Model by Diamond

The model of Diamond (also: existence statement for banks ) is a central research contribution in explaining the existence of banks in the banking theory . The paper written by the US economist Douglas W. Diamond , which regards banks as delegated monitoring , was published in 1984. Many of the ideas below build on Diamond.

Diamond models asymmetric information in the form of ex post uncertainty to infer the existence of banks. In his model, the outcome of the project is only known to the entrepreneur.

Basic model

A number n of risk-neutral entrepreneurs want to carry out an identical project that requires the deposit of a monetary unit. In doing so, you rely on risk-neutral investors. Investors can invest in alternative technologies, which must also be the (minimum) interest rate for corporate projects.

Characterization of the contractual partner

If we assume an entrepreneur and m financiers, each financier provides 1 / m monetary units. The return is randomly between zero and y , but the expected value is greater than the minimum return on the alternative project. With symmetrical information, the project would be advantageous.

Risk neutrality for investors and borrowers means that the question of how the risk is divided is irrelevant.
The entrepreneur has no cash.
There is an unlimited number of investors.
In contrast to the entrepreneur, the investor cannot observe the project result ( ex post information asymmetry ).

Investment project

An entrepreneur's investment project provides income in two possible forms. The financiers have sufficient assets that they can jointly finance the entrepreneur's project. The risk-neutral investors demand at least one repayment in the expected value with interest in the amount of the market return. With symmetrical information , contracts are possible that meet these requirements.

In the case of asymmetrical information , a debt contract with a penalty function is concluded and a repayment amount equal to the repayment amount that each borrower receives. This is to ensure that the borrower does not use his information advantage over the lenders.

Function of the alternative
investment The alternative investment offers investors an additional opportunity to invest at a secure interest rate. This means that investors only finance projects with a minimum return of I.

In competition, the capital providers do not achieve more than the risk-free market return I-1.

Ex post information asymmetry

The information asymmetry gives the borrower the incentive to announce the worst possible result in order to reduce his repayment in this way.
The lender must incur costs to obtain this information himself. Diamond compares two ways for the lender to deal with this information asymmetry: monitoring versus punishment.

Solution: Incentive contract and monitoring

The entrepreneur tries to narrow his own room for maneuver in order to convince the lender of a loan.

Incentive-compatible debt contract

Principle : The entrepreneur should be given an incentive to indicate the true project yield.

The punishment offers a means to induce the borrower, through threatened ex post damage, to state the true outcome of the project and to make appropriate repayment. Possible penalties are imprisonment, loss of reputation or costs of bankruptcy proceedings etc. A monetary punishment would have no effect as the borrower is penniless.

A penalty function describes the amount of the non-monetary penalty that an entrepreneur has to suffer if he does not make a repayment.

Incentive-compatible and minimal
The penalty function should be incentive-compatible and minimal at the same time. ${\ displaystyle \ Phi ^ {*} (z (y))}$

Incentive compatibility means that the entrepreneur pays the repayment amount if he can.
Minimal means that if we chose a lower punishment, the contract could no longer have an incentive effect.

The minimum penalty is the amount of the remaining debt. An entrepreneur who repays the contractually agreed amount is not punished, he pays the repayment amount. There is therefore a constant repayment amount made up of both monetary and non-monetary components.

Problems

A contract with a criminal function is no longer worthwhile for entrepreneurs. The overall welfare decreases due to the resulting contract costs.
The borrower will be punished even if the answer is honest.

Welfare consideration

Penalty function: R - I and results from the comparison of costs for second-best E [ y ] - R and first-best solution E [ y ] - I . ${\ displaystyle E [\ Phi ^ {*} (z (y))]}$

Depending on the distribution of the project income
CN profit: project proceeds-repayment-penalty

This is the loss of welfare if penalties are applied.

Cost of information asymmetry

Risk premium R - I
Expected penalty ${\ displaystyle E [\ Phi ^ {*} (z (y))]}$

Costly monitoring of project earnings

Principle: The lender is given the opportunity to observe the course of the project and the project result.

Monitoring means that the borrower is monitored by the lender. However, this individual project monitoring is inefficient with a large number of small investors . Monitoring causes costs that the borrower must reimburse every investor .

Cost monitoring costs: m · c, depending on the number of lenders m

Profit of the KN: project revenue-repayment-monitoring costs

Optimal solution

${\ displaystyle \ min \ left [m \ cdot c, E [\ Phi ^ {*} (z (y))] \ right]}$

${\ displaystyle E [\ Phi ^ {*} (z (y))]}$ corresponds to the comparison First-Best Second-Best: R - I

if the number of lenders is high, monitoring costs are high
if the project is very risky, then the high cost of the incentive contracts

Financial intermediary

The financial intermediary can use deposits to finance several projects. All projects have a known distribution of income and are stochastically independent of one another . The intermediary monitors the entrepreneurs and has the monitoring costs reimbursed. He agrees on repayment in the event of success and in the event of failure. The default risks are limited. The financial intermediary's zero profit condition is met; this enables the profitability analysis of company profits. Alternatively, contract costs can be determined.

