Chapter 23 - Futures, Swaps, and Risk Management
Chapter 23
Futures, Swaps, and Risk Management
Multiple Choice Questions
1. Which one of the following stock index futures has a multiplier of $250 times the index
value?
A. Russell 2000
B. S&P 500 Index
C. Nikkei
D. DAX-30
E. NASDAQ 100
2. Which one of the following stock index futures has a multiplier of $10 times the index
value?
A. Russell 2000
B. Dow Jones Industrial Average
C. Nikkei
D. DAX-30
E. NASDAQ 100
3. Which one of the following stock index futures has a multiplier of $100 times the index
value?
A. Russell 2000
B. FTSE 100
C. Nikkei
D. NASDAQ 100
E. Russell 2000 and NASDAQ 100
4. Which one of the following stock index futures has a multiplier of $100 times the index
value?
A. Russell 2000
B. FTSE 100
C. S&P Mid-Cap
D. DAX-30
E. Russell 2000 and S&P Mid-Cap
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Chapter 23 - Futures, Swaps, and Risk Management
5. Which one of the following stock index futures has a multiplier of $100 times the index
value?
A. CAC 40
B. S&P 500 Index
C. Nikkei
D. DAX-30
E. NASDAQ 100
6. Which one of the following stock index futures has a multiplier of 10 euros times the
index?
A. CAC 40
B. DJ Euro Stoxx - 50
C. Nikkei
D. DAX-30
E. CAC 40 and DJ Euro Stoxx - 50
7. Which one of the following stock index futures has a multiplier of 10 euros times the
index?
A. FTSE 100
B. DJ Euro Stoxx - 50
C. Nikkei
D. DAX-30
E. FTSE 100 and DJ Euro Stoxx - 50
8. Which one of the following stock index futures has a multiplier of 25 euros times the
index?
A. FTSE 100
B. DJ Euro Stoxx - 50
C. Nikkei
D. DAX-30
E. FTSE 100 and DJ Euro Stoxx - 50
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Chapter 23 - Futures, Swaps, and Risk Management
9. You purchased one S&P 500 Index futures contract at a price of 950 and closed your
position when the index futures was 947, you incurred:
A. a loss of $1,500.
B. a gain of $1,500.
C. a loss of $750.
D. a gain of $750.
E. None of these is correct.
10. You took a short position in two S&P 500 futures contracts at a price of 910 and closed
the position when the index futures was 892, you incurred:
A. a gain of $9,000.
B. a loss of $9,000.
C. a loss of $18,000.
D. a gain of $18,000.
E. None of these is correct.
11. If a stock index futures contract is overpriced, you would exploit this situation by:
A. selling both the stock index futures and the stocks in the index.
B. selling the stock index futures and simultaneously buying the stocks in the index.
C. buying both the stock index futures and the stocks in the index.
D. buying the stock index futures and selling the stocks in the index.
E. None of these is correct.
12. Foreign Exchange Futures markets are __________ and the Foreign Exchange Forward
markets are __________.
A. informal; formal
B. formal; formal
C. formal; informal
D. informal; informal
E. organized; unorganized
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Chapter 23 - Futures, Swaps, and Risk Management
13. Suppose that the risk-free rates in the United States and in the United Kingdom are 4%
and 6%, respectively. The spot exchange rate between the dollar and the pound is $1.60/BP.
What should the futures price of the pound for a one-year contract be to prevent arbitrage
opportunities, ignoring transactions costs?
A. $1.60/BP
B. $1.70/BP
C. $1.66/BP
D. $1.63/BP
E. $1.57/BP
14. Suppose that the risk-free rates in the United States and in the United Kingdom are 5%
and 4%, respectively. The spot exchange rate between the dollar and the pound is $1.80/BP.
What should the futures price of the pound for a one-year contract be to prevent arbitrage
opportunities, ignoring transactions costs?
A. $1.62/BP
B. $1.72/BP
C. $1.82/BP
D. $1.92/BP
E. None of these is correct.
15. Suppose that the risk-free rates in the United States and in Japan are 5.25% and 4.5%,
respectively. The spot exchange rate between the dollar and the yen is $0.008828/yen. What
should the futures price of the yen for a one-year contract be to prevent arbitrage
opportunities, ignoring transactions costs?
