Financial Intermediation and Delegated Monitoring

The Review of Economic Studies Ltd. Financial Intermediation and Delegated Monitoring Author(s): Douglas W. Diamond Source: The Review of Economic Studies, Vol. 51, No. 3 (Jul. , 1984), pp. 393-414 Published by: Oxford University Press Stable URL: http://www. jstor. org/stable/2297430 . Accessed: 03/09/2011 10:01 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www. jstor. org/page/info/about/policies/terms. sp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected] org. Oxford University Press and The Review of Economic Studies Ltd. are collaborating with JSTOR to digitize, preserve and extend access to The Review of Economic Studies. http://www. jstor. rg Review of Economic Studies (1984) LI, 393-414 ? 1984 The Society for Economic Analysis Limited 0034-6527/84/00280393$02. 00 Financial and Intermediation Delegated Monitoring DOUGLAS W. DIAMOND University of Chicago This paper develops a theory of financial intermediation based on minimizing the cost of monitoring information which is useful for resolving incentive problems between borrowers and lenders. It presents a characterization of the costs of providing incentives for delegated monitoring by a financial intermediary.

Diversification within an intermediary serves to reduce these costs, even in a risk neutral economy. The paper presents some more general analysis of the effect of diversification on resolving incentive problems. In the environment assumed in the model, debt contracts with costly bankruptcy are shown to be optimal. The analysis has implications for the portfolio structure and capital structure of intermediaries. INTRODUCTION This paper develops a theory of financial intermediation based on minimum cost production of information useful for resolving incentive problems.

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An intermediary (such as a bank) is delegated the task of costly monitoring of loan contracts written with firms who borrow from it. It has a gross cost advantage in collecting this information because the alternative is either duplication of effort if each lender monitors directly, or a free-rider problem, in which case no lender monitors. Financial intermediation theories are generally based on some cost advantage for the intermediary. Schumpeter assigned such a “delegated monitoring” role to banks, … he banker must not only know what the transaction is which he is asked to finance and how it is likely to turn out but he must also know the customer, his business and even his private habits, and get, by frequently “talking things over with him”, a clear picture of the situation (Schumpeter (1939), p. 116). The information production task delegated to the intermediary gives rise to incentive problems for the intermediary; we can term these delegation costs. These are not generally analysed in existing intermediation theories, and in some cases one finds that the costs are so high that there is no net advantage in using an intermediary.

Schumpeter made a similar point, although he did not consider incentives explicitly: … traditions and standards may be absent to such a degree that practically anyone can drift into the banking business, find customers, and deal with them according to his own ideas…. This in itself… is sufficient to turn the history of capitalist evolution into a history of catastrophes (Schumpeter (1939), p. 116). This paper analyses the determinants of delegation costs, and develops a model in which a financial intermediary has a net cost advantage relative to direct lending and borrowing.

Diversification within the intermediary is key to the possible net advantage of intermediation. This is because there is a strong similarity between the incentive problem between an individual borrower and lender and that between an intermediary and its 393 394 REVIEW OF ECONOMIC STUDIES depositors. The possibility of diversification within the intermediary can make the incentive problems sufficiently different to make it feasible to hire an agent (the intermediary) to monitor an agent (the borrower). Diversification proves to be important even when everyone in the economy is risk neutral.

This model is related to two literatures. It relates to the single agent-single principal literature (e. g. Harris-Raviv (1979), Holmstrom (1979) and Shavell (1979)) which develops conditions when monitoring additional information about an agent will help resolve moral hazard problems. The analysis here extends this to costly monitoring in a many principal setting, where principals are security holders of a firm or depositors in an intermediary. The other related literature is that of financial intermediation based on imperfect information.

Several interesting papers analyse the gross benefits of delegating some informational task to an intermediary without presenting explicit analysis of the costs and feasibility of this delegation (e. g. Leland-Pyle (1977) and Chan (1982)). In addition to developing a model in which overall feasibility of financial intermediation is analysed, we briefly apply our results to determine conditions when intermediation is feasible in the Leland-Pyle model. The basic model developed is of an ex-post information asymmetry between potential lenders and a risk neutral entrepreneur who needs to raise capital for a risky project.

