The Empirical Relationship between Average Asset Correlation, Firm Probability of Default and Asset Size

The asymptotic single risk factor (ASRF) approach is a simplified framework for determining regulatory capital charges for credit risk and has become an integral part of how credit risk capital requirements are to be determined under the second Basel Accord. Within this approach, a key regulatory parameter is the average asset correlation. In this paper, we examine the empirical relationship between the average asset correlation, firm probability of default and firm asset size measured by the book value of assets by imposing the ASRF approach within the KMV methodology for determining credit risk capital requirements. Using data from year-end 2000, credit portfolios consisting of U.S., 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. When compared with the average asset correlations proposed by the Basel Committee on Banking Supervision in November 2001, the empirical average asset correlations further suggest that accounting for firm asset size, especially for larger firms, may be important. In conclusion, the empirical results suggest that a variety of factors may impact average asset correlations within an ASRF framework, and these factors may need to be accounted for in the final calculation of regulatory capital requirements for credit risk. Acknowledgements: The views expressed here are those of the author and not necessarily those of the Federal Reserve Bank of San Francisco or the Federal Reserve System. This work was initiated after several conversations with David Jones from the Federal Reserve Board of Governors, and I gratefully acknowledge his assistance, suggestions and comments. I thank Steven Kealhofer and Jeff Bohn of KMV, LLC for providing me with access to the Portfolio Manager software used in the analysis. I also thank Yim Lee, Ashish Das, Kimito Iwamoto, Sherry Kwok, Amnon Levy and Jing Zhang, all from KMV, for their assistance with the data and the software. Finally, I thank Akira Ieda, Mark Levonian, Phillip Lowe, George Pennacchi, Marc Saidenberg, and participants at the May 2002 BIS conference on “Basel II: An Economic Assessment” for their comments and suggestions. 1 See Gordy (2000a, b) for further discussion of the ASRF approach, 2 The software firm KMV, LLC is a leader in the field of credit risk modeling and capital budgeting. This study was conducted using their Portfolio Manager software, which they kindly provided for this study. Note that the analysis was conducted using Portfolio Manager, version 1.4.7 and prior to the release of Portfolio Manager, version 2.0. 1