Cross-Sectional Dispersion and Expected Aggregate Loan Losses

Debt holders face a concave payoff function. Well-performing borrowers pay back predetermined interest and principal, while poor-performing borrowers may cause losses. Consequently, the losses on a portfolio of loans or bonds depend not only on the mean performance but also on the cross-sectional dispersion in borrowers’ performance. Higher dispersion suggests higher losses due to a larger number of defaulting borrowers and higher loss given default. Thus, for debt holders, aggregate economic conditions should be redefined as a function of both the mean and the cross-sectional dispersion in borrowers’ performance. Empirical analysis of loan and bond portfolio performance confirms our hypotheses.