In this environment, debt is shown to be the optimal contract between an entrepreneur and lenders. Because of the wealth constraint that an entrepreneur cannot have negative consumption (pay lenders more than he has), the debt contracts with which the entrepreneur can raise funds involve some costs. As an alternative to incurring these costs, it is possible for lenders (who contract directly with the entrepreneur) to spend resources monitoring the data which the entrepreneur observes. In the class of contracts written directly between entrepreneurs and lenders, the less costly of these two is optimal.

However, the cost of monitoring may be very high if there are many lenders. If there are m outside security holders in a firm and it costs K > 0 to monitor, the total cost of direct monitoring is m K. This will imply either a very large expenditure on monitoring, or a free rider problem where no securityholder monitors because his share of the benefit is small. The obvious thing to do is for some securityholders to monitor on behalf of others, and we are then faced with analysing the provision of incentives for delegated monitoring. There are many methods by which delegated monitoring might be implemented.

We assume that the information monitored by a given person cannot be directly observed without cost by others. The analysis here focuses on a financial intermediary who raises funds from many lenders (depositors), promises them a given pattern of returns, lends to entrepreneurs, and spends resources monitoring and enforcing loan contracts with without monitoring. The financial entrepreneurs which are less costly than those availabled intermediary monitors entrepreneurs’ information, and receives payments from the entrepreneurs which are not observed by depositors.

An example of useful costly information in a loan contract is a covenant which is costly to monitor. A common covenant is a promise that the firm’s working captial will not fall below some minimum, unless “necessary for expansion of inventory”. (See Smith-Warner (1979). ) If it is costly to determine whether a shortfall is “necessary”, and each of the bondholders has to incur this cost to enforce the contract, the contract using costly information is unlikely to be used if the number of bondholders is large.

A contract specifying an uncontingent working capital requirement might be substituted, when the contingency would have been specified if there had been a single principal. In practice, loan covenants in bank loan contracts specify coarse contingencies which define DIAMOND FINANCIAL INTERMEDIATION 395 a “default”. Conditional on such a default, the intermediary monitors the situation and uses the information to re-negotiate the contract with new interest rates and contingent promises.

A financial intermediary must choose an incentive contract such that it has incentives to monitor the information, make proper use of it, and make sufficient payments to depositors to attract deposits. Providing these incentives is costly, but we show that diversification serves to reduce these costs. As the number of loans to entrepreneurs with projects whose returns are independent (or independent conditional on observables) grows without bound, we show that costs of delegation approach zero, and that for some finite number of loans financial intermediation becomes viable, considering all costs.

Financial intermediaries in the world monitor much information about their borrowers in enforcing loan covenants, but typically do not directly announce the information or serve such an auditor’s function. The intermediary in this model similarly does not announce the information monitored from each borrower, it simply makes payments to depositors. We show that debt is the optimal contract between the intermediary and depositors. The result that the delegation costs go to zero implies that asymptotically no other delegated monitoring structure will have lower costs.

If there is an independent demand by entrepreneurs for monitoring without disclosure of the information monitored, for example to keep competitors from learning the information as suggested by Campbell (1979), then well diversified financial intermediaries can provide it (in addition to simple monitoring services) at almost no cost disadvantage. Diversification is key to this theory, and it is interesting that because of the wealth constraint, diversification is important despite universal risk neutrality.

To develop a more general intuition into the role of diversification, some analysis is presented of a related model with risk averse agents but no wealth constraint. Two types of diversification are considered in the context of two alternative financial intermediary models; one is the traditional diversification by sub-dividing independent risks, while the other is diversification by adding more independent risks of given scale. The latter is what Samuelson (1963) has ermed a “fallacy of large numbers”, because it does not always increase expected utility. This section may be of independent interest because it provides some conditions when the fallacy of large numbers is not a fallacy. The basic model is outlined in Section 2. Delegated monitoring by a financial intermediary in the context of the basic model is analysed in Section 3. Section 4 explores the extension of the basic model to risk averse agents. Section 5 applies the analysis of section 4 to the model of Leland-Pyle.

