Loanable Funds, Securitization, Central Bank Supervision, and Growth

Loanable Funds, Securitization, Central Bank Supervision, and Growth José Penalva VERY PRELIMINARYDO NOT QUOTE First Version: May 11, 2013, This version: May 27, 2013 Abstract We consider the eect of dierent nancial products in the model of HT (QJE97). Within that model, we introduce securitization in the form of an additional set of nancial contracts available to nancial intermedaries. We distinguish between supervised and unsupervised securitizations, where the dierence lies in whether there is an eective third party (such as a central bank, CB) that is in charge of supervising and enforcing monitoring on the part of nancial intermediaries. We nd that in the absence of additional frictions, unsupervised securitizations do not increase the number of projects that can obtain nancing. Supervised monitoring, on the other hand, may increase the number of projects that nd nancing, if the quality of the supervisor's information is suciently good relative to the lower cost of nancing from avoiding the use expensive bank capital. In addition, we characterize the optimal monitoring strategy of a CB with a growth mandate, and nd We would like to thank Rafael Repullo and Javier Suarez for their valuable comments and discussions. We are also grateful to... for their comments. We also thank seminar participants at the National Bank of Serbia. Special acknowledgements go to Jesús Saurina and... as the idea for this paper and the initial work was done while José Penalva was in their group at the Banco de España as Research Fellow. The views expressed in this paper are exclusively those of the authors. The usual caveat applies. We welcome comments, including references we have inadvertently missed. jpenalva@emp.uc3m.es, Universidad Carlos III de Madrid. 1

that the ability of the CB to promote growth is limited by the quality of the information at its disposal, as well as the range of disciplinary measures it can use to discipline banks. Keywords: Securitization, nancial contracts, growth, central bank, supervision, information, small and medium-sized entreprises (SMEs) 1 Introduction A great deal has been said and written about the causes of the nancial crisis of 2008-2009. In the US, securitization (primarily, mortgage securitization) appears prominently in these discussions, and is often portrayed in a very negative light. In this paper we want to incorporate securitization in a standard Holstrom-Tirole model (HT, ), where entrepreneurs face incentive and nancial constraints, and ask whether such contracts can help promote growth. We also want to explore the role of the central bank (CB) in this context, and what kind of positive policies a CB with a growth mandate could follow. 2 The Basic Model The basic model is the same as that of [HT] with a small variation (the parameter representing the cost of monitoring paid the nancial intermediary is valued in terms of cash at the time of the nancing decision, rather than cash at project maturity) and an additional parameter (we introduce a wedge between the cost of capital for the nancial intermediary and that received by uninformed investors). 2.1 The Real Sector As in HT, there is a population of entrepreneurs, each with an amount of capital A i. The distribution of entrepreneur's capital is described by the cumulative distribution function G (A), which, for simplicity of exposition, will have full support on (0, I). The economy has two dates (one and two). Each entrepreneur has one project that requires a xed initial investment of 2

I at date one, so that she needs to obtain at least I A > 0 in external funds. Each project generates a veriable cash payment at date two which is either R (success) or 0 (failure). Entrepreneurs, in the absence of proper incentives or monitoring, can obtain a private benet from the project at the cost of a lower probability of success. Furthermore, the private benet of the project for the entrepreneur can be either low (b > 0) or high (B > b). A project in which the entrepreneur is obtaining private benets is referred to as a bad project (and we have two types of bad projects, depending on the level of private benet enjoyed by the entrepreneur). Projects in which the entrepreneur does not enjoy private benets are referred to as good projects. The probability of the project being successful for either type of bad project is p L, and for good projects it is p H, where p p H p L > 0. When trying to raise external nancing, the entrepreneur needs to take into account the opportunity cost of funds for outside investors, which is captured by the parameter γ. For the relevant ranges of γ we assume that good projects are economically viable, while bad projects are not: p H R γi > 0 > p L R γi + B. (1) 2.2 Investors and the Financial Sector The nancial sector includes a large number of uninformed investors who demand an expected return of γ (which is initially given). There is also a large number of nancial intermediaries that have the capability of monitoring projects and thereby reduce the private benets the entrepreneur can enjoy. We introduce the possibility that the intermediary's cost of capital is dierent from that of outside investors. In particular, assume that the nancial intermediary requires an expected return of γ B = γ (1 + η). We are interested in the case where η > 0. Monitoring by the intermediary alleviates the moral hazard problem of the entrepreneur by preventing her from undertaking high private benet projects (those with a private benet of B). This monitoring is privately costly to the intermediary, who, when monitoring, pays an non-veriable amount c > 0 at date one for each project it monitors. For simplicity, we assume (as in HT), that project payos are perfectly correlated. We assume that entrepreneurs cannot 3

