  We study the role of contingent convertible bonds (CoCos) in a complex
network of interconnected banks. By studying the system's phase transitions, we
reveal that the structure of the interbank network is of fundamental importance
for the effectiveness of CoCos as a financial stability enhancing mechanism.
Our results show that, under some network structures, the presence of CoCos can
increase (and not reduce) financial fragility, because of the occurring of
unneeded triggers and consequential suboptimal conversions that damage CoCos
investors. We also demonstrate that, in the presence of a moderate financial
shock, lightly interconnected financial networks are more robust than highly
interconnected networks. This makes them a potentially optimal choice for both
CoCos issuers and buyers.
