“Financial Intermediation and Delegated Monitoring”
by Douglas W. Diamond 1984 RES
This paper derives a borrower-monitoring-cost advantage for a financial intermediary:
investors find it optimal to “delegate” monitoring to a bank to avoid duplication and avoid a
potential free-rider problem. The paper examines how the intermediary can be given the
incentive to carry out this delegated monitoring.
I. Assumptions
• A one period model. Risk-neutral entrepreneurs are initially endowed with a project requiring an input of one unit of the consumption good. However, the entrepreneur has
no personal wealth.
• There are many risk-neutral potential lenders, each with an endowment of the good 1/m < 1. They will lend if their expected return per unit investment exceeds R, the
日本留学专业competitive return.
• y = end of period return on project, non negative, bounded, and freely obrved only by the entrepreneur.
E[y] > R + K, where K = cost of monitoring for a single lender.
• z = total payment made by entrepreneur to lenders. z < y and y – z is amount绿萝花的作用
retained by entrepreneur.
• A non-pecuniary penalty can be impod on the entrepreneur.
II. Optimal borrower-lender contract when monitoring not allowed.
The entrepreneur knows the realization of y; the lenders do not. A contract specifies a payment z
and a penalty ξ as functions of the entrepreneur’s announcement of y. We look for the optimal
contract among truth-telling contracts.
The optimal contract will satisfy:
Max
E [y – z – ξ] (1a)
z(.), ξ(.)
subject to
0 < z(y) < y for all y (lb)
ξ(y) > 0 for all y (1c)
y – z (y) – ξ (y) > y – z (y´) – ξ (y´) for all y, y´
平凡的世界外星人
(1d)
> R
E[z]
风险规避
(le)
(la) is the expected utility of the entrepreneur. (lb) is feasibility of payments (1c) is feasibility of
punishment, (1d) is the entrepreneur’s incentive compatibility constraint. (le) is the expected
return constraint for the lenders.
Proposition 1: The optimal contract a debt contract with promid payment h such that
E[y | y < h] P(y < h) + h P(y > h) = R
That is,
E[min{h,y}] = R.
The actual payment z(y) is min{h, y}, and the punishment function ξ(y) = φ(z(y)) where φ(z) = max{h – z, 0}.
Note that since there are no mutually obrvable end-of-period state variables, the contract can, at most, be written on a promi to repay some fixed value h. Note also, it is important that the lenders can commit to penalize the entrepreneur. If the entrepreneur decided to pay nothing, the lenders real
ly have no ex-post incentive to punish him. It is assumed that when the entrepreneur is indifferent between veral outcomes, he choos the one giving the lenders as much as possible.
Proof: Clearly z(y) + ξ (y) must be constant for all y. Thus rewrite the problem as
E [y – h] (1a’)
Max
z(.), ξ(.), h
subject to
0 < z(y) < y for all y (lb’)
ξ(y) > 0 for all y (1c’)
z (y) + ξ (y) = h for all y
(1d’)
E[z]
> R (le’)
(1c) and (1d) simplify to z(y) < h (and we can drop ξ since it plays no further role in the maximization). Then combining further with (1b) we have the problem reduced to:
Max
E y [y – h] (1”)
z(.), h
subject to
0 < z(y) < min{h, y} for all y (lb”)
E[z] > R (le”) Clearly we want z as large as possible and h as small as possible in satisfying the constraints. This leads to the specifications of z and h; the specification of ξ then follows from (1d).
III. Optimal borrower-lender contract when costly monitoring is allowed.
Note that the contract in II involves an expected non-pecuniary bankruptcy cost Eφ, so that this opti
mal contract, given asymmetric information, results in lower expected utility relative to the optimal contract in a symmetric information environment.
Now assume that each lender is able can obrve y, individually, if s/he pays a cost of K > 0. Costly monitoring could be attractive if K is less than Eφ. But since it takes m > l investors to fund a single entrepreneur’s project, a free-rider problem can result. If all lenders monitored, with total cost nK, this may well exceed Eφ. In any ca, to avoid costly duplication, it may be possible to create an optimal contract which delegates the monitoring to one individual.
