[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/fip/fedgfe/2002-55.html
   My bibliography  Save this paper

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

Author

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.

Suggested Citation

  • Michael B. Gordy, 2002. "A risk-factor model foundation for ratings-based bank capital rules," Finance and Economics Discussion Series 2002-55, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2002-55
    as

    Download full text from publisher

    File URL: http://www.federalreserve.gov/pubs/feds/2002/200255/200255abs.html
    Download Restriction: no
    File URL: http://www.federalreserve.gov/pubs/feds/2002/200255/200255pap.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Szego, Giorgio, 2005. "Measures of risk," European Journal of Operational Research, Elsevier, vol. 163(1), pages 5-19, May.
    3. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    4. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    5. Mark S. Carey & William F. Treacy, 1998. "Credit risk rating at large U.S. banks," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), vol. 84(Nov), pages 897-921, September.
    6. Dirk Tasche, 2001. "Conditional Expectation as Quantile Derivative," Papers math/0104190, arXiv.org.
    7. 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.
    8. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
    9. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    10. Hermann Haaf & Dirk Tasche, 2001. "Calculating Value-at-Risk contributions in CreditRisk+," Papers cond-mat/0112045, arXiv.org, revised Mar 2002.
    11. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    12. 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.
    13. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Szego, Giorgio, 2005. "Measures of risk," European Journal of Operational Research, Elsevier, vol. 163(1), pages 5-19, May.
    2. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    3. Alexandre Kurth & Dirk Tasche, 2002. "Credit Risk Contributions to Value-at-Risk and Expected Shortfall," Papers cond-mat/0207750, arXiv.org, revised Nov 2002.
    4. Albrecht, Peter, 2003. "Risk measures," Papers 03-01, Sonderforschungsbreich 504.
    5. Dominique Guegan & Bertrand K Hassani, 2014. "Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions," Documents de travail du Centre d'Economie de la Sorbonne 14008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Wächter, Hans Peter & Mazzoni, Thomas, 2013. "Consistent modeling of risk averse behavior with spectral risk measures," European Journal of Operational Research, Elsevier, vol. 229(2), pages 487-495.
    7. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    8. Gao, Jianjun & Xiong, Yan & Li, Duan, 2016. "Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time," European Journal of Operational Research, Elsevier, vol. 249(2), pages 647-656.
    9. Buch, A. & Dorfleitner, G., 2008. "Coherent risk measures, coherent capital allocations and the gradient allocation principle," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 235-242, February.
    10. Robert Jarrow & Feng Zhao, 2006. "Downside Loss Aversion and Portfolio Management," Management Science, INFORMS, vol. 52(4), pages 558-566, April.
    11. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    12. Chen, Zhiping & Wang, Yi, 2008. "Two-sided coherent risk measures and their application in realistic portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2667-2673, December.
    13. Avramidis, Panagiotis & Pasiouras, Fotios, 2015. "Calculating systemic risk capital: A factor model approach," Journal of Financial Stability, Elsevier, vol. 16(C), pages 138-150.
    14. Mario Brandtner, 2016. "Spektrale Risikomaße: Konzeption, betriebswirtschaftliche Anwendungen und Fallstricke," Management Review Quarterly, Springer, vol. 66(2), pages 75-115, April.
    15. Annalisa Di Clemente, 2020. "Modeling Portfolio Credit Risk Taking into Account the Default Correlations Using a Copula Approach: Implementation to an Italian Loan Portfolio," JRFM, MDPI, vol. 13(6), pages 1-24, June.
    16. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    17. Rosen, Dan & Saunders, David, 2009. "Analytical methods for hedging systematic credit risk with linear factor portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 37-52, January.
    18. Fermanian, Jean-David & Scaillet, Olivier, 2005. "Sensitivity analysis of VaR and Expected Shortfall for portfolios under netting agreements," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 927-958, April.
    19. Jiang, Chun-Fu & Peng, Hong-Yi & Yang, Yu-Kuan, 2016. "Tail variance of portfolio under generalized Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 187-203.
    20. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.

    More about this item

    Keywords

    Risk; Econometric models; Capital;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedgfe:2002-55. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ryan Wolfslayer ; Keisha Fournillier (email available below). General contact details of provider: https://edirc.repec.org/data/frbgvus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.