Modeling the Dependence Structure between Bonds and Stocks: A Multidimensional Copula Approach

We apply a copula-GARCH approach to modeling the joint distribution of excess returns of four major assets: one year and ten year Treasury bonds and S&P 500 and Nasdaq indices. We try three approaches in building the multidimensional copula for the dependence structure of multiple variables: (1) n-dimensional normal copula and n-dimensional Student’s t copula, (2) hierarchical Archimedean copula and (3) mixed copula. To ensure better convergence in the estimation, we adopt a two-stage estimation procedure where marginal distributions are estimated separately in the …rst stage and then the copula is estimated in the second stage. Our results show that n-dimensional Student’s t copula yields the highest log-likelihood while hierarchical Archimedean copula yields signi…cantly low log-likelihoods. Moreover, we plot exceedance correlation and tail dependence between the four series and …nd that dependence asymmetries between two stock indices are not as signi…cant as documented as in previous studies. Our estimation results are consistent with plotted dependence measures.