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

FEDS Working Paper No. 2002-55

35 Pages Posted: 2 Dec 2003

See all articles by Michael B. Gordy

Michael B. Gordy

Board of Governors of the Federal Reserve System

Multiple version iconThere are 2 versions of this paper

Date Written: November 2002


When economic capital is calculated using a portfolio model of credit value-at-risk, the marginal capital requirement for an instrument depends, in general, on the properties of the portfolio in which it is held. By contrast, ratings-based capital rules, including both the current Basel Accord and its proposed revision, assign a capital charge to an instrument based only on its own characteristics. I demonstrate that ratings-based capital rules can be reconciled with the general class of credit VaR models. Contributions to VaR are portfolio-invariant only if (a) there is only a single systematic risk factor driving correlations across obligors, and (b) no exposure in a portfolio accounts for more than an arbitrarily small share of total 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.

Keywords: Capital allocation, banking regulation, value-at-risk

JEL Classification: G31, G38

Suggested Citation

Gordy, Michael B., A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules (November 2002). FEDS Working Paper No. 2002-55, Available at SSRN: https://ssrn.com/abstract=361302 or http://dx.doi.org/10.2139/ssrn.361302

Michael B. Gordy (Contact Author)

Board of Governors of the Federal Reserve System ( email )

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