Standard Loan Agreement

The standard credit agreement is a model illustration of the structure of a credit agreement . The standard loan agreement consists of:

Loan amount and term
Determination of the agreed repayment amount
Procedure in the event of non-compliance

In practice, the loan agreement can include more complex regulations.

In a trend-setting article, Gale and Hellwig showed how the economically optimal loan agreement must be constructed.

Theoretical Analysis of the Standard Loan Agreement: The Gale and Hellwig Model

The starting point of the banking theory is the description of the product standard loan agreement . Assuming certain expectations of all contracting parties, an investment project will generate a surplus at a future point in time. The repayment that follows is the sum of the borrowed capital and interest.

Problem

The problem raised by Gale and Hellwig is the incentive for the borrower to report a bad result as a project result. The intention is to reduce his repayment . The lack of verifiability of the project result is also referred to as "costly state verification" .

Assumptions

The interest rate is determined using the Fisher Separation assumption . The internal rate of return is used to assess the success of the project . A comparison with the market interest rate shows whether the investment is worthwhile or whether an investment in the capital market is more profitable.

Risk-neutral borrowers and investors
Project yield depends on the condition: y (s)
Ex post information asymmetry ( costly state verification ): The borrowers experience the realization of the state and report the occurrence of a state to the investor ${\ displaystyle s_ {1}}$ ${\ displaystyle s_ {2}}$
The control of the project yield causes the costs c
The investor's opportunity costs are I, which is K * (1 + i), I is greater than the project return in the worst condition.
The loan agreement contains the loan amount K, the control scheme B (s), where B (s) can assume the values 0 or 1 and the repayment z (s).

Profit Maximization Conditions

The borrower tries to maximize his expected profit. The following conditions must be met:

reachability

The repayment amount must be generated from the project income. I.e. in the event that checks are carried out, z (s) must not exceed y (s) and if there is no control, i.e. the agreed repayment amount is made, this amount does not exceed the project income. This dichotomy requires the control scheme explained below.

Control scheme

The control scheme provides for a control of the borrower in the event that he does not make the repayment provided for in the contract.

Individual rationality

It must be individually worthwhile for the investor to finance the project, i. H. the expected repayment less control costs results in at least the market rate of return on the capital employed.

Another condition is incentive compatibility.

Incentive Compatibility

A credit agreement is incentive-compatible if the following applies to any conditions and to all conditions in which no observation is made: ${\ displaystyle s_ {1}}$ ${\ displaystyle s_ {2}}$

Lying is not possible: ${\ displaystyle y (s_ {1}) <z (s_ {2})}$ ${\ displaystyle y (s_ {1}) <z (s_ {2})}$
- The realized project income is less than the repayment if nothing is observed.

It's not worth lying: ${\ displaystyle z (s_ {1}) \ leq z (s_ {2})}$ ${\ displaystyle z (s_ {1}) \ leq z (s_ {2})}$
- The repayment for an actually realized state may not be greater than the repayment if nothing is observed.

This ensures that an entrepreneur never in an actual state of a state is pretend. ${\ displaystyle s_ {1}}$ ${\ displaystyle s_ {2}}$

The standard loan agreement

{\ displaystyle z ^ {*} (s) = y (s) \}

And if

{\ displaystyle B ^ {*} (s) = 1 \}

{\ displaystyle y (s) <R}

{\ displaystyle z ^ {*} (s) = R \}

And if

{\ displaystyle B ^ {*} (s) = 0 \}

{\ displaystyle y (s) \ geq R \}

The standard loan agreement specifies the repayment to the lender and the net income of the borrower, including the case of uncertainty. In the first case, this is the full repayment amount or (in the event that the project income falls below this) the entire project income. Similarly, the net profit is the project income minus the repayment, but at least zero.

Gale and Hellwig show that this contract is optimal from an efficiency point of view.