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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.

Suggested Citation

  • Hayette Gatfaoui, 2003. "How Does Systematic Risk Impact US Credit Spreads? A Copula Study," Risk and Insurance 0308002, EconWPA.
  • 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.

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    References listed on IDEAS

    1. 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.
    2. Andre Lucas & Pieter Klaassen & Peter Spreij & Stefan Straetmans, 2003. "Tail behaviour of credit loss distributions for general latent factor models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 337-357.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Jan Ericsson & Olivier Renault, 2006. "Liquidity and Credit Risk," Journal of Finance, American Finance Association, vol. 61(5), pages 2219-2250, October.
    5. Hayette Gatfaoui, 2003. "Risk Disaggregation And Credit Risk Valuation In The Merton Like Way," Finance 0308007, EconWPA.
    6. Edwin J. Elton, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, February.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    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. 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.
    10. Ilia D. Dichev, 1998. "Is the Risk of Bankruptcy a Systematic Risk?," Journal of Finance, American Finance Association, vol. 53(3), pages 1131-1147, June.
    11. Thomas C. Wilson, 1998. "Portfolio credit risk," Economic Policy Review, Federal Reserve Bank of New York, issue Oct, pages 71-82.
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    Cited by:

    1. Bargès, Mathieu & Cossette, Hélène & Marceau, Étienne, 2009. "TVaR-based capital allocation with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 348-361, December.
    2. Cossette, Hélène & Côté, Marie-Pier & Marceau, Etienne & Moutanabbir, Khouzeima, 2013. "Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 560-572.
    3. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.

    More about this item


    systematic risk credit risk copulas Archimedean copulas stress testing;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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