Section 6 concludes the paper. 2. A SIMPLE MODEL OF FIRM BORROWING A model of risk neutral entrepreneurs who need to raise capital to operate a large investiment project is used to capture many of the aspects of the agency relationship between commerical borrowers and lenders. We specify a simple environment, and characterize optimal direct contracts between borrower and lender. There are N entrepreneurs indexed by i = 1, … , N in the economy. For the balance of Section 2, we examine one of them, and do not use the index.

The entrepreneur is endowed with the technology for an indivisible investment project with stochastic returns. The scale of inputs for the project greatly exceeds both his personal wealth and the personal wealth of any single lender. For simplicity, the entrepreneur’s wealth is zero. Assume a one good economy with all consumption at the end of the period. The project requires inputs of the good today, and will produce output in one period. Normalize the required initial amount of inputs to one. The expectation of the output that will be 396 REVIEW OF ECONOMIC STUDIES roduced at the end of the period exceeds R, the competitive interest rate in the economy. Therefore, the project would be undertaken if the risk neutral entrepreneur had available to him enough capital inputs. The other investors in the economy are also risk neutral: call them lenders. To undertake the project, the entrepreneur must borrow sufficient resources from them to operate it at its scale of one. Because the interest rate is R, i. e. the lenders have access to a technology which will return R per unit of input, the entrepreneur must convince potential lenders that the rate of return hich he will pay to them has an expected value of at least R. Each lender has available wealth of 1/m, thus the entrepreneur must borrow from m > 1 lenders. The capital market is competitive-if convinced that their expected return equals or exceeds R (R/m per lender), lenders will make the loan. Let the total output of the project be the random variable -. Assume that is bounded between zero and y R + K (where K > 0 and is defined below) and that y =0 is possible. The realization of 9. oes not depend on any actions of the entrepreneur. A simple information asymmetry is introduced which will make the loan contracting problem non-trivial. The realization of is freely observed only by the entrepreneur. With output observed by the entrepreneur alone, he must be given incentives to make payments to lenders. At the end of the period, he will pay a liquidating dividend. It is always feasible for him to claim a very low value of y, and keep for himself the difference between the actual value and what he pays the others.

Let z > 0 be the aggregate payment which the entrepreneur pays to the m lenders. If the realization of output is 9= y, he then keeps y – z for himself. Because consumption cannot be negative the payment which he pays cannot feasibly exceed y (plus any personal wealth he might have, assumed here to be zero). To induce the entrepreneur to select a value of z > 0, he must be provided with incentives. To raise captial to undertake the project, lenders must believe that the expectation of the value of z which he will select is at least R.

The entrepreneur must choose an incentive contract which depends only on observable variables and makes lenders anticipate a competitive expected dividend. The only costlessly observable variable is the payment z itself. Lenders know the distribution of y, and know that the entrepreneur chooses the payment z which is best for him given a realization y = y, and that z E [0, y]. If y exceeded R with probability one, then a full information optimal contract would be feasible-the risk neutral entrepreneur would offer an uncontingent payment of R. (See Harris-Raviv (1979). It might appear that the assumption that y = 0 is a possible outcome of the project rules out any borrowing, because z = 0 must be feasible, and it does not appear incentive compatible for an entrepreneur to choose a payment z > 0 when he can choose z = 0 and retain the rest. However, we will allow contracts with non-pecuniary penalties: penalties where the entrepreneur’s loss is not enjoyed by the lenders. This allows the agent’s utility function to be defined over negative values of its domain without allowing negative consumption to “produce” goods.

We will see that these penalties are best interpreted as bankruptcy penalties. Some examples include a manager’s time spent in bankruptcy proceedings, costly “explaining” of poor results, search costs of a fired manager, and (loosely) the manager’s loss of “reputation” in bankruptcy. Physical punishment is a less realistic example. Projects which could not be undertaken at all without the penalties can be operated using the penalties. DIAMOND FINANCIAL INTERMEDIATION 397 The optimal contract maximizes the risk neutral entrepreneur’s expected return, given a minimum expected return to lenders of R.

