We examine how the tail risk of currency returns over the past 20 years were impacted by central bank (monetary and liquidity) measures across the globe with an original and unique dataset that we make publicly available. Using a standard factor model, we derive theoretical measures of tail risks of currency returns which we then relate to the various policy instruments employed by central banks. We find empirical evidence for the existence of a cross-border transmission channel of central bank policy through the FX market. The tail impact is particularly sizeable for asset purchases and swap lines. The effects last for up to 1 month, and are proportionally higher for joint QE actions. This cross-border source of tail risk is largely undiversifiable, even after controlling for the U.S. dollar dominance and the effects of its own monetary policy stance.