This paper considers the risk management problem of an investor who holds a diversified portfolio of global equities or bonds and chooses long or short positions in currencies to manage the risk of the total portfolio. Over the period 1975-2005, we find that a risk-minimizing global equity investor should short the Australian dollar, Canadian dollar, Japanese yen, and British pound but should hold long positions in the US dollar, the euro, and the Swiss franc. The resulting currency position tends to rise in value when equity markets fall. This strategy works well for investment horizons of one month to one year. In the past 15 years the risk-minimizing demand for the dollar appears to have weakened slightly, while demands for the euro and Swiss franc have strengthened. These changes may reflect the growing role for the euro as a reserve currency in the international financial system. The risk-minimizing currency strategy for a global bond investor is close to a full currency hedge, with a modest long position in the US dollar. Risk-reducing currencies have had lower average returns during our sample period, but the difference in average returns is smaller than would be implied by the global CAPM given the historical equity premium.