Use of a Currency Cylinder to Hedge GE’s Receivable
Cross-Hedging
Hedging with futures is very similar to hedging with forward contracts. However, a firm that wants to manage its exchange risk with futures may find that the exact futures contract it requires is unavailable. In this case, it may be able to cross-hedge its exposure by using futures contracts on another currency that is correlated with the one of interest.
The idea behind cross-hedging is as follows: If we cannot find a futures/forward contract on the currency in which we have an exposure, we will hedge our exposure via a futures/forward contract on a related currency. Lacking a model or theory to tell us the exact relationship between the exchange rates of the two related currencies, we estimate the relationship by examining the historical association between these rates. The resulting regression coefficient tells us the sign and approximate size of the futures/forward position we should take in the related currency. However, the cross-hedge is only as good as the stability and economic significance of the correlation between the two currencies. A key output of the regression equation, such as the one between the Danish krone and euro, is the R2, which measures the fraction of variation in the exposed currency that is explained by variation in the hedging currency. In general, the greater the R2 of the regression of one exchange rate on the other, the better the cross-hedge will be.
Application Hedging a Danish Krone Exposure Using Euro Futures
An exporter with a receivable denominated in Danish krone will not find krone futures available. Although an exact matching futures contract is unavailable, the firm may be able to find something that comes close. The exporter can cross-hedge his Danish krone position with euro futures, as the dollar values of those currencies tend to move in unison.
Suppose it is October 15 and our exporter expects to collect a DK 5 million receivable on December 15. The exporter can always sell the Danish kroner on the spot market at that time but is concerned about a possible fall in the krone’s value between now and then. The exporter’s treasurer has copied the spot prices of the Danish krone and euro from the Wall Street Journal every day for the past three months and has estimated the following regression relationship using this information:
where Δ = et — et—1 and et is the spot rate for day t (that is, Δ is the change in the exchange rate). In addition, the R2 of the regression is 0.91, meaning that 91% of the variation in the Danish krone is explained by movements in the euro. With an R2 this high, the exporter can confidently use euro futures contracts to cross-hedge the Danish krone.
According to this relationship, a 1¢ change in the value of the euro leads to a 0.8¢ change in the value of the DK. To cross-hedge the forthcoming receipt of DK, 0.8 units of euro futures must be sold for every unit of DK to be sold on December 15. With a Danish krone exposure of DK 5 million, the exporter must sell euro futures contracts in the amount of €4 million (0.8 X 5 million). With a euro futures contract size of €125,000, this euro amount translates into 32 contracts (4 million/125,000). The example illustrates the idea that the euro futures can be used to effectively offset the risk posed by the DK receivable.