monitor other entrepreneurs, so that any excess cash can only be invested on the open market and receives a return of γ. 2.3 Equity Financing In this setting, nancial contracts can be simply described in terms of the cash payment received from the payo (R) generated by the successful project on date two (and nothing if the project is unsuccessful). An optimal contract is then for an entrepreneur to pledge all his available capital, A i, and obtain all the additional investment that is needed, I A i, via direct investment from investors by promising them a total cash payment R u upon successful completion of the project. The residual cash generated by the rm R f = R R u is then kept by the entrepreneur. We refer to this as equity nancing. The fact that the entrepreneur's cash payment R f as a proportion of the entrepreneur's cash investments (A i ) is not the same as that of outside investors (it is greater) is not important, as the dierence can be justied in terms of compensation for the entrepreneur's non-cash contributions to the project. Given (1), a necessary condition for the project to obtain direct nance is for the entrepreneur to act diligently. This is incentive compatible if p H R f p L R f + B R f B p. (2) This leaves at most R u R B/ p to outside investors. As the project requires an investment of I A i from them, and the project has to generate an expected return of at least γ, a necessary and sucient condition for the project to obtain direct nancing is: γ (I A i ) R B p. A i A = I 1 γ ( R B ) p (3) To ensure that A > 0, assume p H R γi < p H B/ p. 4

2.4 Bank Financing We will use the term banks to refer to nancial intermediaries. We do this in order to constrast this type of nancing from securitization. As we will see below, there may be no dierence between the two. Banks can reduce the entrepreneur's private benet (to b) by monitoring her activities (at a date one cost of c). As with direct nance, an optimal three-party contract involving the entrepreneur, the bank, and outside investors can be described by the payments received by each of the parties upon successful completion of the project: R f to the entrepreneur, R u to outside investors, and R m to the bank such that R = R f + R u + R m. In case of monitoring, the entrepreneur will run a good project if As we will see below, if R f B p p H R f p L R f + b R f b p. (4) the entrepreneur prefers direct nancing, so assume that R f < B p. In order for the bank to monitor, it must also be true that p H R m γ B c p L R m R m γ B c p. (5) As this implies that p H R m c > 0, banks will compete for monitoring projects by pledging capital. Let I m denote the amount of capital pledged by the bank. As the cost of capital for the bank is γ B, for xed R m, banks will pledge capital until the following holds: p H R m I m + c = γ B I m = p HR m γ B c. (6) Note however that the expected cost of bank capital for the entrepreneur is: β = p HR m I M > γ B > γ. 5

This implies that the entrepreneur will try to use as little bank capital as possible, and c hence will set R m = γ B p, which then implies that I m = 1 ( p H γ B γ B ) c c I m = p Lc p p. (7) As for the outsider investors, a project satisfying both incentive constraints (4) and (5) will leave outside investors with at most an amount of cash equal to R b+γ Bc p. In order for outside investors to accept this, they must be receiving at least γ. This implies the following: ( γ (I A i I m ) p H R b + γ ) Bc p A i A = I I m p H γ ( R ) b + γ (1 + η) c. (8) p The availability of a monitoring technology in the hands of nancial intermediaries may not be socially valuable. The social value from monitoring appears only if there are entrepreneurs who can attain bank nancing, A i A, who would otherwise not be able to raise equity to nance the project, A i < A. This occurs if A > A which occurs i γc (p H (1 + η) p L ) < p H (B b). (9) 3 Securitization In the original HT paper, there is no discussion of the nature of the projects that are being nanced. Nevertheless, entrepreneurs are described as price takers who only make decisions in terms managing and choosing the capital structure of their individual projects. We think of these as small projects from small- and medium-sized enterprises. In such a context, if we interpret A i as the capital available to the entrepreneur from her own wealth and that of those in her immediate social circle, access to nancing from uninformed investors is very limited. Any equity such an entrepreneur may be able to raise outside her immediate circle will usually come from banks or venture capitalists, both of which fall within the scope of nancial intermediaries 6

