Do Riskier Borrowers Borrow More?

This note studies how mortgage borrowers with different levels of default risk would self-select between different loan-to-value ratios. It shows that for large default costs there exists a separating equilibrium in which low-risk borrowers choose bigger loan amounts than high-risk borrowers. This equilibrium offers a theoretical explanation for the seemingly counter-intuitive empirical result of Campbell and Dietrich (1983) that loans with lower initial loan-to-value ratios have higher default rates. If default costs are small, then the separating equilibrium involves high-risk borrowers choosing a bigger loan amount than low risks. For an intermediate value of default costs, the unique equilibrium is a pooling equilibrium.