A. $0.009999/yen
B. $0.009981/yen
C. $0.008981/yen
D. $0.008891/yen
E. None of these is correct.
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Chapter 23 - Futures, Swaps, and Risk Management
16. Let RUS be the annual risk free rate in the United States, RUK be the risk free rate in the
United Kingdom, F be the futures price of $/BP for a 1-year contract, and E the spot exchange
rate of $/BP. Which one of the following is true?
A. if RUS > RUK, then E > F
B. if RUS < RUK, then E < F
C. if RUS > RUK, then E < F
D. if RUS < RUK, then F = E
E. There is no consistent relationship that can be predicted.
17. Let RUS be the annual risk free rate in the United States, RJ be the risk free rate in Japan, F
be the futures price of $/yen for a 1-year contract, and E the spot exchange rate of $/yen.
Which one of the following is true?
A. if RUS > RJ, then E < F
B. if RUS < RJ, then E < F
C. if RUS > RJ, then E > F
D. if RUS < RJ, then F = E
E. There is no consistent relationship that can be predicted.
Consider the following:
18. What should be the proper futures price for a 1-year contract?
A. 1.703 A$/$
B. 1.654 A$/$
C. 1.638 A$/$
D. 1.778 A$/$
E. 1.686 A$/$
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Chapter 23 - Futures, Swaps, and Risk Management
19. If the futures market price is 1.63 A$/$, how could you arbitrage?
A. Borrow Australian Dollars in Australia, convert them to dollars, lend the proceeds in the
United States and enter futures positions to purchase Australian Dollars at the current futures
price.
B. Borrow U. S dollars in the United States, convert them to Australian Dollars, lend the
proceeds in Australia and enter futures positions to sell Australian Dollars at the current
futures price.
C. Borrow U. S. dollars in the United States and invest them in the U. S. and enter futures
positions to purchase Australian Dollars at the current futures price.
D. Borrow Australian Dollars in Australia and invest them there, then convert back to U. S.
dollars at the spot price.
E. There is no arbitrage opportunity.
20. If the market futures price is 1.69 A$/$, how could you arbitrage?
A. Borrow Australian Dollars in Australia, convert them to dollars, lend the proceeds in the
United States and enter futures positions to purchase Australian Dollars at the current futures
price.
B. Borrow U. S. dollars in the United States, convert them to Australian Dollars, lend the
proceeds in Australia and enter futures positions to sell Australian Dollars at the current
futures price.
C. Borrow U. S. dollars in the United States and invest them in the U. S. and enter futures
positions to purchase Australian Dollars at the current futures price.
D. Borrow Australian Dollars in Australia and invest them there, then convert back to U. S.
dollars at the spot price.
E. There is no arbitrage opportunity.
21. Assume the current market futures price is 1.66 A$/$. You borrow 167,000 A$ and
convert the proceeds to U. S. dollars and invest them in the U. S at the risk-free rate. You
simultaneously enter a contract to purchase 170,340 A$ at the current futures prices (maturity
of 1 year). What would be your profit (loss)?
A. Profit of 630 A$
B. Loss of 2300 A$
C. Profit of 2300 A$
D. Loss of 630 A$
E. None of these is correct.
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Chapter 23 - Futures, Swaps, and Risk Management
22. Which of the following is/are example(s) of interest rate futures contracts?
A. Corporate bonds
B. Treasury bonds
C. Eurodollars
D. Treasury bonds and Eurodollars
E. Corporate bonds and Treasury bonds
23. You hold a $50 million portfolio of par value bonds with a coupon rate of 10 percent paid
annually and 15 years to maturity. How many T-bond futures contracts do you need to hedge
the portfolio against an unanticipated change in the interest rate of 0.18%? Assume the market
interest rate is 10 percent and that T-bond futures contracts call for delivery of an 8 percent
coupon (paid annually), 20-year maturity T-bond.
A. 398 contracts long
B. 524 contracts short
C. 1048 contracts short
D. 398 contracts short
E. None of these is correct.
24. A swap
A. obligates two counterparties to exchange cash flows at one or more future dates.
B. allows participants to restructure their balance sheets.
C. allows a firm to convert outstanding fixed rate debt to floating rate debt.
D. obligates two counterparties to exchange cash flows at one or more future dates and allows
participants to restructure their balance sheets.
