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An analytic approach to credit risk of large corporate bond and loan portfolios

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  • Lucas, Andr‚

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

  • Klaassen, Pieter
  • Spreij, Peter

Abstract

We consider portfolio credit loss distributions based on a factor model for individual exposures and establish an analytic characterization of the credit loss distribution if the number of exposures tends to infinity. Using this limiting distribution, we explain how skewness and leptokurtosis of credit loss distributions relate to the underlying factor model and the portfolio composition. A key role is played by the R2 of the factor model regression. Based on the limiting distribution and empirical data, it appears that the Basle 8% rule is not an unreasonable approximation for high confidence (99.9%) quantiles of credit losses of a typical portfolio of rated corporate bonds. The practical relevance of our results for credit risk management is investigated by checking the applicability of the limiting distribution to portfolios with a finite number of exposures. It appears that for relatively homogeneous portfolios a minimum of 300 exposures is enough, while for relatively heterogeneous portfolios a number of 800 exposures suffices to obtain an adequate approximation. Thus, our approach can be a

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Bibliographic Info

Paper provided by VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics in its series Serie Research Memoranda with number 0018.

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Date of creation: 1999
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Handle: RePEc:dgr:vuarem:1999-18

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Web page: http://www.feweb.vu.nl

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Keywords: credit risk; factor model; fat-tailed distributions; skewness; asymptotic analysis;

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  1. Mark Carey, 1998. "Credit Risk in Private Debt Portfolios," Journal of Finance, American Finance Association, vol. 53(4), pages 1363-1387, 08.
  2. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  3. Gregory R. Duffee, 1994. "On measuring credit risks of derivative instruments," Finance and Economics Discussion Series 94-27, Board of Governors of the Federal Reserve System (U.S.).
  4. Chunsheng Zhou, 1997. "Default correlation: an analytical result," Finance and Economics Discussion Series 1997-27, Board of Governors of the Federal Reserve System (U.S.).
  5. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
  6. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  7. Longstaff, Francis A & Schwartz, Eduardo S, 1995. " A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
  8. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  10. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-67, May.
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