How Correlated Are Bank Borrowers? Implied Vasicek Asset Correlations from US Charge-off Rates, 1935–2025, and a Comparison with Basel Values

The Basel internal-ratings-based capital formula rests on the one-factor Vasicek model, in which a single parameter, the asset correlation, sets how much loan losses rise in bad years. I show that in this model the probit of the portfolio loss rate has variance ρ/(1−ρ), so the correlation can be read from the time series of loss rates, and I derive the downward bias of this estimator when the systematic factor is persistent. Applied to FRED charge-off rates for US commercial banks, 1985 to 2025, with loss given default of 100%, 60% and 45%, the implied correlations are 0.023 to 0.033 for credit cards, 0.067 to 0.081 for business loans, 0.205 to 0.277 for residential mortgages and 0.218 to 0.260 for commercial real estate. Correcting the persistence bias by parametric bootstrap raises them, for example from 0.067 to 0.080 for business loans. Mortgage estimates depend strongly on how years with net recoveries are treated (0.103 to 0.329). On FDIC data for 1935 to 2025, the implied correlation for all loans is 0.128, or 0.158 after bias correction, but only 0.036 (0.045) for 1984 to 2025. Credit cards fall below the Basel value of 0.04 for revolving retail, business loans fall below the corporate range of 0.12 to 0.24, and mortgages lie near the Basel value of 0.15 in most specifications.