E. obligates two counterparties to exchange cash flows at one or more future dates, allows
participants to restructure their balance sheets, and allows a firm to convert outstanding fixed
rate debt to floating rate debt.
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Chapter 23 - Futures, Swaps, and Risk Management
25. Credit risk in the swap market
A. is extensive.
B. is limited to the difference between the values of the fixed rate and floating rate
obligations.
C. is equal to the total value of the payments that the floating rate payer was obligated to
make.
D. is extensive and is equal to the total value of the payments that the floating rate payer was
obligated to make.
E. None of these is correct.
26. Trading in stock index futures
A. now exceeds buying and selling of shares in most markets.
B. reduces transactions costs as compared to trading in stocks.
C. increases leverage as compared to trading in stocks.
D. generally results in faster execution than trading in stocks.
E. All of these are correct.
27. Commodity futures pricing
A. must be related to spot prices.
B. includes cost of carry.
C. converges to spot prices at maturity.
D. All of these are correct.
E. None of these is correct.
28. Arbitrage proofs in futures market pricing relationships
A. rely on the CAPM.
B. demonstrate how investors can exploit misalignments.
C. incorporate transactions costs.
D. All of these are correct.
E. None of these is correct.
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Chapter 23 - Futures, Swaps, and Risk Management
29. One reason swaps are desirable is that
A. they are free of credit risk.
B. they have no transactions costs.
C. they increase interest rate volatility.
D. they increase interest rate risk.
E. they offer participants easy ways to restructure their balance sheets.
30. Which two indices had the lowest correlation between them during the 2001–2006
period?
A. S&P and DJIA; the correlation was 0.957
B. S&P and NASDAQ; the correlation was 0.899
C. DJIA and Russell 2000 the correlation was 0.758
D. S&P and NYSE; the correlation was 0.973
E. NYSE and DJIA; the correlation was 0.931
31. Which two indices had the highest correlation between them during the 2001–2006
period?
A. S&P and DJIA; the correlation was 0.957
B. S&P and Russell 2000; the correlation was 0.899
C. DJIA and Russell 2000; the correlation was 0.758
D. S&P and NYSE; the correlation was 0.973
E. NYSE and DJIA; the correlation was 0.931
32. The value of a futures contract for storable commodities can be determined by the
_______ and the model __________ consistent with parity relationships.
A. CAPM; will be
B. CAPM; will not be
C. APT; will not be
D. APT; will be
E. CAPM and APT; will be
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Chapter 23 - Futures, Swaps, and Risk Management
33. In the equation Profits = a + b*($/₤ exchange rate), b is a measure of
A. the firm's beta when measured in terms of the foreign currency.
B. the ratio of the firm's beta in terms of dollars to the firm's beta in terms of pounds.
C. the sensitivity of profits to the exchange rate.
D. the sensitivity of the exchange rate to profits.
E. the frequency with which the exchange rate changes.
34. Hedging one commodity by using a futures contract on another commodity is called
A. surrogate hedging.
B. cross hedging.
C. alternative hedging.
D. correlative hedging.
E. proxy hedging.
You are given the following information about a portfolio you are to manage. For the longterm you are bullish, but you think the market may fall over the next month.
35. If the anticipated market value materializes, what will be your expected loss on the
portfolio?
A. 14.29%
B. 16.67%
C. 15.43%
D. 8.57%
E. 6.42%
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Chapter 23 - Futures, Swaps, and Risk Management
36. What is the dollar value of your expected loss?
A. $142,900
B. $16,670
C. $85,700
D. $30,000
E. $64,200
37. For a 200-point drop in the S&P500, by how much does the value of the futures position
change?
A. $200,000
B. $50,000
C. $250,000
D. $500,000
E. $100,000
38. How many contracts should you buy or sell to hedge your position? Allow fractions of
contracts in your answer.