Let the function c, from the nonnegative reals to the non-negative reals, be the non-pecuniary penalty function, which depends on z, the payment to lenders selected by the entrepreneur. Assume that if the entrepreneur is indifferent between several values of z, he chooses the one preferred by the lender. The optimal contract with penalties 4*( – ) _ 0 solves1 ymax4,(. )E ^[maxzE[O,-] z – ( z)] Subject to and yE [arg maxZ,[O,-] z-(z)]_ R, z e arg maxZE[O, y- z (z) (la) (lb) (ic) where the notation “arg max” denotes the set of arguments that maximize the objective function that follows.

Proposition 1. The optimal contract which solves (1) is given by +*(z)= max (h – z, 0), where h is the smallest solution to (P(y-; h) *Ey[yJy; h]) + (P(y ;: h) *h) = R. (2) That is, it is a debt contract with face value h and a non-pecuniary bankruptcypenalty equal to the shortfallfrom face, h, where h is the smallest face value which provides lenders with an expected return of R. Proof. Given +*(z), arg maxz[o,y] z-zy (Z) {= if y 0 for each principal to monitor, and the cost must be incurred before the output realization is known to anyone, including the entrepreneur.

See Townsend (1979) for some interesting analysis of the optimal contingent monitoring policy when the decision to monitor can be made after the entrepreneur has made a payment to a lerlder. This additional complication is not introduced because given some specified probability of monitoring it would not influence our results. If it is possible for lenders to observe the outcome at some cost, there are three types of contracting situations possible. The contract can be as described above, with no monitoring. A second possiblility is for each of the m lenders to spend resources to monitor the outcome.

Thirdly, the lenders can delegate the monitoring to one or more monitoring agents. The least costly of these will be selected. If there were a single lender so m = 1 (rather than m ; 1 as we assume), monitoring would be valuable if its cost were less than the expected deadweight penalty without monitoring or K BE[p*(9)]. With many lenders and direct contracting between the entrepreneur and lenders, if each lender monitors, monitoring is valuable if and only if m K _ Ej[o*(9)]. When m is large this is unlikely because each lender’s loan is small.

Even if this condition for valuable monitoring is satisfied, it implies a large expenditure on monitoring and some sort of delegated monitoring might be desirable in this case. To obtain the benefits of monitoring, when m is large the task must be delegated rather than left to each individual lender. The entity doing the monitoring (“the monitor”) must be provided with incentives to monitor and enforce the contract. We assume that the actions taken and the information observed by the monitor are not directly observed by the lenders. It will generally be costly to provide incentives to the monitor, and below we analyse these costs.

The total cost of delegated monitoring is the physical cost of monitoring by the monitor, K, plus the expected cost of providing incentives to the monitor, which we call the cost of delegation and denote the cost per project by D. Delegated monitoring pays when K+D’ min[E k*(9)], (m. K)]. The costs of delegation are analysed when the monitor is a financial intermediary who receives payments from entrepreneurs and makes payments to principals. 3. DELEGATED MONITORING BY A FINANCIAL INTERMEDIARY A financial intermediary obtains funds from lenders and lends them to entrepreneurs.

Economists have tried to explain this intermediary role by arguing that the financial DIAMOND FINANCIAL INTERMEDIATION 399 intermediary has a cost advantage in certain tasks. When such tasks involve unobserved actons by the intermediary or the observation of private information, then an agency/incentive problem for the intermediary may exist. Any theory which tries to explain the role of intermediaries by an information cost advantage must net out the costs of providing incentives to the intermediary from any cost savings in producing information.

