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)(T-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.

Transcribed Image Text:

Oct 2017 Feb 2019 Aug 2019 Feb 2018 Aug 2018 Date Spot Price Mar 2018 Futures Price Sep 2018 Futures Price Mar 2019 Futures Price Sep 2019 Futures Price 372.00 377.00 388.00 369.00 365.00 372.30 369.10 372.80 370.20 364.80 364.30 376.70 370.70 388.20 364.20 376.50