5.23. A U.S. company is interested in using the futures contracts traded by the CME Group to hedge its Australian dollar exposure. Define r as the interest rate (all maturities) on the U.S. dollar and rf as the interest rate (all maturities) on the Australian dollar. Assume that r and rf are constant and that the company uses a contract expiring at time T to hedge an exposure at time t (T > t). (a) Show that the optimal hedge ratio is e(rf-r) (Tt) (b) Show that, when t is 1 day, the optimal hedge ratio is almost exactly So/Fo, where So is the current spot price of the currency and Fo 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 1 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.