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

It is well known that some relationship between systematic risk and credit risk prevails in financial markets. In our study, the return of S&P 500 stock index 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 and exhibit some negative relationship between S&P 500 return and credit spreads. Indeed, 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 the 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 the empirical Kendall's tau statistics observed for each bivariate dependence structure, we estimate the related 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