A U$.$S$.$ company is interested in using the futures contracts traded by the CME Group tohedge its Australian dollar exposure. Define r as the interest rate $($all maturities$)$ on theU.S$.$ dollar and rf as the interest rate $($all maturities$)$ on the Australian dollar. Assumethat r and rf are constant and that the company uses a contract expiring at time T tohedge an exposure at time t $1$T $7$ t$2.($a$)$ Show that the optimal hedge ratio is e$1$rf$-$ r$21$T$-$ t$2,$ ignoring daily settlement.$($b$)$ Show that, when t is $1$ day, the optimal hedge ratio is almost exactly S$0>$F$0,$ where S$0$ isthe current spot price of the currency and F$0$ is the current futures price of thecurrency for the contract maturing at time T$.($c$)$ Show that the company can take account of the daily settlement of futures contractsfor a hedge that lasts longer than $1$ day by adjusting the hedge ratio so that it alwaysequals the spot price of the currency divided by the futures price of the currency.