The choice of debt maturity by credit ratings. (Diamond, 1991)

Diamond (1991) explained the choice of debt maturity related to the credit rating. His model splits the borrowers in two ‘projects’, Project G and Project B. The model evaluates two periods. Both projects have a capital of 1$ in period 0 and a cashflow (X) in period two. There is no cashflow in period one. Long term loans will have a maturity of two periods. Short term loans will have a maturity of one period. The lender will receive a return (R) each period. The maturity of the loan depends if the lender will receive the expected return each period. If the loan will mature two periods the lenders receive 2 x R, which is R².  If the return is lower than expected, the loan will be liquidated. Lenders has the rights to liquidate the short term after period one. This right is not permitted in long term loans. Long term loans has a fixed maturity for period two. Liquidity risk is the risk that a solvent but illiquid borrower is unable to obtain refinancing. The definition of liquidity need to be broadly interpreted. In all cases where the borrower lose control of the loan after period one, the loan is liquidated. In this model both project could be liquidated after period one. The projects are short term loans. In period one the projects can be liquidated for the liquidation value (L). If the liquidation value is higher than the expected return, the lenders will not liquidate the project. This model has no liquidation value after period two. In this model only the borrowers knows the cashflows and expected information. Borrowers and lenders are risk neutral.

Project G receive cashflows (X) higher than the return of the lenders (R). For two periods this means that the cashflows are higher than de total return (R²). ( X> R²) This project results in a positive net present value in terms of cashflows.

Project B receive a probability (π) of the cashflow (X). The probability of no cashflows is 1 - π. For two periods the probability of cashflow (π X) is lower dan the returns of the lender (R²). (πX <R² ) This project results in a negative net present value of the cashflows.

This model explained the debt maturity related to the credit rating. If a borrower has low credit rating the return (R) will be higher. If the R is high the chance for project B is higher and this results in a chance for a negative net present value of the cashflows. The probability of the credit rating for project G is ƒ. The probability of the credit rating for project B is 1 -  ƒ. With this information, the probability of repayment of a loan after period two is: π + ƒ ( 1 - π). This is the probability of cashflows plus the credit rating for project G multiplied by one minus the probability of the cashfows.

After period one there is new information about the borrowers. The credit rating could upgrade or downgrade. Project G can get a upgrade or a downgrade. є is the downgrade and 1 – є is the upgrade for project G. Poject B can only be downgraded because of the negative net present value. The probability of this downgrade depends on the credit rating. Ƒdown is the creditrating for a downgrade. The project will stay project B. ƒ is the credit rating for project G. This is explained by this formula:  (ƒdown ( 1 - ƒ ))/(ƒ ( 1 - ƒdown ))

Because the lenders will have the possibility to liquidate the projects after period one. The choice for the lenders to liquidate or not depends on the value of the loan. The value is equal to the face value (r₁) in period 0. If there is a upgrading in period 1 the face value is equal tot he face value of period 0 multiplied by the returns. (r₁R). The chance for a upgrade is P^u = (1 – є )  ƒ.

The figure illustrate the project conditions.

The research of Diamond (1991) concludes that short debt has a shorter maturity than new investments. New short debt depends on the future credit rating. If the borrowers has a high credit rating they will use more short debt, because of the lower risk. Long term debt matured after new investments. The borrowers do not depend of the new credit rating. If borrowers has a lower credit ratings, they prefer long term loans, because of the risk of downgrading.