises. In our analysis above, the roblem is assumed away given that M is able to monitor the two rojects by herself. When there are large number of rojects, M would need to delegate the monitoring activities to others. Given that monitoring is not observable by third arties, M faces the roblem of monitoring these monitors. Define as internal control cost the cost incurred by M to ensure that a monitor incurs the cost c by monitoring the assigned roject. The following roosition makes clear that the Bank structure suffers more from internal control roblems than the Fund structure does. Proosition 6 If each monitor can only monitor one roject and the internal control cost is larger than c, then the only equilibrium structure is Fund. Proof. See the Aendix. The reason that Bank suffers more from internal control roblems is rooted in the very feature that enables it to save on incentive costs. Under the Bank structure, each monitor imoses some negative externality, cross ledging, uon other monitors given that failure to monitor on his art reduces their exected income. It is exactly because of this externality that Bank saves on incentive costs relative to Fund. Thus, if each monitor s behavior is not controlled to internalize the externality, cross ledging would not work and the Bank structure would collase. In contrast, the Fund does not incur internal control costs since each monitor s contract can be arranged indeendently with each monitor obtaining a ositive share of the outut from the roject she monitors. Thus, our main conclusions about the trade-off between the two main financial intermediation structures is robust to the consideration of full diversification since internal control roblems limit the Bank s caacity for diversification. 4.2 Generalizing the Contractual Environment One restriction that we have imosed on contract design is that each entrereneur can condition the terms of his agreement with M only on the outcome of his own roject. This seems to be reasonable given the otential high costs of information gathering associated with conditioning the terms of each contract on the outcomes of other rojects. In any case, the following roosition demonstrates that the equilibrium structures derived above are also solutions to the contracting roblem where no such restriction is imosed as long as monitoring costs are not too high. 18

19 Proosition 7 As longs as c min 2, z s2 s, allwing fro multilateral contracting does not change the equilibrium allocation. Proof. See the Aendix. What gives rise to the constraint in the statement of Proosition 7 is the requirement that the otimal mechanism satisfies MC. However, from Proosition 5 we know that any mechanism, direct or intermediated, will be similarly restricted if a MC must be satisfied, and b the contracts between each entrereneur and M cannot be conditioned on the outcomes of both rojects. 4.3 Emirical Predictions Our model yields a number of emirical redictions about a the ability of each organization structure to raise ledgeable income, b the relationshi between firm-secific characteristics and the two sources of funds, and c the oerations of the two organization structures. Prediction 1 Keeing rofitability constant Bank is more likely to dominate when monitoring costs are high and the ayoff to monitoring is low. The ayoff to monitoring is directly related to the difference q q which, as in Holmström and Tirole 1997, is a measure of agency costs. By monitoring good quality rojects the onitor increases their robability of success from q to q. Clearly, as the difference between these two robabilities declines the ayoff to monitoring declines too. Then the rediction follows directly from Theorem 1 by noticing that c is increasing in the size of the monitoring cost c and decreasing in q q. Prediction 2 Keeing monitoring costs and the ayoff to monitoring constant Fund is more likely when rofitability is high. Measuring rofitability by R the rediction follows directly from Figure 2. Our next rediction follows directly from Predictions 1 and 2. Prediction 3 The Fund structure is more attractive for firms in high-tech innovative sectors and startu firms. Our model redicts that firms with high q, low q q and low R, which, according to evidence rovided by Dunne, Roberts and Samuelson 1988, these are the characteristics of mature firms, are 19

20 more likely to be financed by banks. In contrast, according to Sahlman 1990 the rofitability of young firms in high-risk innovative sectors is very strong conditional on survival, and also these are the firms more likely to be financed by venture caitalists. Prediction 4 Fund structured intermediaries monitor more intensively that Bank structured intermediaries. This rediction is an immediate consequence of Proositions 1 and 2. When it is otimal to monitor only when the quality of both rojects are tye h we find that the otimal organization structure is Bank. In contrast, as long as the incentives for monitoring are not too low, when it is always otimal to monitor a tye h roject the otimal organization structure is Fund. In our model monitoring takes the form of active articiation in decision-making which is consistent with the activities of equity-based funs and, as Gomers 1995 and Sahlman 1990 observe, esecially those of venture caitalists. In contrast, bank monitoring is more related to screening and information gathering which are outside the scoe of this aer. 5 Conclusion We have used a mechanism design aroach to solve a delegated monitoring roblem and we have found that the organization structure of financial intermediation can take one of two forms, namely, Bank or Fund. For each structure we have derived both their asset and liability contracts and then by comaring the solutions we have identify their advantages and disadvantages. The trade-off between the two structures is that it is cheaer to offer incentives a monitor using the Bank otion but the Fund alternative is more robust to the arrival of bad news. The model is quite simle, but is still rich enough to exlain many emirical regularities. For examle, we find that Fund is more likely than Bank in financing start-u firms and firms in innovative industries, and Fund, on average, monitors more intensively its clients than Bank does. The simlicity of the model triggers the question about the theory s robustness and relevance. We have found that our results are robust to generalizing the contracting environment and to increasing the number of rojects. We have demonstrated that the Bank organization structure cannot be relicated by bilateral relationshis and that the same is true for Fund as long as multilateral contracting is costly. Financial intermediaries channel trillions of funds from investors to entrereneurs roviding various 20

