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A risk-factor model foundation for ratings-based bank capital rules

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  • Michael B. Gordy

Abstract

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.

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Bibliographic Info

Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2002-55.

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Date of creation: 2002
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Handle: RePEc:fip:fedgfe:2002-55

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Keywords: Risk ; Econometric models ; Capital;

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  1. C. Gourieroux & J.P. Laurent & O. Scaillet, 2000. "Sensitivity analysis of values at risk," THEMA Working Papers 2000-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  2. William F. Treacy & Mark S. Carey, 1998. "Credit risk rating at large U.S. banks," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Nov, pages 897-921.
  3. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
  4. Dirk Tasche, 2001. "Conditional Expectation as Quantile Derivative," Papers math/0104190, arXiv.org.
  5. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
  6. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
  7. Szego, Giorgio, 2002. "Measures of risk," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1253-1272, July.
  8. Michael B. Gordy, 1998. "A comparative anatomy of credit risk models," Finance and Economics Discussion Series 1998-47, Board of Governors of the Federal Reserve System (U.S.).
  9. Jones, David, 2000. "Emerging problems with the Basel Capital Accord: Regulatory capital arbitrage and related issues," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 35-58, January.
  10. Mark Carey, 2001. "Dimensions of Credit Risk and Their Relationship to Economic Capital Requirements," NBER Chapters, in: Prudential Supervision: What Works and What Doesn't, pages 197-232 National Bureau of Economic Research, Inc.
  11. repec:fth:inseep:2000-05 is not listed on IDEAS
  12. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  13. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1317-1334, July.
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