Dependence and Systemic Risk Analysis Between S&P 500 Index and Sector Indexes: A Conditional Value-at-Risk Approach

In order to investigate the dynamic dependency structure  between the S&P 500 stock index and 11 different U.S. sector indexes, and measure systemic risk. We first propose a new dynamic copula model with Markov regime-switching and macroeconomic component, and use a simulation study to verify its advantages. Macroeconomic components identified by principal component analysis and independent component analysis are added into the evolution of the copula parameter as exogenous variables to study the influence of macroeconomic factors on the interdependence between variables. Then, the estimation method of systemic risk measure conditional value-at-risk (CoVaR) in the proposed dynamic copula model is given. Finally, we provide an empirical analysis based on the above data and models. We find that when extreme events occur in the S&P500, the CoVaRs corresponding to sector indexes are distinctly time-varying, and the occurrence of major events have a greater impact on the CoVaR of each index. The consideration of Markov regime-switching parameters and macroeconomic factors improves the ability to estimate dependent structures. In addition, different macroeconomic factors have different influences on the interdependence between sector indexes and the overall S&P. U.S. unemployment rate is the most important macroeconomic factor for most sectors.