with monitoring skills, which we are calling banks. Thus, we can consider that all external nancing, A i I, is coming from banks who may or may not be actively monitoring these projects, and this nancing comes in the form of non-tradeable nancial contracts. The process of securitization, in this context, is dened as banks that package the nancing agreements they have made with entrepreneurs and resell them to (uniformed) investors in capital markets in the form of tradeable securities (such as securitized bond issues). In keeping with the spirit of the original HT paper, we will assume the packaging of the banks loans into securitized securities does not generate additional frictions, beyond those already present in the model (the incentive problems of entrepreneurs and nancial intermediaries). 3.1 Unsupervised Securitization A bank that transfers all its claims on a project to nancial markets is then transferring the right on R R f if the project is successful in exchange for a cash investment of I A i. By transferring all the bank's claims to the nancial market, the bank no longer has a stake in the project's outcome, and hence has no incentives to monitor the project. The expected return on the resulting pool of loans thus depends on the proportion of good loans in the pool, those that come from the richest entrepreneurs who pledged A i A of their own capital to the project. The presence of bad loans in the pool lowers the average return and generates a negative externality on the entrepreneurs with good projects. This generates an incentive for these entrepreneurs to migrate to banks that pool their projects with other good projects and lower their cost of capital. In equilibrium, this will result in a situation where loans to entrepreneurs with A i A are pooled into high quality securitized issues and those with A i < A are not securitized. [[This is similar to the situation in Spain where only the highest quality mortgages are securitized.]] In the US, securitization usually involves the pooling of claims that are known to contain a signicant proportion of lower quality ones. To counterbalance this, issuers usually keep a fraction of the issue. In the current setting this corresponds to a partial transfer of claims to nancial markets. This then translates to a three-way contract which can then be analyzed in 7

the same way as bank nancing above, where R f corresponds to the payments retained by the entrepreneur, R u those that accrue to outside investors who purchase the part of the securitized issuance that is sold on the open market, and R m corresponds to the payments that accrue to the issuer of pooled security. Naturally, this will result in the same solution we studied above: only entrepreneurs with A i A will be able to obtain sucient nancing. Thus, securitization per se does not improve on the outcomes considered above, where entrepreneurs could access uninformed investors directly, either with or without bank nancing. Nevertheless, securitization could have positive eects on the real sector if, as considered at the beginning of this section, entrepreneurs did not have direct access to uninformed investors (with lower expected returns, γ) but had, instead, to access capital markets indirectly, through banks with a higher expected returns (which required at least γ B even for the highest quality projects that required no monitoring). 3.2 Supervised Securitization An alternative method to organize project nancing not considered in HT is to separate the nancing from the monitoring role of informed intermediaries. So far, informed intermediaries that provided monitoring services have competed amongst themselves by providing nancing for the project. But, as we saw above, bank capital is expensive on two counts: it must cover the monitoring fee, c, and it came from a more expensive source of funding, as bank funds carried the extra charge represented by η > 0. Ideally, one would want to exploit the monitoring skills of banks, pay c, and raise all remaining capital from nancial markets directly to at least save on extra cost of capital, η (via securitization). Let us consider this possibility: the entrepreneur pays a monitoring fee of C to an informed nancial intermediary, and raises the capital needed for the project, plus that needed to pay the monitoring fee, I A i +C, directly from nancial markets with a cost of capital of γ. This form of nancing is not unusual in large rms, that may pay an auditor to supervise their accounts and issue tradable equity directly to investors through the stock exchange. Alternatively, large rms may also obtain outside certication of the probability of future expected payments in the 8