Optimal form of contract

Repayment amount

For symmetrical information: Market return I . However, there is asymmetrical information here. The amount of the contractually agreed repayment amount can be derived as follows:

Repayment function: ${\ displaystyle z (y) = {\ begin {cases} R & {\ textrm {if}} \ quad y> R \\ y & {\ textrm {if}} \ quad y <R \ end {cases}}}$

use in: ${\ displaystyle E [z (y)] = I \ quad \ Rightarrow}$

${\ displaystyle P (y <R) E [y | y <R] + P (y> R) R = I}$

${\ displaystyle P (y <R) E [y | y <R]}$ : Expected value of the partial repayment
${\ displaystyle P (y> R) R}$ : Expected value of full repayment

The equation can be solved for R. The difference between R and I is called the risk premium.

Monitoring costs c

With a financial intermediary, the monitoring costs can be reduced through economies of scale.

However, new costs (delegation costs) of information asymmetry arise from the lender-financial intermediary relationship. The problem of cooperation has only been postponed

even a financial intermediary can cheat.

Factors influencing the level of monitoring costs are:

Type of distribution of project income
Number of entrepreneurs financed
Amount of monitoring costs

Delegation costs d

Delegation costs are the costs that are necessary to solve the cooperation problem between the financial intermediary and the lender. It is a kind of risk premium in the contract between the financial intermediary and the lender.

Delegation costs can be greatly reduced if

simultaneously several projects are financed and one
Diversification of default risks

he follows.

With a large number of financed companies, the delegation costs are negligibly small, so that a virtually risk-free debt contract is created. The repayment amount R decreases.

Lowering delegation costs through diversification
In the case of a large number of projects, the financial intermediary demands an additional amount in addition to reimbursement of monitoring costs. The portfolio is diversified to such an extent that there is no longer any risk of default. The non-monetary penalty is never used, so the delegation costs are zero ${\ displaystyle d = E [\ Phi ^ {*} (z (y))]}$ . A financial intermediary can not reduce the costs that arise from monitoring . The welfare losses only exist in the amount of the monitoring costs.

Private diversification
In the case of private diversification, i. H. If one investor finances several entrepreneurs instead of one entrepreneur, the penalty costs are not reduced.

The reason for this is that debt contracts with a penal function are excluded between the investor and the company. The penalty costs are only dependent on the project risk of the entrepreneur and not on the number of financiers. The total penalty costs are always the same. A replication of the contractual relationship between the entrepreneur and the financial intermediary (debt contract with monitoring) does not succeed here.

Comparison of financial intermediaries and direct financing with only one company

If investors invest in the "financial intermediary" project and if this finances only one company, the risk of default is essentially the same as with a direct relationship. The project's revenues are even reduced by the monitoring costs. Accordingly, the expected penalty costs cannot be lower than with direct funding.

No reduction in penalty costs

Cost :, this is not beneficial as the penalty is the same as direct funding. ${\ displaystyle c + E [\ Phi ^ {*} (z (y))]}$

Results

Monitoring costs must be reduced by blaming the information asymmetry on the financial intermediary. If this type of delegation takes place, the solution with the involvement of an intermediary is more efficient than without an intermediary. This is Diamond's rationale for banks.

With funding only a borrower, the cooperation only problem is postponed and will cost a total of: . Diversification will decrease. ${\ displaystyle c + E [\ Phi ^ {*} (z (y))]}$ ${\ displaystyle d = E [\ Phi ^ {*} (z (y))]}$

Financial intermediation for diversification is advantageous if:

${\ displaystyle c + d <\ min [m \ cdot c, E [\ Phi ^ {*} (z (y))]]}$

Through diversification ( n towards infinity), d tends towards zero.
If the one-off monitoring is more favorable than the punitive function, financial intermediation makes sense, since c < mc . This is usually the case.

regulation

A regulation of credit risks is not necessary in Diamond's model. Because in Diamond's model, the bank can reduce the overall risk at will through a sufficiently diversified portfolio , since all credit default risks are stochastically independent by assumption .

literature

Douglas W. Diamond, (1984): Financial Intermediation and Delegated Monitoring. In: Review of Economic Studies. Volume 51, pp. 393-414 ( ( page no longer available , search in web archives: fee.uva.nl ) PDF).@1@ 2Template: Dead Link / www1.fee.uva.nl