We establish generalized autoregressive conditional heteroscedasticity–dynamic conditional correlation (GARCH–DCC) and constant conditional correlation (CCC) copula model frameworks to study time-varying correlation among credit default swap (CDS) single names (SNs) and its impact on certain risk measures of CDS portfolios that consist of names from different sectors within the eurozone (EU) and North America (NA). Our purpose is to better understand the direction and magnitude of impacts on such risk measures due to correlation changes. This study covers 188 NA SNs and 145 EU SNs from January 2008 to August 2017. We find that correlations between CDS SNs go through different correlation regimes during this period. As a result, CDS portfolio risk measures in the form of value-at-risk or expected shortfall show sizable variation due to correlation regime shifts from historical means. Depending on the correlation level (high or low) and the portfolio type, risk measures could be either underestimated or overestimated. Both directional and balanced portfolios could experience a sizable underestimation of the margin depending on the direction in which the correlation deviates from historical means.