Exercise $1$

Suppose that you enter into a short futures contract to sell July silver for $$17\mathrm{.}20$ per ounce. The size of the contract is $5,000$ ounces. The initial margin is $$4,000,$ and the maintenance margin is $$3,000.$ What change in the futures price will lead to a margin call? What happens if you do not meet the margin call?

Exercise $2$

A trader buys two July futures contracts on orange juice. Each contract is for the delivery of $15,000$ pounds. The current futures price is $160$ cents per pound, the initial margin is $$6,000$ per contract, and the maintenance margin is $$4,500$ per contract. What price change would lead to a margin call? Under what circumstances could $$2,000$ be withdrawn from the margin account?

Exercise $3$

At the end of one day a clearing house member is long $100$ contracts, and the settlement price is $$50,000$ per contract. The original margin is $$2,000$ per contract. On the following day the member becomes responsible for clearing an additional $20$ long contracts, entered into at a price of $$51,000$ per contract. The settlement price at the end of this day is $$50,200.$ How much does the member have to add to its margin account with the exchange clearing house?

Exercise $4$

A trader owns $55,000$ units of a particular asset and decides to hedge the value of her position with futures contracts on another related asset. Each futures contract is on $5,000$ units. The spot price of the asset that is owned is $$28$ and the standard deviation of the change in this price over the life of the hedge is estimated to be $$0\mathrm{.}43.$ The futures price of the related asset is $$27$ and the standard deviation of the change in this over the life of the hedge is $$0\mathrm{.}40.$ The coefficient of correlation between the spot price change and futures price change is $0\mathrm{.}95.$

$($a$)$ What is the minimum variance hedge ratio?

$($b$)$ Should the hedger take a long or short futures position?