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How Does Systematic Risk Impact US Credit Spreads? A Copula Study

  • Hayette Gatfaoui

    (The University of Paris 1 - Panthéon-Sorbonne)

It is well known that some relationship between systematic risk and credit risk prevails in financial markets. In our study, S&P 500 stock index return is our market risk proxy whereas credit spreads represent our credit risk proxy as a function of maturity, rating and economic sector. We address the problem of studying the joint distributions and evolutions of S&P 500 return and credit spreads. Graphical and non parametric statistical analysis (i.e.: Kendall’s tau and Spearman’s rho) show that such bivariate distributions are asymmetric with some negative relationship between S&P 500 return and credit spreads. In-deed, credit spreads widen when S&P 500 return decreases or drops under some given level. We investigate then this stylized fact using copula functions to characterize observed dependence structures between S&P 500 return and credit spreads. We focus at least on one parameter copulas and at most on one parameter Archimedean copulas, namely Gumbel, FGM, Frank and Clayton copula functions. Starting from empirical Kendall’s tau observed for each bivariate dependence structure, we induce parameter values for each copula type function belonging to our copulas set. Finally, we exhibit optimal characterizations for such dependence structures and use the optimal selected copulas to achieve a scenario analysis among which stress testing.

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File URL: http://128.118.178.162/eps/ri/papers/0308/0308002.pdf
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Paper provided by EconWPA in its series Risk and Insurance with number 0308002.

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Length: 27 pages
Date of creation: 25 Aug 2003
Date of revision:
Handle: RePEc:wpa:wuwpri:0308002
Note: Type of Document - Acrobat PDF; prepared on PC; to print on HP/PostScript; pages: 27 ; figures: included. This paper is under submission for the special issue of the European Investment Review.
Contact details of provider: Web page: http://128.118.178.162

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  1. Ilia D. Dichev, 1998. "Is the Risk of Bankruptcy a Systematic Risk?," Journal of Finance, American Finance Association, vol. 53(3), pages 1131-1147, 06.
  2. Hayette Gatfaoui, 2003. "Risk Disaggregation And Credit Risk Valuation In The Merton Like Way," Finance 0308007, EconWPA.
  3. Thomas C. Wilson, 1998. "Portfolio credit risk," Economic Policy Review, Federal Reserve Bank of New York, issue Oct, pages 71-82.
  4. Olivier Renault & Jan Ericsson, 2000. "Liquidity and Credit Risk," FMG Discussion Papers dp362, Financial Markets Group.
  5. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  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. Edwin J. Elton, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, 02.
  8. Jarrow, Robert A. & Turnbull, Stuart M., 2000. "The intersection of market and credit risk," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 271-299, January.
  9. repec:dgr:uvatin:20010023 is not listed on IDEAS
  10. Gregory R. Duffee, 1998. "The Relation Between Treasury Yields and Corporate Bond Yield Spreads," Journal of Finance, American Finance Association, vol. 53(6), pages 2225-2241, December.
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