Fixed versus variable rate loans under state-dependent preferences
This paper examines the optimal mix of fixed and variable rate loans of a competitive bank facing uncertain funding costs. The bank's preferences are state-dependent in that the utility function depends on a state variable. We show that the optimal amount of loans extended by the bank depends neither on the state-dependent preferences of the bank, nor on the joint distribution of the marginal cost of funds and the state variable. The bank, however, optimally lends less should it be forced to assume all interest rate risk by exclusively extending fixed rate loans. We show further that a non-positive spread between fixed and variable rate loans is no longer a necessary and sufficient condition for the bank to refrain from extending fixed rate loans should the marginal cost of funds be correlated with the state variable in the sense of expectation dependence. State-dependent preferences as such play a pivotal role in determining the bank's optimal choice between fixed and variable rate loans.
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