Existing intermediary theories do not make this final step. We now introduce a financial intermediary between entrepreneurs and lenders (whom we call depositors from now on), and examine conditions when this intermediary function is viable considering all costs. A financial intermediary is a risk neutral agent, with personal wealth equal to zero. The intermediary receives funds from depositors to lend to entrepreneurs and is delegated the task of monitoring the outcomes of entrepreneurs’ projects on behalf of depositors. Monitoring the i-th entrepreneur costs the intermediary K units of goods. Depositors can observe the payment they receive from the intermediary, but cannot observe the project outcomes, payments by entrepreneurs to the intermediary, or the resources expended by the intermediary in monitoring the outcomes. Each entrepreneur’s project requires one unit of initial capital. Each depositor has available capital of 1/m, as in Section 2. An intermediary which contracts with N entrepreneurs has m N depositors. To analyse the conditions when intermediation is beneficial (when the monitoring cost savings exceed the delegation costs of providing incentives) we must first characterize the delegation costs.

If the intermediary could monitor at no cost, it could enforce contracts with entrepreneurs which imposed no deadweight bankruptcy costs on them. However, there would remain an incentive problem for the intermediary, because the payments it receives from entrepreneurs are not observed by depositors. The intermediary could claim that payments from entrepreneurs were low, and pay a small amount to depositors. We now extend the results in Section 2 to analyse the optimal contract to provide incentives for an intermediary to make payments to depositors. We later show that it provides incentives to monitor as well.

Let us re-introduce the subscript i on the outcome yi of the i-th entrepreneur. For i= 1, . . . , N, the 9i are distributed independently and all are bounded below by zero and above by the real number y. The probability distribution functions of the 9i are common knowledge to all. Let gi ( *) be the non-negative real valued function which is the payment to the intermediary by the i-th entrepreneur as a function of the outcome yi, assuming the intermediary monitors yi. Because yi is then observed by the intermediary, this implies no deadweight penalties will be imposed on the i-th entrepreneur.

If the intermediary does not monitor, it must use a contract with deadweight bankruptcy penalties, as. in Section 2, but in that case there would be no reason to have an intermediary. Due to the constraint that an entrepreneur can pay only what he has, we require gi(yi) ‘-yi. The intermediary monitoring N entrepreneurs receives total payments GN when ? – = Y, Y2= Y2, * * , YN= YNequal to GN 1i GN=N gi(Yi). Let GN be the random variable with realization GN. It is bounded above by GN, and below by zero. The intermediary must make total payments to depositors with expectation R per project, or N- R in total.

Let ZN be the total payment to depositors by entrepreneurs. The intermediary can pay only what it has, thus ZN – GN. By an argument identical to that of Section 2, we see that deadweight bankruptcy penalties must be imposed on the intermediary unless the intermediary will always receive aggregate payments of at least N* R, or P(GN ‘ N R) = 1. Because of the constraint that entrepreneurs can pay the 400 REVIEW OF ECONOMIC STUDIES intermediary at most yi, we know P( GN ; N- R) C P(E,i=1yi ‘-NV R ). Any entrepreneur, i, with P(. _ R) = 1 could finance directly, with no bankruptcy penalties, thus entrepreneurs who choose to use intermediaries will lead the intermediary to incur expected deadweight bankruptcy penalties. Let 1D(ZN) be the deadweight non-pecuniary penalty imposed on the intermediary when payment ZN is made to depositors. From Proposition 1, the optimal FD(ZN)which gives incentives to make payments with expectation N- R, is given by (D(ZN) = max [HN ZN, 0], where the constant HN is the smallest solution to {(P(GNNHN The expected return of the intermediary net of expenditure NK on monitoring is EGN(GN)-HN-NK=[N. R+K+DN)]-[N(R+2N)1 =-DN>O. -(N-K) N 2 (satisfying the constraint that this be non-negative. ) The aggregate expected return to depositors is given by PN. Ec;N[GNIGN-HN]+(1-PN). HN where PN-P(GN-HN). 0 and that the aggregate expected R DN Notice that GNi-0 implying EcN[GNIGN-? HN] rerurn of depositors is greater than or equal to: ( 1-PN) *HN = ( 1 PN) (N > NX R 2 for smallPN>0 i. e. for PN E (0, (DN/2)/(R +DN/2)). There exists N* HN. This implies that the delegation cost DN can be made arbitrarily small for large N. 11 402 REVIEW OF ECONOMIC STUDIES

Proposition 2 demonstrates the key role of diversification in the provision of delegated monitoring. The intermediary need not be monitored because it takes “full responsibility” and bears all penalties for any short-fall of payments to principals. The diversification of its portfolio makes the probability of incurring these penalties very small and allows the information collected by the intermediary to be observed only by the intermediary. Proposition 1 characterized the optimal incentive compatible mechanism for financial intermediation, and this is the optimal incentive compatible mechanism with “privacy”.