form of credit ratings or from due diligence reports from investment banks involved in an IPO. Furthermore, there is an implicit requirement of monitoring involved in the legal structure of nancial contracts between rms and banks, emanating from due diligence obligations on the part of the bank or bank agent, regardless of the magnitude of the contract (loan). What we are proposing here is to consider these (implicit or explicit) contractual monitoring obligations as a potential alternative way to soften the incentive problem of the entrepreneur, other than having the intermediary taking a large stake in every project's future performance, and combine them with securitization of loans to small and medium-sized enterprises to give them direct access to investors. 3.2.1 The Supervisor In the context of the original HT article, monitoring is costly (c > 0) for any entity and a fee-for-monitoring structure is not enforceable because the monitor's monitoring decision is not observable. We are going to allow an entity, which we call the supervisor, to observe the monitoring activity of the informed nancial intermediary. Above, we have listed possible monitoring entities all of which are private rms, or private agreements that are enforceable through the Courts. So, we think of the supervisor as either an explicit supervisory entity, such as the Central Bank, or the Court. For simplicity, we will assume that the supervisor receives a costless and imperfect signal of the monitoring activity of the bank, represented by the random variable π. One could make it costly to acquire the signal, and add a parameter to capture its cost, and it will modify the analysis in the obvious way. Nevertheless, one can also think of the signal as a byproduct of the supervisor's other activities (in the case of the CB) or obtained from a previous sunk investment or costless to the supervisor, though possibly not to society (in the case of the Court). Let H denote the state of the world when there is monitoring by the bank, and L the state that there is no monitoring. The signal has the following properties: it is described by the probability distributions{f (π H), f (π L)} where distributions are absolutely continuous (with respect to Lebesgue measure) on the support of the distribution (which we assume is equal to [0, 1]) with increasing hazard rates, and satisfy the monotone likelyhood ratio property: 9

f (π H) /f (π L) is strictly increasing in π. Thus, a high π is good news about monitoring (in the sense of [Milgrom ]), that is, for all prior, the probability that monitoring has taken place conditional on the realization of the signal, π, is increasing in π. Thus, the supervisor has a non-trivial, imperfect signal of the bank's monitoring eort. In addition to having information on the bank's monitoring eort, the supervisor can discipline the bank if he decides that the bank is not monitoring. Let D < be the maximum (per project) penalty the supervisor can impose on the bank. We assume that the supervisor can only impose non-negative penalties. 1 The supervisor can commit to a disciplinary strategy, where a disciplinary strategy is a function τ : [0, 1] [0, 1], where τ (π) represents the fraction of the maximal penalty imposed on the bank conditional on observing π. 3.2.2 The Monitor's Incentives Given a disciplinary strategy τ, and a monitoring fee C, the incentives of the bank to monitor are given by the following incentive compatibility constraint: C D τ (π) f (π H) dπ π }{{} Expected PenaltyH c C D τ (π) f (π L) dπ, π }{{} Expected Penalty L (10) plus the participation constraint: C D τ (π) f (π H) dπ c 0. (11) π Competition amongst intermediaries to provide monitoring services will make constraint (11) bind so that the competitive monitoring fee, C, is given by C = c + D τ (π) f (π e H ) dπ. π 1 The model can be easily restated to allow the supervisor to impose negative penalties, that is, rewards for good behavior, as long as these are bounded. 10

We can thus separate the monitoring fee into a monitoring cost, c, and the cost of imperfect supervision D π τ (π) f (π e H) dπ. Thus, the supervisor can aect the real sector through an additional channel, its choice of a disciplinary strategy, τ (π). 3.2.3 Equilibrium Project Financing If banks have incentives to monitor in the fee-for-monitoring nancing structure, then the entrepreneur faces the same incentive problem as in the loan nancing structure, so that the project will be good if R f b p. Then, the nancing problem for the entrepreneur is to raise the amount of capital I A i +C from investors, with the promise of a payment of R R f from the project, if it is successful. This can be done, via nancial intermediaries, using securitization. The new nancing needs together with the incentive compatibility constraint of the entrepreneur translates into the following nancing condition: p H ( R b ) γ (I + C A i ) A i A = I + C p ( H R p γ b ), (12) p from which we obtain a new level of own capital, A, needed for the entrepreneur to be able to exploit this new nancing option. Suppose loan nancing is ecient, A A, then, the combination of supervised monitoring and securitization (supervised securitization for short) will be ecient if A A C s c η p H p. (13) Condition (13) describes how the eciency of supervised monitoring depends on whether the gains, in terms of the savings in additional nancing cost η from using bank capital, are greater than the relative cost of supervision. 11