21 services to their customers. There is a lot of rogress made in understanding their advantages over direct finance. However, there are still questions about them that are not very well understood. Do the roviders of the monitoring services considered in this aer need to be organized as intermediaries? Given that these roviders are organized as intermediaries what determines their organization structure? Put differently, why rivate equity funds and commercial banks coexist? This aer is an attemt to further understand these interesting roblems. 6 Aendix 6.1 Proof of Proosition 1 Let m Z denote the otimal symmetric solution for m. Constraint IC1 can be written as: m Z r 1 1 q q 1 q q 1 q + 2m Z r 2 q 2 qq c m Z r 1 q q 1 + 2m Z r 2 q q q c m Z 1 r 1 + qr 2 c A1 IC2 can be written as: 2 m Z r 1 q 1 q q 1 q + 2m Z r 2 q 2 q 2 2c 2 m Z r 1 1 q q q q + 2m Z r 2 q + q q q 2c 1 m Z q q r1 + q + q 2 r 2 c A2 PC1 can be written as: We can then write Problem 1 as: [ 2 q1 q q1 q]2r 1 + [ 2 q q 2 ]r 2 2 A3 We rove the following results: min m Z, s.t.a1, A2, IC3 and A3; and m Z,r 1,r 2 0 r 1 m Z R, 0 r 2 2m Z. 21

22 Lemma 1 If IC2 A2 is binding then IC3 is not binding. Proof. The lemma follows by setting equal the two sides of A2 and then substitutiong the righthand side for the left-hand side of A1. QED Lemma 2 A2 is binding. Proof. First, notice that minimization of m Z imlies that either A1 or A2 must be binding. Second, notice that A2 imlies A1 if and only if 1 q qr r 2 1 r 1 + qr 2 q qr 1 q q 2 r 2 r 1 r 2 2. And vice versa. Thus, if A1 is binding, contrary to the lemma, then r 1 r2 2. In this case, mz = 1 r 1 + qr 2 + c and the roblem of the two entrereneurs is equivalent to: min H 1 = 1 r 1 + qr 2 subject to A3 and 0 r 1 m Z R, 0 r 2 2m Z. Certainly A3 is binding and it follows that dr 2 = 2[2 q1 q+1 2 q1 q] 2 q q dr 2 1. Then, [ ] dh 1 = 1 q 2[2 q1 q q1 q] 2 q q 2 dr 1. Consider the exression in the square brackets 1 < q 2[2 q1 q q1 q] 2 q q 2 2 q q 2 < 2 q q q1 q q1 q 2 q q 2 < 2 q q where given that q > q the last inequality clearly holds. Thus dh1 dr 1 < 0 and the solution for this case is to set r 1 = r2 2, which imlies that the overall otimal solution for Problem 1 is in the region r 1 r2 2, that is, A2 is binding. QED With A2 binding, m Z = 1 q qr r 2 + c and the roblem of the two entrereneurs is equivalent to: min H 2 = 1 q qr 1 + q + q 2 r 2 subject to A3 and 0 r 1 m Z R, 0 r 2 2m Z. 22