It was the optimal mechanism when the agent monitoring entrepreneurs was constrained not to announce the values of the project outcomes he observed and could only use the information privately to enforce his contract with each entrepreneur. Proposition 2 shows that financial intermediation is, asymptotically, the optimal incentive compatible mechanism for financing entrepreneurs’ projects, without imposing the constraint of “privacy”. If the number of entrepreneurs monitored is N = 1, then delegation costs are so large that intermediation is never viable.

If N — oo, then expected delegation costs approach zero, and intermediation is viable whenever direct monitoring pays. There exists some N> 1 at which intermediation becomes just viable (when DN min [E5[b*(-)], m- K]). If the assumption is made that each entrepreneur’s project has the same variance, then the expected delegation costs are a monotonically decreasing function of N. This leads to increasing returns to scale due to diversification, but asymptotic constant returns to scale because expected delegation costs per project are bounded elow by zero, and they may be small for moderate values of N. The incentive contract is debt with bankruptcy penalties and high leverage. Asymptotically, the debt is riskless (as DN — 0). The leverage is high, as the face value of the debt is H(N) = N- (R + DN/2), while the expected future value of the intermediary (including value of the debt) is N (R + DN+ K). The importance of the diversification is not simply a way for principals to hold welldiversified portfolios. Principals are risk neutral, and are not made directly better off by the diversification.

Diversification within the financial intermediary organization is important, and cannot be replaced by diversification across intermediaries by principals. Correlated returnsof entrepreneurs The assumption of independently distributed project returns across entrepreneurs is quite strong. It can be weakened somewhat. Instead of independence, assume that entrepreneur’s project returns depend on several common factors which are observable. Factors might include GNP, interest rates, input prices, etc. Since these are observable, they can be used as the basis for contingent contracts.

There might exist futures markets for these variables, and the financial intermediary could hedge changes in these factors in those markets. An example is a bank’s hedging of interest rate risk using interest rate futures. If there are not active futures markets, then the intermediary can write contracts with depositors which depend on the values of these factors, rather than taking responsibility for all risks. An example of this is matching the maturity of assets and liabilities by banks, which places all interest rate risk on depositors.

In either case, the intermediary retains responsibility for (and potentially fails as a result of) all risks which are not observable. The result of Proposition 2, that DN-; 0 as N-; o follows given this alternative assumption in place of independence. This is stated in the following corollary. DIAMOND FINANCIAL INTERMEDIATION 403 Corollary to Proposition 2. If it is common knowledge that the returnsof the projects of entrepreneursi = 1,… N, are given by Yi]-= [ 13ij Fj + ?i where the Fj are observable ex post, the ? are independent and bounded and E[9 ]; R + K, then the result of Proposition 2 follows. Proof. Choose gi(yi) = ai yi where R+K+DN =ti Ey[]Yi Let the penalty contract be either +(Z) =Z+[~7i=1 Em1 * [3ij*FJA-H(N) where H(N) = N- R +DN ]E[ = 1 E ml (Xi 13ij F-J, * or let 4+(Z) be as in Proposition 2, and let the position in the futures market be aA=1i* in futures markets j = 1, . . . , M The transformed random variables are now independent, and the result Proposition 2 follows. II The intermediary monitors firm specific information, which is independent across entrepreneurs, and hedges out all systematic risks.

The description of the process generating project returns is consistent with the Arbitrage Pricing Theory of Ross (1976). The intuition behind this result is that the intermediary must bear certain risks for incentive purposes, but that risks which have no incentive component because they are common information should be shared optimally. 4 There has been a debate among various bankers and bank regulators over the desirability of allowing hedging in futures markets by banks. Our analysis suggests a reason why it is desirable. 4.

