The asymptotic single risk factor approach is a framework for determining regulatory capital charges for credit risk, and it has become an integral part of the second Basel Accord. Within this approach, a key parameter is the average asset correlation. We examine the empirical relationship between this parameter, firm probability of default and firm asset size measured by the book value of assets. Using data from year-end 2000, credit portfolios consisting of US, Japanese, and European firms are analyzed. The empirical results suggest that average asset correlation is a decreasing function of probability of default and an increasing function of asset size. The results suggest that these factors may need to be accounted for in the final calculation of regulatory capital requirements for credit risk.

We use Call Report data to examine the effects of the Paycheck Protection Program (PPP) and the PPP Liquidity Facility (PPPLF) on small business and farm lending by individual commercial banks. As program participation was associated with small business lending, we adopt an instrumental variables approach to identify causal implications based on historical bank relationships with the Small Business Administration and the Federal Reserve’s discount window. Our results indicate that both programs encouraged lending growth over the first half of 2020. However, while the PPP encouraged greater lending across all banks, only small and medium-sized bank lending growth was significantly related to participation in the PPPLF.