This paper investigates the variance minimizing currency forward hedge of an exporting firm that is exposed to different sources of risk. In an empirical study, we quantify the corresponding hedge ratios of a "typical" German firm for different hedge horizons. Based on cointegrated vector autoregressive models of prices, interest rates and exchange rates, we show that hedge ratios decrease substantially with the hedge horizon for different currencies, reaching values of one half or less for a ten-years horizon. Our findings can partly explain underhedging of long-term exchange rate exposures and have important implications for the design of risk management strategies.