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.

A common assumption in the academic literature and in the supervision of banking systems is that franchise value plays a key role in limiting bank risk-taking. As market power is the primary source of franchise value, reduced competition in banking markets has been seen as promoting banking stability. A recent paper by Martínez-Miera and Repullo (MMR, 2010) shows that a nonlinear relationship theoretically exists between bank competition and risk-taking in the loan market. We test this hypothesis using data from the Spanish banking system. After controlling for macroeconomic conditions and bank characteristics, we find support for this nonlinear relationship using standard measures of market concentration in both the loan and deposit markets. When direct measures of market power, such as Lerner indices, are used, the empirical results are more supportive of the original franchise value hypothesis, but only in the loan market. Overall, the results highlight the empirical relevance of the MMR model, even though further analysis across other banking markets is needed.

The Monetary Control Act of 1980 requires the Federal Reserve System to provide payment services to depository institutions through the 12 Federal Reserve Banks at prices that fully reflect the costs a private-sector provider would incur, including a cost of equity capital (COE). Although Fama and French [Fama, E.F., French, K.R., 1997. Industry costs of equity. Journal of Financial Economics 43, 153–193] conclude that COE estimates are “woefully” and “unavoidably” imprecise, the Reserve Banks require such an estimate every year. We examine several COE estimates based on the CAPM model and compare them using econometric and materiality criteria. Our results suggest that the benchmark CAPM model applied to a large peer group of competing firms provides a COE estimate that is not clearly improved upon by using a narrow peer group, introducing additional factors into the model, or taking account of additional firm-level data, such as leverage and line-of-business concentration. Thus, a standard implementation of the benchmark CAPM model provides a reasonable COE estimate, which is needed to impute costs and set prices for the Reserve Banks’ payments business.