4.20. A U.S. company is interested in using the futures contracts traded on the CME to hedge its Australian dollar exposure. Definer as the interest rate (all maturities) on the U.S. dollar and ry as the interest rate (all maturities) on the Australian dollar. Assume that r and ry are constant and that the company uses a contract expiring at time 7 to hedge an exposure at time t (T>t).

a. Using the results in Chapter 3, show that the optimal hedge ratio is

b. Show that, when is one day, the optimal hedge ratio is almost exactly S_o/F_o. where So is the current spot price of the currency and F_o is the current futures price of the currency for the contract maturing at time T.

c. Show that the company can take account of the daily settlement of futures contracts for a hedge that lasts longer than one day by adjusting the hedge ratio so that it always equals the spot price of the currency divided by the futures price of the currency.

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