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Using a novel method of isolating the oil price shocks, we study how different sources of oil price shocks are connected to exchange rates of major oil-dependent countries using daily data from March 1996 to February 2019. We find that oil price shocks resulting from changes in demand and risk significantly contribute to variation in exchange rates, while supply shocks have virtually no impact. The connectedness of this relationship between oil price shocks and exchange rates has significantly increased after the global financial crisis. We also find that oil price shocks do not explain the variation in exchange rate volatility but we document significant volatility connectedness among exchange rates. Our findings have important implications for policy makers and financial market participants.