A. sell 1.714
B. buy 1.714
C. sell 4.236
D. buy 4.236
E. sell 11.235
39. You sold S&P 500 Index futures contract at a price of 950 and closed your position when
the index futures was 947, you incurred:
A. a loss of $1,500.
B. a gain of $1,500.
C. a loss of $750.
D. a gain of $750.
E. None of these is correct.
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Chapter 23 - Futures, Swaps, and Risk Management
40. You took a short position in three S&P 500 futures contracts at a price of 900 and closed
the position when the index futures was 885, you incurred:
A. a gain of $11,250.
B. a loss of $11,250.
C. a loss of $8,000.
D. a gain of $8,000.
E. None of these is correct.
41. Suppose that the risk-free rates in the United States and in the Canada are 3% and 5%,
respectively. The spot exchange rate between the dollar and the Canadian dollar (C$) is
$0.80/C$. What should the futures price of the C$ for a one-year contract be to prevent
arbitrage opportunities, ignoring transactions costs.
A. $1.00/ C$
B. $1.70/ C$
C. $0.88/ C$
D. $0.78/ C$
E. $1.22/ C$
42. Suppose that the risk-free rates in the United States and in the Canada are 5% and 3%,
respectively. The spot exchange rate between the dollar and the Canadian dollar (C$) is
$0.80/C$. What should the futures price of the C$ for a one-year contract be to prevent
arbitrage opportunities, ignoring transactions costs.
A. $1.00/ C$
B. $0.82/ C$
C. $0.88/ C$
D. $0.78/ C$
E. $1.22/ C$
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Chapter 23 - Futures, Swaps, and Risk Management
43. Suppose that the risk-free rates in the United States and in the United Kingdom are 6%
and 4%, respectively. The spot exchange rate between the dollar and the pound is $1.60/BP.
What should the futures price of the pound for a one-year contract be to prevent arbitrage
opportunities, ignoring transactions costs.
A. $1.60/BP
B. $1.70/BP
C. $1.66/Bp
D. $1.63/BP
E. $1.57/BP
You are given the following information about a portfolio you are to manage. For the longterm you are bullish, but you think the market may fall over the next month.
44. If the anticipated market value materializes, what will be your expected loss on the
portfolio?
A. 7.58%
B. 6.52%
C. 15.43%
D. 8.57%
E. 6.42%
45. What is the dollar value of your expected loss?
A. $142,900
B. $65,200
C. $85,700
D. $30,000
E. $64,200
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Chapter 23 - Futures, Swaps, and Risk Management
46. For a 75-point drop in the S&P500, by how much does the futures position change?
A. $200,000
B. $50,000
C. $250,000
D. $500,000
E. $18,750
47. How many contracts should you buy or sell to hedge your position? Allow fractions of
contracts in your answer.
A. sell 3.477
B. buy 3.477
C. sell 4.236
D. buy 4.236
E. sell 11.235
48. Covered interest arbitrage ____________.
A. ensures that currency futures prices are set correctly
B. ensures that commodity futures prices are set correctly
C. ensures that interest rate futures prices are set correctly
D. ensures that currency futures prices are set correctly and ensures that commodity futures
prices are set correctly
E. None of these is correct.
49. A hedge ratio can be computed as ____________.
A. profit derived from one futures position for a given change in the exchange rate divided by
the change in value of the unprotected position for the same exchange rate
B. the change in value of the unprotected position for a given change in the exchange rate
divided by the profit derived from one futures position for the same exchange rate
C. profit derived from one futures position for a given change in the exchange rate plus the
change in value of the unprotected position for the same exchange rate
D. the change in value of the unprotected position for a given change in the exchange rate
plus by the profit derived from one futures position for the same exchange rate
E. None of these is correct.
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Chapter 23 - Futures, Swaps, and Risk Management
50. E-Minis typically have a value of ____________ percent of the standard contract and exist
for ____________.
A. 50; individual stocks and commodities
B. 50; stock indexes and foreign currencies
C. 40; stock indexes and commodities
D. 20; individual stocks and commodities
E. 20; stock indexes and foreign currencies
51. The most common short term interest rate used in the swap market is
A. the U.S. discount rate.
B. the U.S. prime rate.
C. the U.S. fed funds rate.
D. LIBOR.
E. None of these is correct.
52. If interest rate parity holds,
A. covered interest arbitrage opportunities will exist.
B. covered interest arbitrage opportunities will not exist.
C. arbitragers will be able to make risk-free profits.
D. covered interest arbitrage opportunities will exist and arbitragers will be able to make riskfree profits.
E. covered interest arbitrage opportunities will not exist and arbitragers will be able to make
risk-free profits.
