This paper contributes to the primarily empirical literature by conducting the first extensive empirical analysis of the impact of the degree of co-movement in the main standardized credit default swap (CDS) indices on the group of large complex financial institutions (LCFIs). We attempt to account for the dynamics between banks' equity returns and most liquid CDS market indices, the investment grade 5-year CDX North America and the investment grade 5-year iTraxx Europe, through conditioning our analysis on the historical correlation between the variables. Our most important findings are threefold. First, we find that equity returns for all the LCFIs are negatively correlated to both the CDX and the iTraxx indices. Second, the CDX index is the dominant factor driving shocks across all the LCFIs and this effect is stronger for European than US banks. Third, the impact of CDS market volatility on the equity return volatility of LCFIs appears very pronounced, suggesting a transmission mechanism which results in the destabilisation of banks and a subsequent increase in their default risk.