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Risk factor contributions in portfolio credit risk models

  • Rosen, Dan
  • Saunders, David
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    Determining contributions to overall portfolio risk is an important topic in risk management. For positions (instruments and sub-portfolios), this problem has been well studied, and a significant theory built, around the calculation of marginal contributions. We consider the problem of determining the contributions to portfolio risk of risk factors. This cannot be addressed through an immediate extension of techniques for position contributions, since the portfolio loss is a nonlinear function of the risk factors. We employ the Hoeffding decomposition of the portfolio loss into a sum of terms depending on the factors. This decomposition restores linearity, but includes terms arising from joint effects of groups of factors. These cross-factor terms provide information to risk managers, since they can be viewed as best hedges of the portfolio loss involving instruments of increasing complexity. We illustrate the technique on multi-factor portfolio credit risk models, where systematic factors represent industries, geographical sectors, etc.

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    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 34 (2010)
    Issue (Month): 2 (February)
    Pages: 336-349

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    Handle: RePEc:eee:jbfina:v:34:y:2010:i:2:p:336-349
    Contact details of provider: Web page: http://www.elsevier.com/locate/jbf

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    1. Sandro Merino & Mark Nyfeler, 2004. "Applying importance sampling for estimating coherent credit risk contributions," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 199-207.
    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. Diana Bonfim, 2006. "Credit Risk Drivers: Evaluating the Contribution of Firm Level Information and of Macroeconomic Dynamics," Economic Bulletin and Financial Stability Report Articles, Banco de Portugal, Economics and Research Department.
    4. 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.
    5. Susanne Emmer & Dirk Tasche, 2003. "Calculating credit risk capital charges with the one-factor model," Papers cond-mat/0302402, arXiv.org, revised Jan 2005.
    6. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers 2000-05, Centre de Recherche en Economie et Statistique.
    7. 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.).
    8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    9. Medema, Lydian & Koning, Ruud H. & Lensink, Robert, 2009. "A practical approach to validating a PD model," Journal of Banking & Finance, Elsevier, vol. 33(4), pages 701-708, April.
    10. Dirk Tasche, 2007. "Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle," Papers 0708.2542, arXiv.org, revised Jun 2008.
    11. Dirk Tasche, 2005. "Measuring sectoral diversification in an asymptotic multi-factor framework," Papers physics/0505142, arXiv.org, revised Jul 2006.
    12. repec:cup:cbooks:9780521496032 is not listed on IDEAS
    13. Lemieux, Christiane & L’Ecuyer, Pierre, 2001. "On selection criteria for lattice rules and other quasi-Monte Carlo point sets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 139-148.
    14. 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.
    15. Bellini, Fabio & Rosazza Gianin, Emanuela, 2008. "On Haezendonck risk measures," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 986-994, June.
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