This study examines the extent of systemic risk embedded in the credit and equity markets using a conditional value-at-risk (CoVaR) measure. We implement a copula-based CoVaR approach with different perspectives of a dependence structure based on a generalized autoregressive score model. In parallel, we select the credit default swap spread and stock price data of five companies in the financial sector – American Express, BBVA, Goldman Sachs, Morgan Stanley, and Wells Fargo – from 2001 to 2013, and include data on the global financial crisis of 2007–2008. We then divide the data into three time periods: pre-crisis, during the crisis, and post-crisis. We conduct time-varying marginal modelling, and copula parameter estimation, and then compute CoVaR values with the best-fit copula model. Comparative empirical tests provide financial implications for systemic risk management.