The Term Structure of Currency Hedge Ratios

Abstract

Many firms face product price risk in foreign currency, uncertain costs in home currency and exchange rate risk. If prices and exchange rates in different countries interact, natural hedges of foreign exchange risk might result. If the effectiveness of such hedges depends on the hedge horizon, they might affect a firm's usage of foreign exchange derivatives at different horizons and lead to a term structure of optimal hedge ratios. We analyze this issue by deriving the variance minimizing hedge position in currency forward contracts within a basic model of an exporting firm that is exposed to different risks. In an empirical study, we quantify the term structure of hedge ratios for a typical German firm that is exporting either to the United States, the United Kingdom or Japan, using a cointegrated vector autoregressive models of prices, interest rates and exchange rates. Our main empirical result shows that the term structure of hedge ratios is clearly decreasing for all currencies considered, going down to a half or less for a hedge horizon of ten years. We have found that one explanation is that revenue risk increases more strongly with the hedge horizon than does exchange rate risk. The main reason, however, lies in the correlation structure between different risks that varies with the hedge horizon due to cointegration relations; i.e., we observe natural hedges at long horizons. As a consequence, hedging effectiveness decreases much less with the hedge horizon than hedge ratios. For long horizons, there can also be substantial differences between currencies. For instance, the ten-years hedge ratio for the British Pound still amounts to 53% in comparison to 34% for the US Dollar. In contrast, the difference for shorter horizons of up to two years is very small. In conclusion, our findings can (partly) explain the severe underhedging of long-term exchange rate exposures that is frequently observed and have important implications for the design of risk management strategies.