23 Notice that the limited liability conditions imly: 0 r 1 1 q qr 1 + q + q 2 r 2 + c A4 0 r 2 21 q qr 1 + q + qr 2 + 2c A5 Lemma 3 a If c z then r 1 = 1 z + z c, r 2 = 2 z 1 z c, m Z = r 1, and b if c z then r 1 = 1 z, r 2 = 0, m Z = 1 q q z + c. Proof. Once more the binding A3 imlies that dr 2 = 2[2 q1 q+1 2 q1 q] 2 q q dr 2 1. Then, dh 2 = [ ] 1 q qdr dr 2 = 1 q q 2[ 2 q1 q+1 2 q1 q] 2 2 q q dr 2 1. Next, we show that the exression in the square brackets is negative. 1 q q < q + q 2 2[ 2 q1 q q1 q] 2 q q 2 2 q q 2 q + q[ 2 q q 2 ] < q + q[ 2 q1 q q1 q] 2 q q 2 < q + q 2 q q qq < 0 where the last inequality clearly holds. Thus dh2 dr 1 < 0, which imlies the entrereneurs must set r 1 as high as ossible. Therefore, the second inequality of A4 is binding, unless the first inequality of A5 0 r 2 is binding, given that from the binding A3 we know that r 1 and r 2 are negatively related. Part a of the lemma follows when the first inequality of A5 is not binding. Then, from the binding second inequality of A4 and the binding A3 we get the values of r 1 and r 2 which is the solution obtained when r 2 0, which will be the case if c z. Part b of the lemma follows when the first inequality of A5 is binding and thus r 2 = 0. Then it follows from the binding A3 that r 1 = 1 z. QED Therefore, as long as finance is feasible, that is the limited liability condition of the two entrereneurs is satisfied, the solution given in Lemma 3 is the solution to Problem 1. Now we are left to check the feasibility of finance, namely, that the constraint m Z R is satisfied. Let T 1, T z 2 zr 1 and T 3 R 1 q q z. Then we have the following result: Lemma 4 Finance is feasible if and only if c mint 2, T 3. Proof. If c T 1, then from Lemma 2 we have m Z = 1 z + z c. Therefore, m Z R if and only if c T 2. If c T 1, then from Lemma 2 we have m Z = 1 q q z only if c T 3. To comlete the roof we consider the following two cases: + c. Therefore, m z R if and 23

24 a If R 1 z then T 1 T 3 T 2 which in turn imlies that T 1 > maxt 2, T 3. In this case, if c T 1, then c > T 3 and thus finace is not feasible. If c < T 1, finance is feasible if c T 2. Therefore, if R 1 z finance is feasible if and only if c T 2. b If R 1 z then T 1 T 3 T 2 which in turn imlies that T 1 mint 2, T 3. In this case, if c < T 1, then c < T 2. Thus finance is feasible. If c T 1, then finance is feasible if and only if c T 3. Therefore, in this case, finance is feasible if and only if c T 3. Then the lemma follows from T 3 T 2 if and only if R 1 z. QED Proosition 1 follows directly from Lemma 3 and Lemma 4. QED 6.2 Proof of Proosition 2 We begin with the roof of art ii. In the solution obtained in art ii-a of Proosition 1, MC that is r 2 r 1 is satisfied as long as c solution for art ii-b set r 2 = r 1 and then use A3. and this comletes the roof of art ii-a. To obtain the Next, we to check the feasibility of finance, namely, that the constraint m Z R is satisfied. Let T1 2, T z 2 zr 1 and T3 R 2. Then we have the following result: Lemma 5 Finance is feasible if and only if c mint 2, T 3. Proof. Suose that c T 1, that is MC is satisfied. Then as in Proosition 1 m Z R requires that c T 2. If c T1, then r 2 = r 1 and we have m Z = c It follows that z mz R if and only if c T 3. To comlete the roof we observe that: a If R 2 then T 1 T 3 T 2 and b if R 2 then T 1 T 3 T 2. The roof is comleted by following exactly the same stes as those used for the roof of Lemma 4. QED This comletes the roof of Proosition 2. QED 6.3 Proof of Proosition 3 Let m S denote the otimal symmetric solution for m. Constraints A1 and A2 must also be satisfied by the solution of Problem 2. We also need to add IC4 which can be written as 24

25 q q q + 1 q q q m S r 1 + q q q 2m S r 2 c 1 m S r 1 + q2m S r 2 c m S 1 r 1 + qr 2 c. A6 And PC2 which can be written as: 2 s 1 s r sr 2 2 A7 The roblem of the two entrereneurs is to min m S, s.t.a1, A2, A6 and A7; and m Z,r 1,r 2 0 r 1 m S R, 0 r 2 2m S. Lemma 6 A6 is binding. Proof. Notice that A6 imlies A2 if and only if 1 m S r 1 + q2m S r 2 1 q qm S r 1 + q + q 2 2mS r 2 q q m S r 1 q q 2 2mS r 2 r 1 r 2 2. Thus, if r 1 r2 2, then A6 imlies A2 which, in turn, imlies A1 and vice versa. We first consider the case r 1 r2 2. Following a similar argument as the one used for the roof of Proosition 1, we find that the roblem of the two entrereneurs is equivalent to min H 1 = 1 r 1 + qr 2 subject to A7 [ ] From the binding A7 it follows that dr 2 = 21 s s dr 1. Then dh 2 = 1 q 21 s s dr 1. Next, we show that the exression in the square brackets is negative. 1 < q 21 s s s < which clearly holds. Thus dh2 dr 1 < 0 for r 1 r2 2 and the solution for this case is r 1 = r2 2. Therefore, the otimal solution for Problem 2 must lie in the region r 1 r2 2. This imlies A6 is binding. QED Therefore, m S = 1 r 1 + qr 2 + c 25