We develop a new technique to estimate vector autoregressions with a common factor error structure by quantile regression. We apply our technique to study credit risk spillovers among a group of 17 sovereigns and their respective financial sectors between January 2006 and December 2017. We show that idiosyncratic credit risk shocks propagate much more strongly in both tails than at the conditional mean or median. Furthermore, we develop a measure of the relative spillover intensity in the right and left tails of the conditional distribution that provides a timely aggregate measure of systemic financial fragility and that can be used for risk management and monitoring purposes. This paper was accepted by Gustavo Manso, finance.