In May, Mr$.$ Smith planted a wheat crop, which he expects to harvest in September. He anticipates

the September harvest to be $100,000$ bushels and would like to hedge the price he can get for his

wheat by taking a position in a September wheat futures contract.

a$.$ Explain how Mr$.$ Smith could lock in the price he sells his wheat with a September wheat futures

contract trading in May at f$0=$ $$4\mathrm{.}50/$bu$.($contract size of $5,000$ bushels$).$

b$.$ Show in a table Mr$.$ Smith$$s revenue at the futures' expiration date from closing the futures

position and selling $100,000$ bushels of wheat on the spot market at possible spot prices of

$$4\mathrm{.}00/$bu$.,$ $$4\mathrm{.}50/$bu$.,$ and $$5\mathrm{.}00/$bu$.$ Assume no quality, quantity, or timing risk.

c$.$ Give examples of the three types of hedging risk in the context of problem b$.$

d$.$ How much cash or risk$-$free securities would Mr$.$ Smith have to deposit to satisfy an initial

margin requirement of $5\%?$