The problem of how to stabilize the financial system has attracted considerable attention since the global financial crisis of 2007-2009. Recently, Beal et al. (2011, gIndividual versus systemic risk and the regulatorfs dilemmah, Proc Natl Acad Sci USA 108: 12647-12652) demonstrated that higher portfolio diversity among banks would reduce systemic risk by decreasing the likelihood of simultaneous defaults. Here, I show that this result is overturned once a financial network comes into play. In a networked financial system, the failure of one bank can bring about a contagion of failure. The optimality of individual risk diversification, as opposed to economy-wide risk diversification, is thus restored. I also present a new method to quantify how the diversity of bank size affects the stability of a financial system. It is shown that a higher diversity of bank size itself makes the financial system more fragile even if external risk exposure is controlled for. The main reason for this is that larger banks are more likely to become a gsuper spreaderh of infectious defaults. In this situation the social cost of letting a bank fail is not uniform and depends on the size of the failing bank. This strongly implies that larger banks are systemically more important than smaller banks, and preventing large banks from being exposed to high external risks would therefore be the most effective vaccine against financial crisis.
