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A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules

Published in Journal of Financial Intermediation 12(3), July 2003, pp. 199-232..

Abstract:
I demonstrate that ratings-based capital rules, including both the current Basel Accord and its proposed revision, can be reconciled with the general class of credit value-at-risk models. Each exposure's contribution to VaR is portfolio-invariant only if (a) dependence across exposures is driven by a single systematic risk factor, and (b) no exposure accounts for more than an arbitrarily small share of total portfolio exposure. Analysis of rates of convergence to asymptotic VaR leads to a simple and accurate portfolio-level add-on charge for undiversified idiosyncratic risk. There is no similarly simple way to address violation of the single factor assumption.

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Michael B Gordy
Email: michael.gordy@frb.gov
Last update: 21-Aug-2003