An Intertemporal Linear Programming Model with Deterministic Loan- Deposit Relationships for Optimal Credit Expansion Strategy in a Bank

This paper presents an intertemporal linear programming model for exploring optimal credit expansion strategies of a commercial bank in the framework of dynamic balance sheet management assuming that it is both technically feasible and economically relevant to establish a linear relationship between the bank's credit expansion and the deposits received by the bank induced by the credit expansion process. The inclusion of the relationship between the credit expansion and the deposits induced thereby in the inter temporal model leads to optimal solutions which run counter to intuitive reasoning. The optimal solution may, e.g., exclude the purchase of investment securities in favor of loans to be granted even in the case where the nominal yield on securities is higher than the yield on loans. The optimal solution may also contain a variable representing the utilization of a source of funds, e.g., funds obtained from the central bank, which implies the payment of a rate of interest on these funds higher than any yield obtained on the bank's portfolio of loans and securities. Since the objective function of the model is the maximization of the difference between the total yield on the securities and loans portfolio and the total interest on the various deposits and other liabilities that the bank obtains, it would be hard to arrive at these results by intuitive reasoning. The explanation for the results obtained is the dynamic relationship between the loans granted and deposits received. This relationship seems to be particularly relevant in Finnish banking due to high market shares for the largest commercial banks.