Question 1

A dollar-based American corporation has decided that it will have to pay 6 million UK pounds in three months. Assume that the current exchange rate is 1.250 dollars per pound.

(a) Explain in brief and clear terms what is meant by a forward contract and what is meant by an options contract.

(b) Explain how forward contracts and options contracts might be used by the firm to hedge its exposure to the exchange rate.

(c) What are the risks that are entailed with these strategies?

Question 2

A trader who is working in the gold markets is able to borrow money at the interest rate of 7% per annum. The spot price for an ounce of gold is currently $1,400. The forward price for delivery of one ounce of gold in one year is $1,550.

(a) Explain in brief and clear terms with one or two examples what is meant by
the “convenience yield” of a storable commodity.

(b) Suppose that the cost of storing gold is negligible and that gold provides
no income. What strategy should the trader adopt?

(c) Suppose instead that the storage cost of gold is 2% per annum and that gold provides a convenience yield of 1% per annum. Then what strategy would the trader adopt

Question 3

The share price of a certain stock today is $42.50, and five-month European style call options with a strike price of $45 currently sell for $4.25. A client who feels that the share price is going up is trying to decide between buying 100 shares of the stock or buying 1,000 call options. Both strategies involve an initial investment of $4,250.

(a) What happens to each of these investments if the share price remains at
$42.50 after five months?

(b) What happens if the share price rises from $42.50 to $55 over the five month period?

(c) How high does the share price have to rise for the option strategy to be the
more profitable of the two alternatives

Question 4

A grapefruit juice futures contract is for 15,000 pounds of frozen grapefruit
juice. Suppose that in September 2016 a company sells a March 2018 grapefruit juice futures contract for $2.40 per pound. In December 2016 the
futures price is $2.80; in December 2017 the futures price is $2.20; and in February 2018 the contract is closed out at $2.50. The firm’s accounts have a
December year end.

(a) What does it mean to “close out” a short position in a futures contract?

(b) What is the company’s profit or loss on the grapefruit juice futures
contract?

(c) How is the profit or loss realized if the company is classified as (i) a hedger
or (ii) a speculator?

Question 5

Let the current share price be S for some stock. The current price of a three month European-style call option on the same stock, with strike K, is C. An investor is considering whether to buy n shares or N options.

(a) What condition on S, K, C, n, and N ensures that the initial investments in
the two strategies are the same?

(b) Assuming that the initial investments are the same, work out the breakeven value S’ that the share price must be below in three months’ time in order to ensure that the share strategy will be more profitable than the option strategy. Express S’ as a function of K, N, and n.

(c) It is well known that arbitrage arguments can be used to show that S > C. Assuming this result, show that the return on the option investment is greater than the return on the stock investment if S’/S > K/(S-C).

Question 6

This question concerns margin requirements in futures markets.

(a) In the context of a short futures contract, explain what is meant by the “initial margin” and the “maintenance margin.”

(b) A trader at a commodity exchange enters into a short futures contract to sell 5,000 bushels of corn for $15.20 per bushel. The initial margin is $6,000 and the maintenance margin is $4,000. What change in the price of corn would lead to a margin call?

(c) Under what circumstances is the trader able to withdraw $3,000 from the margin account?

Question 7

This question concerns oil futures contracts. Let us assume that the dollar interest rate is 7% per annum and that there are no storage costs or convenience benefits for holding crude oil.

(a) How could a commodity trader make money if the May and November crude oil futures contracts for a particular year are trading at $100 and $109 per barrel, respectively?

(b) How would the result change if the spot price of crude oil dropped to $105
per barrel in November?

(c) How would the result change if the storage cost of crude oil was
1.5% per annum?

Question 8

Let the interest rate be r when it is compounded annually, where r is expressed as a decimal fraction. Thus, if the interest rate is 6% we write r = 0.06, and so on. Let R(n) denote the interest rate when it is compounded n times per year. Thus, R(1) = r, R(2) is the interest rate for biannual compounding, R(4) is the interest rate for quarterly compounding, and so forth. All interest rates are quoted on an annualized basis.

(a) Find an expression for R(n) in terms of r and n. Show your work.

(b) Hence deduce that if the annually compounded interest rate is 44% then the corresponding biannually compounded rate is R(2) = 40%.

(c) What is the relationship between R(n) (n = 1, 2, 3, . . . ) and the continuously compounded rate? You may use the fact that in the limit as n goes to infinity, the function f(n) = n [x^(1/n) -1] converges for each value of x to log x.

Question 9

A firm enters into a three-year forward contract on a certain non-dividend paying stock. The share price in dollars is S and the interest rate is r per annum with continuous compounding. The interest rate r is expressed as a decimal fraction; for example, one writes r = 0.07 if the interest rate is 7%

(a) Give expressions for the three-year forward price and the initial value of the three-year forward contract.

(b) One year later, the price of the stock is S’ and the interest rate remains at r. What is the value of the forward contract at that time? Show your reasoning.

Question 10

Let the 3-month, 6-month, 9-month, and 12-month zero-coupon rates with semi-annual compounding be denoted A, B, C, and D, respectively, expressed as decimal fractions. Thus, for example, if the 3-month zero-rate is 4.5% with quarterly compounding, then A = 0.45. Note that all rates are quoted on an annualized basis.

(a) What are the corresponding rates with continuous compounding? Express your answers in terms of A, B, C, and D. Show your reasoning.

(b) What is the forward rate for the six-month period beginning in 18 months?

(c) What is the value of an FRA (Forward Rate Agreement) that promises to pay 4.5% (compounded quarterly) on a principal of ten million dollars for the three-month period starting in nine months?