We estimate volatility- and quantile (depreciation)-based spillovers across 20 global currencies against the US Dollar. In so doing, we reveal significant asymmetries in the propagation of risk across global currency markets. The quantile-based statistic reacts more significantly to events that have a sizable impact on FX markets (e.g. Brexit vote and the FX crash following the subprime crisis), which are missed by the volatility-based statistic. As such, our tail-spillover estimates constitute a new financial stability index for the FX market. This index has the advantages of being easy to build, of not requiring intraday data and of being more informative about currency crises and pressures than traditional spillover statistics based on v...