Posted: May 22nd, 2022
Assignment 3 Details
Complete and submit Assignment 3, which is worth 15% of your final grade, after you have finished Unit 6. If you have any questions about this assignment and how to complete it, contact the Student Support Centre.
This assignment contains ten problems and is worth a total of 100 marks.
Read the requirements for each problem and plan your responses carefully. Ensure that you answer each of the required questions as concisely and as completely as possible and include supporting calculations where required.
1. (7 marks) You are a bright new analyst in the risk-management division at RMS, a multinational technology company, and have recently been put in charge of managing the Euro/CAD exchange-rate risk that RMS faces. Consider RMS’s operations in Europe and Canada.
a. Suppose monthly revenues in Europe average 10 million Euros and monthly production and distribution costs average 8 million Euro. If the resulting profits are repatriated to the production unit in Canada monthly, what risk does this production unit face? How might it hedge this risk? (2 marks)
b. RMS’s worldwide retirement benefits unit is located in Canada and has the obligation to pay its retired European employees 20 million Euros monthly. What does this unit face and how could it hedge the risk? (2 marks)
c. Given the transactions of the production and retirement units as given previously, what do you conclude are the exchange-rate risks faced by RMS as a whole in Europe? Does RMS need to enter into forward contracts? (3 marks)
2. (10 marks) Suppose the spot exchange rate between U.S. dollar and Canadian dollar is US$1.03/C$. The U.S. dollar risk-free rate is 2% per annum, compounded annually. The price of a two-year European call option and put option with an exercise price of US$1.05/C$ is US$4.45 and US$4.54, respectively. What is the Canadian dollar risk-free rate?
3. (10 marks) Two firms have the borrowing rates shown below.
Firm |
Fixed Rate |
Floating Rate |
AAA |
5 yr T-bond + 60 bp |
LIBOR |
BBB |
5 yr T-bond + 75 bp |
LIBOR + 30 bp |
As the CFO of firm AAA, you always consider an interest rate swap before borrowing money. Explain how, if at all, a swap with BBB would be advantageous to you if
a. you wanted to borrow at a fixed rate. (7 marks)
b. you wanted to borrow at a floating rate. (3 marks)
4. (10 marks) A corporation enters into a $35 million notional principal plain vanilla interest rate swap. The swap calls for the corporation to pay a fixed rate and receive a floating rate of LIBOR. The payments will be made every three months for one year. The term structure of LIBOR when the swap is initiated is as follows:
Months |
Rate (%) |
3 |
7.00 |
6 |
7.25 |
9 |
7.45 |
12 |
7.55 |
Assume all of rates are continuously compounded.
a. Determine the fixed rate on the swap. (7 marks)
b. Calculate the first net payment on the swap. (3 marks)
5. (10 marks) Suppose that the British pound interest rate is 0.65% per annum and Canadian dollar interest rate is 1% per annum for all maturities, annually compounded. The current exchange rate is 1.6033 CAD/£. Under the terms of a swap agreement, a bank receives 2% per annum in Canadian dollars and pays 3% per annum in British pounds. Payments are exchanged every year, with one exchange having just taken place. The principal amounts are $10 million Canadian dollars and $6 million British pounds. The swap will last two more years.
a. Determine the cash flows to the bank. (4 marks)
b. What is the value of the swap to the bank in terms of Canadian dollars? (6 marks)
6. (6 marks) PQR Company longs a FRA on 2-month LIBOR with a fixed rate of 5.25 percent and a notional principal of $38 million. If the market LIBOR rate is 6.125 percent at expiration, what would be the payoff of this FRA to PQR? Assume that there are 30 days in a month.
7. (6 marks) A portfolio consists of 1,000 shares of stock and 500 short calls on that stock. If the delta for the call is 0.5, what would be the dollar change in the value of the portfolio in response to a one dollar increase in the stock price?
8. (16 marks) A firm has a portfolio composed of stock A and B with normally distributed returns. Stock A has an annual expected return of 10% and annual volatility of 25%. The firm has a position of $100 million in stock A. Stock B has an annual expected return of 20% and an annual volatility of 20% as well. The firm has a position of $50 million in stock B. The correlation coefficient between the returns of these tow stocks is 0.2.
a. Compute the 5% annual VAR for the portfolio. (8 marks)
b. If the firm sells $10 million of stock A and buys $10 million of stock B, by how much does the 5% annual VAR change? (8 marks)
9. (16 marks) A firm has total assets with a market value of $1,500,000. It has one issue of 1,000 zero coupon bonds outstanding, each with a face value of $1,000 and a maturity of 3 years. The volatility of the assets is 20%, and the risk-free rate is 5%.
a. What is the market value of the firm’s equity? (7 marks)
b. What is the market value of the bonds? (2 marks)
c. What is the continuously compounded yield on the bonds? (2 marks)
d. Analyze the credit risk structure for this firm by varying the maturity on the bonds from 3 to 7 years. Discuss this credit risk structure. (5 marks)
10. (9 marks) Given interest rate options with notional principals of $10 million on an underlying 120-day LIBOR. The options have exercise rates of 6% and will expire in 30 days.
a. What is the payoff on the call option if the LIBOR in 30 days is 7%, in 60 days is 8%, and in 90 days is 9%? (3 marks)
b. What is the payoff on the put option if the LIBOR in 30 days is 3%, in 60 days is 4%, and in 90 days is 5%? (3 marks)
c. Discuss the difference between the payoff on an FRA and the payoff on an interest rate option. (3 marks)
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