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A general approach to integrated risk management with skewed, fat-tailed risks

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  • Joshua V. Rosenberg
  • Til Schuermann

Abstract

The goal of integrated risk management in a financial institution is to measure and manage risk and capital across a range of diverse business activities. This requires an approach for aggregating risk types (market, credit, and operational) whose distributional shapes vary considerably. In this paper, we use the method of copulas to construct the joint risk distribution for a typical large, internationally active bank. This technique allows us to incorporate realistic marginal distributions that capture some of the essential empirical features of these risks-such as skewness and fat tails-while allowing for a rich dependence structure. ; We explore the impact of business mix and inter-risk correlations on total risk, whether measured by value at risk or expected shortfall. We find that given a risk type, total risk is more sensitive to differences in business mix or risk weights than it is to differences in inter-risk correlations. A complex relationship between volatility and fat tails exists in determining the total risk: whether they offset or reinforce each other will depend on the setting. The choice of copula (normal versus student-t), which determines the level of tail dependence, has a more modest effect on risk. We then compare the copula-based method with several conventional approaches to computing risk, each of which may be thought of as an approximation. One easily implemented approximation, which uses empirical correlations and quantile estimates, tracks the copula approach surprisingly well. In contrast, the additive approximation, which assumes no diversification benefit, typically overestimates risk by about 30 to 40 percent.

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Bibliographic Info

Paper provided by Federal Reserve Bank of New York in its series Staff Reports with number 185.

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Date of creation: 2004
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Handle: RePEc:fip:fednsr:185

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Keywords: Risk management ; Bank reserves ; Bank capital;

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References

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  1. 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.
  2. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
  3. Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-44.
  4. 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.
  5. repec:fth:inseep:2000-05 is not listed on IDEAS
  6. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  7. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
  8. Jean-David FERMANIAN & Olivier SCAILLET, 2003. "Nonparametric Estimation of Copulas for Time Series," FAME Research Paper Series rp57, International Center for Financial Asset Management and Engineering.
  9. Beverly J. Hirtle, 2003. "What market risk capital reporting tells us about bank risk," Economic Policy Review, Federal Reserve Bank of New York, issue Sep, pages 37-54.
  10. 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.
  11. Eric Bouy?, 2001. "Multivariate Extremes at Work for Portfolio Risk Measurement," Working Papers wp01-02, Warwick Business School, Finance Group.
  12. Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February.
  13. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value-at-Risk with Heavy-Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269.
  14. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
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