3.2.4 Contractual Implementation As mentioned above, supervised monitoring is already (sometimes implicitly) included in certain kinds existing contracts. For example, a lender that resells a loan to be securitized assumes certain due diligence obligations. These due diligence obligations can be formalized as a constant monitoring requirement and enforced both by courts and a central/federal supervisor. We now turn to the role of the central bank (CB), and the issues that arise when trying to fulll this role. 4 The Central Bank Having identied the main factors that determine the level of project nancing in the economy we now turn to the possibilities available to the CB to aect growth (via the expansion of the use of credit). 4.1 The Central Bank and Loanable Funds As HT point out, in the baseline model there are no externalities that cannot be internalized just as eectively by the entrepreneur as by a social planner with the same informational constraints. Thus, there is little a CB can do, both in the case of equity nancing as well as with bank nancing (and monitoring). The introduction, on our part, of a wedge between the cost of capital of nancial intermediaries and the expected return required by uninformed investors, η > 0, opens an avenue for the CB to inuence growth (in the sense of inuencing the number of projects that can obtain nancing). As can be observed from inspecting the level of capital needed by the marginal project in the case of monitored bank nance (Equation (8), an increase in η leads to an increase in A. The CB may be able to aect this parameter, as it may depend on factors under the CB's control (reserve requirements, cost of compliance with CB policies,...). Thus, a CB with a growth mandate should try to adapt its policies so as not to increase the cost of capital of nancial intermediaries more than absolutely necessary. Alternatively, quantitative easing in this context translates into an overall reduction in the expected return on 12

investment, γ, that would act as a stimulant for growth both in term of equity as well as bank nanced projectswhether through direct bank nancing or via unsupervised securitization. [[Though the total level of loans may be smaller see HT]]. 4.2 The Supervisor's Optimal Disciplinary Strategy The opportunities for the CB to inuence project nancing is greater if the CB is acting as supervisor in an economy where supervised securitization is (or can be made to be) ecient. Let us consider the CB's choice of disciplinary strategy. As we have seen above, the disciplinary strategy selected by the supervisor aects real activity through its eect on the expected cost of supervision, C s. This parameter appears in the condition that determines whether supervised securitization is ecient, Condition (13). A lower cost of supervision lowers increases the set of parameter values for which securitization is ecient. This eect comes about because a lower cost of supervision lowers the threshold level of own capital needed to nance projects via supervised securitization, lowers A. Therefore, it is natural that a CB with a growth mandate should try to minimize C s while ensuring that its disciplinary strategy encourages eective monitoring of securitized loans on the part of banks. Thus, we can write the supervisor's problem as min τ s.t. π τ (π) f (π H) dπ D τ (π) f (π H) dπ + c D π τ (π) f (π L) dπ. We are ignoring the participation constraint, as market forces will set C = c+ τ (π) f (π H) dπ D in equilibrium. This problem has been studied in detail in [[Ganuza et al (2013), GGP]] and from their analysis we obtain: Proposition 1. The optimal disciplinary strategy is characterized by a cuto level of the signal π, and a threshold rule such that If π < π, impose the maximum penalty, τ (π) = 1 13

if π > π, impose the minimal penalty, τ (π) = 0, and if π = π, set τ (π)\in[0, 1]. As the signal increases is monotone in monitoring, a low signal is indicative of no monitoring. From the monotonicity of the signal, it is shown that the CB's optimal disciplinary strategy is to impose the maximum penalty if the signal is too low (below π) and to do nothing (even reward the bank, if that is possible) if the signal is suciently high (above π). Then, the CB's problem is: min π F (π e)d s.t. F (π e H ) c D F (π e L) (IC) Following the analysis in GGP, we can rewrite the CB's problem in terms of the policies errors, where T I = F (π H) denotes the Type I error (false positivesdisciplining banks that monitor adequately) and T II = 1 F (π L) denotes Type II error (false negativesnot disciplining banks that are not monitoring). Then, the supervisor's problem is equivalent to: min π T I s.t. T II + T I 1 c D. Let Φ(π) = T II +T I = 1 F (π L)+F (π H) denote the sum of error function. This function has some very useful properties: Lemma 1. The sum of error function has a unique minimum on the interval [0, 1] at π min. The function takes values: Φ (0) = 1 and Φ (1) = 1. Let D = [0, π min ] denote the interval where Φ is decreasing and let Φ D denote the weighted error function restricted to this domain. The solution to the CB's problem is then given by the following result: 14