53. If interest rate parity does not hold,
A. covered interest arbitrage opportunities will exist.
B. covered interest arbitrage opportunities will not exist.
C. arbitragers will be able to make risk-free profits.
D. covered interest arbitrage opportunities will exist and arbitragers will be able to make riskfree profits.
E. covered interest arbitrage opportunities will not exist and arbitragers will be able to make
risk-free profits.
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Chapter 23 - Futures, Swaps, and Risk Management
54. If covered interest arbitrage opportunities do not exist,
A. interest rate parity does not hold.
B. interest rate parity holds.
C. arbitragers will be able to make risk-free profits.
D. interest rate parity does not hold and arbitragers will be able to make risk-free profits.
E. interest rate parity holds and arbitragers will be able to make risk-free profits.
55. If covered interest arbitrage opportunities exist,
A. interest rate parity does not hold.
B. interest rate parity holds.
C. arbitragers will be able to make risk-free profits.
D. interest rate parity does not hold and arbitragers will be able to make risk-free profits.
E. interest rate parity holds and arbitragers will be able to make risk-free profits.
Short Answer Questions
56. Why are commodity futures prices different from other futures prices? Explain the
difference and give an example of a commodity and the factors involved.
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Chapter 23 - Futures, Swaps, and Risk Management
57. Suppose that the risk-free rate is 4% and the market risk premium is 6%. You are
interested in a cocoa futures contract. The beta of cocoa is −0.291.
- What is the required annual rate of return on the cocoa contract?
- You plan to hold the contract for three months, then take delivery of the cocoa. At that time,
you expect the spot price of cocoa to be $900 per ton. What is the present value of this threemonth deferred claim?
What would the proper price be for this contract?
58. Explain how a firm that has issued $1 million of long-term bonds with a fixed 6% interest
rate can convert its fixed-rate debt into floating-rate debt. Give two numerical examples that
show the possible outcomes, one favorable and one unfavorable.
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Chapter 23 - Futures, Swaps, and Risk Management
Chapter 23 Futures, Swaps, and Risk Management Answer Key
Multiple Choice Questions
1. Which one of the following stock index futures has a multiplier of $250 times the index
value?
A. Russell 2000
B. S&P 500 Index
C. Nikkei
D. DAX-30
E. NASDAQ 100
The multiplier is used to calculate contract settlements. See Table 23.1.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
2. Which one of the following stock index futures has a multiplier of $10 times the index
value?
A. Russell 2000
B. Dow Jones Industrial Average
C. Nikkei
D. DAX-30
E. NASDAQ 100
The multiplier is used to calculate contract settlements. See Table 23.1.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-18
Chapter 23 - Futures, Swaps, and Risk Management
3. Which one of the following stock index futures has a multiplier of $100 times the index
value?
A. Russell 2000
B. FTSE 100
C. Nikkei
D. NASDAQ 100
E. Russell 2000 and NASDAQ 100
The multiplier is used to calculate contract settlements. See Table 23.1.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
4. Which one of the following stock index futures has a multiplier of $100 times the index
value?
A. Russell 2000
B. FTSE 100
C. S&P Mid-Cap
D. DAX-30
E. Russell 2000 and S&P Mid-Cap
The multiplier is used to calculate contract settlements. See Table 23.1.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-19
Chapter 23 - Futures, Swaps, and Risk Management
5. Which one of the following stock index futures has a multiplier of $100 times the index
value?
A. CAC 40
B. S&P 500 Index
C. Nikkei
D. DAX-30
E. NASDAQ 100
The multiplier is used to calculate contract settlements. See Table 23.1.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
6. Which one of the following stock index futures has a multiplier of 10 euros times the
index?
A. CAC 40
B. DJ Euro Stoxx - 50
C. Nikkei
D. DAX-30
E. CAC 40 and DJ Euro Stoxx - 50
The multiplier is used to calculate contract settlements. See Table 23.1.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-20
Chapter 23 - Futures, Swaps, and Risk Management
7. Which one of the following stock index futures has a multiplier of 10 euros times the
index?
A. FTSE 100
B. DJ Euro Stoxx - 50
C. Nikkei
D. DAX-30
E. FTSE 100 and DJ Euro Stoxx - 50
The multiplier is used to calculate contract settlements. See Table 23.1.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
8. Which one of the following stock index futures has a multiplier of 25 euros times the
index?