RISK AVERSION AND DIVERSIFICATION Diversification proved to be important to reduce delegation costs despite universal risk neutrality because of the wealth constraint of non-negative consumption and the asymmetry of information about project outcomes. The wealth constraint gives rise to a special type of “risk aversion”. In this section, we investigate the role of diversification within the intermediary when the agents within the intermediary are risk averse in the usual sense. To focus on risk sharing issues, we drop the wealth constraint to allow any promise to be made good.

A complete re-analysis of the model of Section 2 is not presented. This section does not present a realistic intermediary model, but simply a further investigation of the role of diversification in reducing the costs of delegation. The basic set-up is as in Section 2, each entrepreneur is endowed with a project with outcome -i which is freely observed only the entrepreneur, which has zero as a possible realization. Absent monitoring by lenders, no incentive compatible payment schedule can depend on the realization yi, because the entrepreneur could always claim a low value occurred.

For simplicity, assume that all agents in the economy, including the 404 REVIEW OF ECONOMIC STUDIES entrepreneurs, are identical and risk averse. Risk aversion implies that the payment to lenders will be a constant, rather than a random amount independent of -i, (see Holmstr6m (1979)). This implies that, absent monitoring, the risk averse entrepreneur bears all of the risk from fluctuations in -i. This is inconsistent with the optimal risk sharing which would occur if yi were observed, and this provides a potential benefit from monitoring Yi.

In this risk averse setting, we could introduce other actions, e. g. effort, which the entrepreneur could privately select to give rise to a more general motivation for monitoring. This would not change the essence of our results. We focus again on delegated monitoring by a financial intermediary. A financial intermediary raises funds from depositors who do not monitor, lends these funds to entrepreneurs, and can offer improved risk sharing with an entrepreneur because the intermediary’s monitoring reduces or eliminates the incentive problem.

In Section 2, we showed that an intermediary monitoring a single entrepreneur would have an incentive problem just as severe as would an entrepreneur. Almost the same result is true here. Because depositors do not monitor the intermediary and cannot observe its information, incentive compatible payments from the intermediary to depositors cannot depend on outcomes, and will be constant. It is true, however, that a single intermediary and a single entrepreneur can now share yi risk, but this has little to do with intermediation. an share risk with the entrepreneur Any lender who spends resources to monitor Ya without being called an “intermediary”. For a financial intermediary in an economy where everyone is risk averse to viably provide delegated monitoring services, it must have lower delegation costs than an entrepreneur. Equivalently, since risk sharing is the issue here, a viable financial intermediary which monitors many entrepreneurs with independently distributed projects must charge a lower Arrow-Pratt risk premium for bearing the risk of an entrepreneur’s project than does the entrepreneur.

This will carry over to more general settings, because if the intermediary can bear risks at a lower risk premium it will generally face a less severe trade-off between risk sharing and incentives, and can thus efficiently be delegated a monitoring task. Two types of diversification There are two ways in which an intermediary in an economy of risk averse agents might use diversification. They correspond to two different models of an intermediary. One model increases the number of agents working together within the intermediary organization as the intermediary monitors a larger number of entrepreneurs.

The second model assumes that the intermediary consists of a single agent who monitors a large number of entrepreneurs with independent projects. Beginning with the first model, assume that each identical agent (“banker”) in the intermediary is risk averse, and that by spending resources to monitor, each banker within the intermediary can observe the information monitored by all other bankers within the intermediary. This implies that there are no incentive problems within the intermediary.

The extreme assumption that incentive problems are absent is intended to capture the idea that there may be different mechanism for controlling incentive problems within an organization. This approach is followed in Ramakrishnan-Thakor (1983), to generalize the risk neutral analysis we present in Section 2. This model leads to the traditional “risk subdividing” type of diversification. This type of diversification works because each independent risk is shared by an increasing number of bankers.

For example, each risk averse agent will obtain a higher expected utility if each of N agents invests in a fraction 1/N of N identical independent gambles than in any single one of the gambles. DIAMOND FINANCIAL INTERMEDIATION 405 The second type of diversification, “adding risks”, occurs in the second model where a single banker bears 100% of N independent risks, with diversification occurring as N grows. This is quite different from risk subdivision, because it is not a form of risk sharing at all. The total risk imposed on the agent rises with N, while with subdivision of risks it falls with N.