Theorem 1. Given D, there exists a c max (D) that is decreasing in D such that if c c max it is possible to induce monitoring, and there is an optimal standard π (c) = Φ 1 ( ) D 1 c D that is increasing in c. If c > c max it is not possible for the supervisor to induce banks to monitor. These results determine if supervised securitization is feasible, and, if it is, identify the threshold that denes the supervisor's optimal disciplinary strategy. From Theorem 1 it follows that as the cost of monitoring increases (or the maximum penalty decreases), the supervisor uses a higher disciplinary threshold, which implies more frequent disciplinary actions. This then implies a higher cost of monitoring and hence less nancing of projects through supervised securitization, and lower growth. Theorem 1 also tells us that even if supervised securitization is much preferred to bank nancing (say, because η is very large), it may still occur that it is impossible for the supervisor to induce monitoring, if c > c max. 5 Conclusion Within the context of the incentive model of economic activity of HT, we have explored securitization as an alternative nancing mechanism to bank loans. We have described two fundamentally dierent ways to implement securitization: unsupervised and supervised securitization. The rst, unsupervised securitization, essentially implements the nancing channel proposed by HT. Unsupervised securitization provides a potential mechanism to implement HT's theoretical proposal that small entrepreneurs access uninformed investor nancing and limit the use of more expensive bank capital to the minimal amount required to ensure that it is credible that the bank is monitoring them. Thus, for entrepreneurs from small and medium-sized rms who cannot sell securities directly to uninformed investors, unsupervised securitization provides a potential mechanism to do so. The second form of securitization, supervised securitization, is a mechanism that was not considered by HT. Supervised securitization is based on the presence of a supervisory entity that can credibly enforce monitoring agreements between entrepreneurs and banks. The ability of a 15

supervisor, such as a CB, to be eective in this way is determined by two factors: the quality of the supervisor's information on the bank's monitoring activity, and the range of possible penalties it can apply to banks perceived not to be adequately monitoring their loans. If these conditions are met, then it may be possible to separate the monitoring role of banks from their nancing role. Banks can then sell their monitoring services for a fee and loanable funds can be obtained (through securitization) from capital markets at a lower cost. This mechanism may be more ecient than direct bank nancing, where the eciency of this mechanism depends on the quality of the supervisor's information, reected in the expected costs imposed by false positives when the supervisor is trying to detect banks that are not monitoring, relative to the gains in terms of the dierence in the cost of bank capital versus direct investor capital. Finally, we have characterized the supervisor's optimal disciplining policy. We have found that higher costs of monitoring does not only have a direct impact on the nancing possibilities of entrepreneurs, but that this eect is exacerbated as it requires the supervisor to impose more frequent penalties, and thereby also increases the cost of supervision. Also, we found that if the direct cost of monitoring is too high, it may be impossible for the supervisor to induce banks to monitor their loans, regardless of how high the cost of capital of banks is, relative to that from direct investors. We have made this analysis in order to study the ways in which a CB with a growth mandate may be able to pursue this mandate. The conclusions that we draw are: (1) as anticipated in HT, there is no potential for the CB to encourage growth directly in the bank nancing setup, as all eciency gains can be internalized via private contracts; (2) the CB can encourage growth by lowering the overall cost of capital; (3) the CB may be able to encourage growth if it can reduce the wedge between the cost of bank nancing versus investor nancing; and (4) the CB may have the opportunity to exploit its information on bank activities to promote supervised securitization, if the quality of its information is suciently good, it can impose suciently harsh penalties on banks that are perceived to be inadequately monitoring their loans, and if the direct cost of monitoring is not too high (relative to the supervisor's penalties and the quality of its information). 16

We have focused on a single, growth-oriented supervisor as a way to separate the monitoring from the nancing role of banks. Alternatively, it is possible that private rms, competing in the market, may be able to fulll the same role as the supervisor and provide credible certication that banks are adequately monitoring their loans, but this a subject-matter for another paper. 17