We test if large swings in currency prices are driven by economic fundamentals. Theoretically, we apply extreme value theory (EVT) to a monetary approach exchange rate model to investigate the contribution of the heavy-tailed macroeconomic fundamentals to the tail behavior of FX returns. Empirically, using the data of 34 countries from three continents, we provide evidence that both exchange rate returns and fundamentals are heavy tailed, and the variables are asymptotically dependent. The strongest tail links are between Asian and Latin American currency depreciations and fundamentals. The main drivers are monetary and financial variables. Real income shocks appear disconnected.