A. FTSE 100
B. DJ Euro Stoxx - 50
C. Nikkei
D. DAX-30
E. FTSE 100 and DJ Euro Stoxx - 50
The multiplier is used to calculate contract settlements. See Table 23.1.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-21
Chapter 23 - Futures, Swaps, and Risk Management
9. You purchased one S&P 500 Index futures contract at a price of 950 and closed your
position when the index futures was 947, you incurred:
A. a loss of $1,500.
B. a gain of $1,500.
C. a loss of $750.
D. a gain of $750.
E. None of these is correct.
(−$950 + $947) × 250 = −$750.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
10. You took a short position in two S&P 500 futures contracts at a price of 910 and closed
the position when the index futures was 892, you incurred:
A. a gain of $9,000.
B. a loss of $9,000.
C. a loss of $18,000.
D. a gain of $18,000.
E. None of these is correct.
($910 − $892) × 250 × 2 = $9,000.
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Topic: Risk management
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Chapter 23 - Futures, Swaps, and Risk Management
11. If a stock index futures contract is overpriced, you would exploit this situation by:
A. selling both the stock index futures and the stocks in the index.
B. selling the stock index futures and simultaneously buying the stocks in the index.
C. buying both the stock index futures and the stocks in the index.
D. buying the stock index futures and selling the stocks in the index.
E. None of these is correct.
If one perceives one asset to be overpriced relative to another asset, one sells the overpriced
asset and buys the other one.
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Risk management
12. Foreign Exchange Futures markets are __________ and the Foreign Exchange Forward
markets are __________.
A. informal; formal
B. formal; formal
C. formal; informal
D. informal; informal
E. organized; unorganized
The forward market in foreign exchange is a network of banks and brokers allowing
customers to enter forward contracts to purchase or sell currency in the future at a currently
agreed upon rate of exchange. The currency futures markets are formal markets established by
the Chicago Mercantile Exchange where contracts are standardized as to size and daily
marking to market is observed. A clearinghouse is also involved.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-23
Chapter 23 - Futures, Swaps, and Risk Management
13. Suppose that the risk-free rates in the United States and in the United Kingdom are 4%
and 6%, respectively. The spot exchange rate between the dollar and the pound is $1.60/BP.
What should the futures price of the pound for a one-year contract be to prevent arbitrage
opportunities, ignoring transactions costs?
A. $1.60/BP
B. $1.70/BP
C. $1.66/BP
D. $1.63/BP
E. $1.57/BP
$1.60(1.04/1.06) = $1.57/BP.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
14. Suppose that the risk-free rates in the United States and in the United Kingdom are 5%
and 4%, respectively. The spot exchange rate between the dollar and the pound is $1.80/BP.
What should the futures price of the pound for a one-year contract be to prevent arbitrage
opportunities, ignoring transactions costs?
A. $1.62/BP
B. $1.72/BP
C. $1.82/BP
D. $1.92/BP
E. None of these is correct
$1.80(1.05/1.04) = $1.82/BP.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
23-24
Chapter 23 - Futures, Swaps, and Risk Management
15. Suppose that the risk-free rates in the United States and in Japan are 5.25% and 4.5%,
respectively. The spot exchange rate between the dollar and the yen is $0.008828/yen. What
should the futures price of the yen for a one-year contract be to prevent arbitrage
opportunities, ignoring transactions costs?
A. $0.009999/yen
B. $0.009981/yen
C. $0.008981/yen
D. $0.008891/yen
E. None of these is correct
$0.008828 (1.0525/1.045) = $0.008891/yen.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
16. Let RUS be the annual risk free rate in the United States, RUK be the risk free rate in the
United Kingdom, F be the futures price of $/BP for a 1-year contract, and E the spot exchange
rate of $/BP. Which one of the following is true?
A. if RUS > RUK, then E > F
B. if RUS < RUK, then E < F
C. if RUS > RUK, then E < F
D. if RUS < RUK, then F = E
E. There is no consistent relationship that can be predicted.
If RUS > RUK, then (1 + RUS)/(1 + RUK) > 1 and E < F.
AACSB: Analytic
Bloom's: Understand
Difficulty: Challenge
Topic: Risk management
23-25
Chapter 23 - Futures, Swaps, and Risk Management
17. Let RUS be the annual risk free rate in the United States, RJ be the risk free rate in Japan, F
be the futures price of $/yen for a 1-year contract, and E the spot exchange rate of $/yen.
