1.Your start-up company has negotiated a contract to provide a database installation for a manufacturing company in Poland. That firm has agreed to pay you $100,000 in three months time when the installation will occur. However, it insists on paying in Polish zloty (PLN). You don’t want to lose the deal (the company is your first client!), but are worried about the exchange rate risk. In particular, you are worried the zloty could depreciate relative to the dollar. You contact Fortis Bank in Poland to see if you can lock in an exchange rate for the zloty in advance.
a. You find the following table posted on the bank’s Web site, showing zloty per dollar, per euro, and per British pound:
What exchange rate could you lock in for the zloty in three months? How many zloty should you demand in the contract to receive $100,000?
b. Given the bank forward rates in part (a), were short-term interest rates higher or lower in Poland than in the United States at the time? How did Polish rates compare to euro or pound rates? Explain.
2.You are a broker for frozen seafood products for Choyce Products. You just signed a deal with a Belgian distributor. Under the terms of the contract, in one year you will deliver 4000 kilograms of frozen king crab for 100,000 euros. Your cost for obtaining the king crab is $110,000. All cash flows occur in exactly one year.
a. Plot your profits in one year from the contract as a function of the exchange rate in one year, for exchange rates from $0.75/€ to $1.50/€. Label this line “Unhedged Profits.”
b. Suppose the one-year forward exchange rate is $1.25/€. Suppose you enter into a forward contract to sell the euros you will receive at this rate. In the figure from part (a), plot your combined profits from the crab contract and the forward contract as a function of the exchange rate in one year. Label this line “Forward Hedge.”
c. Suppose that instead of using a forward contract, you consider using options. A one-year call option to buy euros at a strike price of $1.25/€ is trading for $0.10/€. Similarly a one year put option to sell euros at a strike price of $1.25/€ is trading for $0.10/€. To hedge the risk of your profits, should you buy or sell the call or the put?
d. In the figure from parts (a) and (b), plot your “all in” profits using the option hedge (combined profits of crab contract, option contract, and option price) as a function of the exchange rate in one year. Label this line “Option Hedge.” (Note : You can ignore the effect of interest on the option price.)
e. Suppose that by the end of the year, a trade war erupts, leading to a European embargo on U.S. food products. As a result, your deal is cancelled, and you don’t receive the euros or incur the costs of procuring the crab. However, you still have the profits (or losses) associated with your forward or options contract. In a new figure, plot the profits associated with the forward hedge and the options hedge (labeling each line). When there is a risk of cancellation, which type of hedge has the least downside risk? Explain briefly.
3.Suppose the current exchange rate is $1.80/£, the interest rate in the United States is 5.25%, the interest rate in the United Kingdom is 4%, and the volatility of the $/£ exchange rate is 10%. Use the Black-Scholes formula to determine the price of a six-month European call option on the British pound with a strike price of $1.80/£.
4.Assume each of the following securities has the same yield-to-maturity: a five-year, zero-coupon bond; a nine-year, zero-coupon bond; a five-year annuity; and a nine-year annuity. Rank these securities from lowest to highest duration.
5.You have been hired as a risk manager for Acorn Savings and Loan. Currently, Acorn’s balance sheet is as follows (in millions of dollars):
When you analyze the duration of loans, find that the duration of the auto loans is two years, while the mortgages have a duration of seven years. Both the cash reserves and the checking and savings accounts have a zero duration. The CDs have a duration of two years and the long-term financing has a 10-year duration.
a. What is the duration of Acorn’s equity?
b. Suppose Acorn experiences a rash of mortgage prepayments, reducing the size of the mortgage portfolio from $150 million to $100 million, and increasing cash reserves to $100 million. What is the duration of Acorn’s equity now? If interest rates are currently 4% but fall to 3%, estimate the approximate change in the value of Acorn’s equity.
c. Suppose that after the prepayments in part (b), but before a change in interest rates, Acorn considers managing its risk by selling mortgages and/or buying 10-year Treasury STRIPS (zero-coupon bonds). How many should the firm buy or sell to eliminate its current interest rate risk?
6.The Citrix Fund has invested in a portfolio of government bonds that has a current market value of $44.8 million. The duration of this portfolio of bonds is 13.5 years. The fund has borrowed to purchase these bonds, and the current value of its liabilities (i.e., the current value of the bonds it has issued) is $39.2 million. The duration of these liabilities is four years. The equity in the Citrix Fund (or its net worth) is obviously $5.6 million. The market-value balance sheet below summarizes this information:
Assume that the current yield curve is flat at 5.5%. You have been hired by the board of directors to evaluate the risk of this fund.
a. Consider the effect of a surprise increase in interest rates, such that the yields rise by 50 basis points (i.e., the yield curve is now flat at 6%). What would happen to the value of the assets in the Citrix Fund? What would happen to the value of the liabilities? What can you conclude about the change in the value of the equity under these conditions?
b. What is the initial duration of the Citrix Fund (i.e., the duration of the equity)?
c. As a result of your analysis, the board of directors fires the current manager of the fund. You are hired and given the objective of minimizing the fund’s exposure to interest rate fluctuations. You are instructed to do so by liquidating a portion of the fund’s assets and reinvesting the proceeds in short-term Treasury bills and notes with an average duration of two years. How many dollars do you need to liquidate and reinvest to minimize the fund’s interest rate sensitivity?
d. Rather than immunizing the fund using the strategy in part (c), you consider using a swap contract. If the duration of a 10-year, fixed-coupon bond is seven years, what is the notational amount of the swap you should enter into? Should you receive or pay the fixed rate portion of the swap?
7.Your firm needs to raise $100 million in funds. You can borrow short term at a spread of 1% over LIBOR. Alternatively, you can issue 10-year, fixed-rate bonds at a spread of 2.50% over 10- year Treasuries, which currently yield 7.60%. Current 10-year interest rate swaps are quoted at LIBOR versus the 8% fixed rate.
Management believes that the firm is currently “underrated” and that its credit rating is likely to improve in the next year or two. Nevertheless, the managers are not comfortable with the interest rate risk associated with using short-term debt.
a. Suggest a strategy for borrowing the $100 million. What is your effective borrowing rate?
b. Suppose the firm’s credit rating does improve three years later. It can now borrow at a spread of 0.50% over Treasuries, which now yield 9.10% for a seven-year maturity. Also, seven-year interest rate swaps are quoted at LIBOR versus 9.50%. How would you lock in your new credit quality for the next seven years? What is your effective borrowing rate now?