a. Is the interest rate parity holding? You may ignore transaction costs. b. Is there an arbitrage opportunity? If yes, show what steps need to be taken to make arbitrage profit. Assuming that James Clark is authorized to work with $1,000,000, compute the arbitrage profit in dollars. Answer: a) Applying the formula of IRP. b) The arbitrage profit six months later is $8,429.
Q2. Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 to invest for six months. The six-month interest rate is 8 percent per annum in the United States and 7 percent per annum in Germany. Currently, the spot exchange rate is €1.01 per dollar and the six-month forward exchange rate is €0.99 per dollar. The treasurer of IBM does not wish to bear any exchange risk. Where should he/she invest to maximize the return? Answer: Option 1: Investing $100,000,000 in the U.S., with the maturity value in six months and interest rate is 8% per annum, we will have $104,000,000 Option 2: Converting $100,000,000 into euros and invested at the German interest rate (7%), and signing the forward contract at the same time. We will have $105,590,909 The option 2 is better.
Q3. While you were visiting London, you purchased a Jaguar for £35,000, payable in three months. You have enough cash at your bank in New York City, which pays 0.35% interest per month, compounding monthly, to pay for the car. Currently, the spot exchange rate is $1.45/£ and the three-month forward exchange rate is $1.40/£. In London, the money market interest rate is 2.0% for a three-month investment. There are two alternative ways of paying for your Jaguar. (a) Keep the funds at your bank in the U.S. and buy £35,000 forward. (b) Buy a certain pound amount spot today and invest the amount in the U.K. for three months so that the maturity value becomes equal to £35,000.
Evaluate each payment method. Which method would you prefer? Why? Answer: Option a: When you buy £35,000 forward, you will need $49,000 (= £35,000 × $1.40/£) in three months to fulfill the forward contract. The present value of $49,000 is computed as follows: $49,000/(1.0035)3 = $48,489. Thus, the cost of Jaguar as of today is $48,489. Option b: The present value of £35,000 is £34,314 = £35,000/(1.02). To buy £34,314 today, it will cost $49,755 = 34,314x1.45. Thus the cost of Jaguar as of today is $49,755. Choose the option a
Q4. Airbus sold an aircraft, A400, to Delta Airlines, a U.S. company, and billed $30 million payable in six months. Airbus is concerned with the euro proceeds from international sales and would like to control exchange risk. The current spot exchange rate is $1.05/€ and sixmonth forward exchange rate is $1.10/€ at the moment. Airbus can buy a six-month put option on U.S. dollars with a strike price of €0.95/$ for a premium of €0.02 per U.S. dollar. Currently, six-month interest rate is 2.5% in the euro zone and 3.0% in the U.S.
a. Compute the guaranteed euro proceeds from the American sale if Airbus decides to hedge using a forward contract. b. If Airbus decides to hedge using money market instruments, what action does Airbus need to take? What would be the guaranteed euro proceeds from the American sale in this case? c. If Airbus decides to hedge using put options on U.S. dollars, what would be the ‘expected’ euro proceeds from the American sale? Assume that Airbus regards the current forward exchange rate as an unbiased predictor of the future spot exchange rate. d. At what future spot exchange rate do you think Airbus will be indifferent between the option and money market hedge? Answer: a. Airbus will sell $30 million forward for €27,272,727 = ($30,000,000) / ($1.10/€). b.Airbus will borrow the present value of the dollar receivable, i.e., $29,126,214 = $30,000,000/1.03, and then sell the dollar proceeds spot for euros:
(=$29,126,214/$1.05/€). This is the euro amount that Airbus is going to keep. c. Since the expected future spot rate is less than the strike price of the put option, i.e.,
€0.9091< €0.95, Airbus expects to exercise the put option on $ and receive €28,500,000 = ($30,000,000) (€0.95/$). This is gross proceeds. Airbus spent €600,000 (=0.02x30,000,000) upfront for the option and its future cost is equal to €615,000 = €600,000 x 1.025. Thus the net euro proceeds from the American sale is €27,885,000, which is the difference between the gross proceeds and the option costs. d. At the indifferent future spot rate, the following will hold: €28,432,732 = ST (30,000,000) - €615,000. Solving for ST, we obtain the “indifference” future spot exchange rate, i.e., €0.9683/$, or $1.0327/€. Note that €28,432,732 is the future value of the proceeds under money market hedging: €28,432,732 = (€27,739,251) (1.025). Q5. A speculator is considering the purchase of five three-month Japanese yen call options with a striking price of 96 cents per 100 yen. The premium is 1.35 cents per 100 yen. The spot price is 95.28 cents per 100 yen and the 90-day forward rate is 95.71 cents. The speculator believes the yen will appreciate to $1.00 per 100 yen over the next three months. As the speculator’s assistant, you have been asked to prepare the following: 1. Graph the call option cash flow schedule. 2. Determine the speculator’s profit if the yen appreciates to $1.00/100 yen. 3. Determine the speculator’s profit if the yen only appreciates to the forward rate. 4. Determine the future spot price at which the speculator will only break even. Answer: 2. (5 x ¥1,000,000) x [(100 - 96) - 1.35]/10000 = $1,325.00. 3.
Since the option expires out-of-the-money, the speculator will let the option expire
worthless. He will only lose the option premium. 4. ST = E + C = 96 + 1.35 = 97.35 cents per 100 yen.
Q6. Assume today’s settlement price on a CME EUR futures contract is $1.3140/EUR. You have a short position in one contract. Your performance bond account currently has a balance of $1,700.
The next three days’ settlement prices are $1.3126, $1.3133, and $1.3049.
Calculate the changes in the performance bond account from daily marking-to-market and the balance of the performance bond account after the third day. Answer:
With the contract size EUR125,000, so The balance of performance bond account in the third day will be $2,837.50 Q7. Due to the integrated nature of their capital markets, investors in both the U.S. and U.K. require the same real interest rate, 2.5%, on their lending. There is a consensus in capital markets that the annual inflation rate is likely to be 3.5% in the U.S. and 1.5% in the U.K. for the next three years. The spot exchange rate is currently $1.50/£. a. Compute the nominal interest rate per annum in both the U.S. and U.K., assuming that the
Fisher effect holds. b. What is your expected future spot dollar-pound exchange rate in three years from now? c. Can you infer the forward dollar-pound exchange rate for one-year maturity?
Answer: a. Nominal rate in US = (1+ρ) (1+E(π$)) – 1 = (1.025)(1.035) – 1 = 0.0609 or 6.09%. Nominal rate in UK= (1+ρ) (1+E(π₤)) – 1 = (1.025)(1.015) – 1 = 0.0404 or 4.04%. b. E(ST) = [(1.0609)3/(1.0404)3] (1.50) = $1.5904/₤. c. F = [1.0609/1.0404](1.50) = $1.5296/₤.