Assignment: Interest rate futures, Swaps, more:due per syllabus(hardcopy due in class)
1. The price of a 90-day Treasury Bill is quoted as 9.00. What continuously compounded return (on an actual/365 day) does an investor earn on the Treasury bill for the 90-day period?
2. It is May 5, 2013. The quoted rice of a U.S. government bond with a 10% coupon that matures on July 27, 2024, is 110-07. What is the cash price?
3. Suppose that the Treasury bond future price is 101-12. Which of the following four bonds is cheapest to deliver?
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Bond
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Price
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Conversion factor
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1
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125-05
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1.2131
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2
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142-15
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1.3792
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3
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115-31
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1.1149
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4
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144-02
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1.3900
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4. Suppose that the nine-month LIBOR interest rate is 8.25 % per annum and the six-month LIBOR interest rate is 7.5% per annum (both with actual /365 and continuous compounding). What is the three-month Eurodollar futures price quote for a contact maturing in six months?
5. A five-year bond with a yield of 10% (continuously compounded) pays an 8% coupon at the end of each year.
a. What is the bond price?
b. What is the bond's duration?
c. Use duration to calculate the impact on the bond price of a 0.2% decrease in yield.
6. Companies X and Y have been offered the following rates per annum on a $5 million 10-year investment:
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Fixed Rate
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Floating Rate
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Company X
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8.0 %
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LIBOR
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Company Y
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8.6 %
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LIBOR
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Company X requires a fixed-rate investment and company Y requires a floating-rate investment. Design a swap that will net a bank, acting as an intermediary, 0.2% per annum and will appear equally attractive to X and Y.
7. A financial institution (FI) has entered into an interest rate swap with Company X. Under the terms of the swap the FI receives 10% per annum and pays six-month LIBOR on a principal of $10 million for five years. Payments are made every six months. Suppose that company X default on thesixth payment date (end of year 3) when the LIBOR/swap interest rate (with semi-annual compounding) is 8% per annum for all maturities.Assume that six-month LIBOR was 9.4% per annum halfway through year 3. Use LIBOR discounting.What is the loss to the financial institution?
8. A financial institution has entered into a ten-year currency swap with company Y. Under the terms of the swap, the financial institution received interest at 3% per annum in Swiss francs and pays interest at 8% per annum in U.S. dollars. Interest payments are exchanged once a year. The principal amounts are 7 million dollars and 10 million francs. Suppose that company Y declares bankruptcy at the end of year 6, when the exchange rate is $0.75 per franc. What isthe cost to the financial institution? Assume that, at the end of the year 6, the interest rate is 3% per annum in Swiss francs and 8% per annum in U.S. dollars. For all maturities. All interest rates are quoted with annual compounding.
9. Companies A and B face the following interest rates (adjusted for differential impact of taxes):
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A
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B
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U.S. dollars (floating rate)
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LIBOR + 0.5 %
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LIBOR + 1.0%
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Canadian dollars (fixed rate)
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5.0 %
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6.5 %
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Assume that A wants to borrow U.S. dollars at a floating rate of interest and B wants to borrow Canadian dollars at a fixed rate of interest. A financial institution is planning to arrange a swap and requires a 40-basis-point spread. If the swap is to appear equally attractive to A and B, what rates of interest will A and B end up paying?
10. The LIBOR zero curve is flat at 5% (continuously compounded) out to 1.5 years. Swap rates for 2- and 3- year semiannual pay swaps are 5.4% and 5.7%, respectively. Estimate the LIBOR zero rates for maturities of 2.0, 2.5, and 3.0 years. (Assume that the 2.5 year swap rate is the average for the 2- and 3-year swap rates and use LIBOR discounting.)
11. Suppose that a European call option to buy a share for $100.00 costs $4.00 and is held until maturity. Under what circumstance will the holder of the option make a profit? Under what circumstances will the option be exercised?
12. Suppose that a European put option to sell a share for $60 costs $7 and is held until maturity. Under what circumstance will the option writer make a profit? Under what circumstance will it be exercised?
13. A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the same maturity. The call costs $3 and the put costs $3.75.Over what range(s) does this combination generate a profit? Over which range(s) a loss?
14. Consider an exchange-traded call option contract to buy 500 shares with a strike price of $38 and maturity in four months. How do the terms of the option contract change when (a.) 10% stock dividend, (b.) a 10 % cash dividend, (c.) 2-for-1 stock split?
15. Suppose that a European call option to buy a share for $100.00 costs $4.00 and is held until maturity. Assume that at maturity the share costs $108, what is the call buyer's profit?
16. Suppose the stock price is $80, the strike price is $76, and the risk-free interest rate is 10 % per annum. What is the lower bound for the price of a six-month call option on the non-dividend paying stock?
17. A non-dividend-paying stock's price is $58, the strike price is $66, and the risk-free interest rate is 5% per annum. What is a lower bound for the price of a two-month European put option?
18. The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. The term structure is flat, with all risk-free interest rates being 9%. What is the price of a European put option that expires in six months and has a strike price of $30?
19. The price of an American call on a non-dividend-paying stock is $3.75. The stock price is $31, the strike price is $30, and the expiration date is in three months. The risk-free interest rate is 8%. Derive upper and lower bounds for a price of an American put on the same stock with the same strike price and expiration date.
20. Consider a five-year call option on a non-dividend -paying stock granted to employees. The option can be exercise at any time after the end of the first year. Unlike a regular exchange-traded call option, the employee stock option cannot be sold. What is the likely impact of this restriction on the early exercise?