Samuelson (1963) termed diversification by adding risks a “fallacy of large numbers”, because it is not true for all risk averse utility functions that the risk aversion toward the N-th independent gamble is a decreasing function of N. Samuelson provides no analysis of conditions when this type of diversification is beneficial, and I know of none in the literature. 5 We provide a partial characterization of conditions when the certainty equivalent of a given gamble is higher (and the risk premium lower) when another independent risky gamble is also held.

That is, when is the per asset certainty equivalent higher with N = 2 than with N = 1? We turn first to the relatively straightforward model of diversification by subdivision of risks. Assume that it takes one banker in the intermediary to monitor one entrepreneur, and this requires an expenditure in goods of K (or that the disutility of this monitoring task is additively separable). All bankers are identical, have increasing, concave utility of wealth functions U( W).

By spending K to monitor their entrepreneur, each banker can also observe information monitored by the other bankers within the intermediary, implying that there is no incentive problem within the intermediary. Depositors are not assumed to be able to observe any of the information generated within the intermediary, and are paid a fixed unconditional payment of NR. As N-; oo, Ramakrishnan-Thakor (1983) shows that each banker bears an arbitrarily small risk, with perfect risk sharing within the intermediary.

The interpretation of this result is that the diversification which occurs when bankers within the intermediary can share independent risks does serve to reduce the severity of its incentive problem. This occurs because the incentive problem here imposes a constraint on optimal risk sharing, and if there is improved risk sharing within the intermediary (where incentive problems may be controlled directly, or absent as assumed here), then this is analogous to reducing the risk aversion of a single agent, which reduces the tradeoff between risk sharing and the provision of incentives.

In the second model, where the intermediary consists of a single agent, diversification by adding risks is at work. The intermediary agent monitoring N loans, receives payments from each entrepreneur and bears all of the risk because he pays an unconditional return, N- R, to depositors. The financial intermediary can provide monitoring and risk sharing services superior to an individual lender if and only if his risk aversion toward the Nth independent risk is a decreasing function of N.

Put another way, when there is no wealth constraint an intermediary monitoring a single entrepreneur (N = 1) is equivalent to direct monitoring by a lender. Intermediation becomes potentially viable when the delegation cost (equal to the risk premium here) is reduced by the centralization of monitoring to a single intermediary. This is therefore equivalent to the conditions when adding independent risks reduces per-entrepreneur risk aversion, which are the conditions when the fallacy of large numbers is not a fallacy.

To provide a partial characterization of conditions when the per-risk risk premium declines, we initially focus on the case of two risks. That is, given two bounded and independent random variables gl and g2, when is the risk premium for bearing the risk of the bounded random variable l + g2 less than the sum of the two risk premia for bearing either risk separately. If both random variables represent payment chedules from entrepreneurs which a risk averse intermediary would voluntarily accept, both must have expectation greater than R + K, because the intermediary promises N- R to depositors and spends N K on monitoring. It will ease exposition to provisionally assume 406 REVIEW OF ECONOMIC STUDIES – R – K, for i =1,2. With this notation, the Egj[g] = R + K. In addition, define xi net effect of contracting to monitor an entrepreneur with payment schedule g- is equivalent to receiving the random variable x1. (In this notation, our temporary assumption is E [XI1]= 0. An agent has a four times differentiable, increasing and strictly concave von NeumanMorganstern utility function U( W), and initial wealth W0. The random variables x1 and x2 are bounded and independent. The risk premium, pi, for bearing the risk, of the single random variable xi (i = 1, 2), satisfies U( Eg-i[ Wo+ Xi+ Pi)] = U( Wo+ EJxjixi). The risk premium, P1+2, for bearing the risk of the random variable xl + x2, satisfies U( + EX1Ex2[ W0+ Xl + X2 P1+2)]= U( WO El[xl] + Adding risks reduces the risk premium if P1+2



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