Assume that the actions of the “monitor” are not obrved by the other lenders. Then we end up with a similar problem of monitoring the monitor. A contract between the lenders and the monitor must be structured that gives the lenders their required rate of return while giving the entrepreneurs the incentive to obtain financing from the monitor rather than directly with the lenders. Conceptually, this condition is that
K + D < min {Eφ, nK}
where D is the cost of providing incentives to the monitor. We will have to specify this cost more carefully.
IV. Contracting with multiple entrepreneurs
Now think of the monitor as a manager of an intermediary (a.k.a. a bank). It contracts with N entrepreneurs and nN investors (who will turn out to be depositors).
The total payments received by the bank equals G N where
N
G N = Σ g i(y i)
i=l
where g i(y i) is the payment of the i th entrepreneur to the bank, assuming the bank monitors the entrepreneur. Further, assume that the y i are independently distributed.
Bank monitoring caus the monitor disutility of NK but requires no resources (initial wealth) on the part of the monitor.
The bank must make payments to the nN investors that, in total, have an expectation of NR.
Define Z N < G N as the amount that the bank actually pays the investors. The problem between the bank and the investors is then identical to the problem we analyzed in II between the entrepreneur and the lenders. From Proposition 1, the optimal contract between the monitor and the investors is a debt (deposit?) contract with promid payment H N and a non-pecuniary penalty function Φ(Z N) = max[H N – Z N,0]. As before, the promid payment, H N, satisfies
E[min{G N, H N}] = NR.
Now note that given this contract, the bank’s expected return (including the penalty) is E[G N] - H N (compare this with equation (1a’). Given H N, the bank will want to take actions to maximize G N, which means it will want to monitor efficiently, i.e., when K < Eφ.
V. The Role of Diversification
Becau loans are assumed to be independently distributed, diversification of the bank’s asts (via an increa in the size of the bank) will make the rate of return on the bank’s asts more and more certain. As N goes to infinity, the rate of return on the bank’s asts will be certain via the law of large numbers. This implies:
Proposition 2: The cost of non-pecuniary penalties, per entrepreneur monitored, D N, goes to zero as N goes to infinity, if projects are independently distributed.
Proof: Suppo that the expected payments by each entrepreneur pay a competitive rate of return plus the cost of monitoring and the delegation cost of the monitor:
李可人
E[g i(y i)] = R + K + D N.
This assumes that any rents from the project (above the delegation and monitoring costs) go to the entrepreneur, i.e., banking is competitive. Now consider the following contract. Let ΦN(Z N) = max[(H N – Z N),0] and
H N = N(R + ½ D N). As in Proposition I, given this contract, the bank has the incentive to make payments to depositors equal to Z N = min{G N , H N}. Given this payment structure, can the bank make a non-negative profit? Yes since the expected return to the bank is
E[G N] – H N – NK = N(R + K + D N) – N(R – ½ D N) – NK = ½ N D N
which is positive.
Finally, will this contract give an adequate rate of return to the depositors? Their expected return is
E[min{G N, H N)}]
Now for P(G N > H N) clo enough to 1, this will exceed the required expected return of NR. More precily, if P(G N > H N) > R /(R + ½ D N ), then the depositors will obtain their required rate of return. Since E[G N] > HN = N(R + ½ D N), by the weak law of large numbers, there exists a finite N such that P(G N > H N) can be made sufficiently clo to 1. Hence the above contract is feasible for any level of delegation cost, D N.
Comment: This result holds even if the projects are not independent but imperfectly correlated, as long as the correlation between projects is common knowledge. In practice, a bank could hedge this “systematic” risk by positions in futures markets, if they exist. Note that the paper predicts economies of scale in banking, though at the margin, the benefits of scale asymptote to zero. Note that this could also be a theory of conglomerate mergers as a way of reducing monitoring costs. This leads us to think about how the amount of control possd by a bank differs from that of a conglomerate. Diversification is the esnce of banking, while the “diversification discount” suggests that it is a sign of weakness for industrial firms.
35903 N o t e s o n D e l e g t e d M o n i t o i r i n g D o u g D i a m o n d S p r i n g 2004
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