In this paper we identify some of the main factors behind systemic risk in a set of international large-scale complex banks using the novel CoVaR approach. We find that short-term wholesale funding is a key determinant in triggering systemic risk episodes. In contrast, we find no evidence that a larger size increases systemic risk within the class of large global banks. We also show that the sensitivity of system-wide risk to an individual bank is asymmetric across episodes of positive and negative asset returns. Since short-term wholesale funding emerges as the most relevant systemic factor, our results support the Basel Committee's proposal to introduce a net stable funding ratio, penalizing excessive exposure to liquidity risk.