Which one of the following is true?
A. if RUS > RJ, then E < F
B. if RUS < RJ, then E < F
C. if RUS > RJ, then E > F
D. if RUS < RJ, then F = E
E. There is no consistent relationship that can be predicted.
If RUS > RJ, then (1 + RUS)/(1 + RJ) > 1 and E < F.
AACSB: Analytic
Bloom's: Understand
Difficulty: Challenge
Topic: Risk management
Consider the following:
18. What should be the proper futures price for a 1-year contract?
A. 1.703 A$/$
B. 1.654 A$/$
C. 1.638 A$/$
D. 1.778 A$/$
E. 1.686 A$/$
1.03/1.04(1.67 A$/$) = 1.654 A$/$.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
23-26
Chapter 23 - Futures, Swaps, and Risk Management
19. If the futures market price is 1.63 A$/$, how could you arbitrage?
A. Borrow Australian Dollars in Australia, convert them to dollars, lend the proceeds in the
United States and enter futures positions to purchase Australian Dollars at the current futures
price.
B. Borrow U. S dollars in the United States, convert them to Australian Dollars, lend the
proceeds in Australia and enter futures positions to sell Australian Dollars at the current
futures price.
C. Borrow U. S. dollars in the United States and invest them in the U. S. and enter futures
positions to purchase Australian Dollars at the current futures price.
D. Borrow Australian Dollars in Australia and invest them there, then convert back to U. S.
dollars at the spot price.
E. There is no arbitrage opportunity.
E0(1 + rUS) − FO(1 + rA); use the U. S. $values for the currency: 0.5988(1.04) −
0.6135(1.03) = −0.009153; when relationship is negative, action b will result in arbitrage
profits.
AACSB: Analytic
Bloom's: Understand
Difficulty: Challenge
Topic: Risk management
23-27
Chapter 23 - Futures, Swaps, and Risk Management
20. If the market futures price is 1.69 A$/$, how could you arbitrage?
A. Borrow Australian Dollars in Australia, convert them to dollars, lend the proceeds in the
United States and enter futures positions to purchase Australian Dollars at the current futures
price.
B. Borrow U. S. dollars in the United States, convert them to Australian Dollars, lend the
proceeds in Australia and enter futures positions to sell Australian Dollars at the current
futures price.
C. Borrow U. S. dollars in the United States and invest them in the U. S. and enter futures
positions to purchase Australian Dollars at the current futures price.
D. Borrow Australian Dollars in Australia and invest them there, then convert back to U. S.
dollars at the spot price.
E. There is no arbitrage opportunity.
0.5988(1.04) − 0.5917(1.03) = 0.013301; when this relationship is positive; action a will result
in arbitrage profits.
AACSB: Analytic
Bloom's: Understand
Difficulty: Challenge
Topic: Risk management
23-28
Chapter 23 - Futures, Swaps, and Risk Management
21. Assume the current market futures price is 1.66 A$/$. You borrow 167,000 A$ and
convert the proceeds to U. S. dollars and invest them in the U. S at the risk-free rate. You
simultaneously enter a contract to purchase 170,340 A$ at the current futures prices (maturity
of 1 year). What would be your profit (loss)?
A. Profit of 630 A$
B. Loss of 2300 A$
C. Profit of 2300 A$
D. Loss of 630 A$
E. None of these is correct
[A$167,000 / 1.67 × 1.04 × 1.66] − (A$167,000 × 1.03) = A$630.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Risk management
22. Which of the following is/are example(s) of interest rate futures contracts?
A. Corporate bonds.
B. Treasury bonds.
C. Eurodollars.
D. Treasury bonds and Eurodollars
E. Corporate bonds and Treasury bonds
Interest rate futures are traded on Treasury bonds and Eurodollars. Examples that use these
contracts to hedge are given in the textbook.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-29
Chapter 23 - Futures, Swaps, and Risk Management
23. You hold a $50 million portfolio of par value bonds with a coupon rate of 10 percent paid
annually and 15 years to maturity. How many T-bond futures contracts do you need to hedge
the portfolio against an unanticipated change in the interest rate of 0.18%? Assume the market
interest rate is 10 percent and that T-bond futures contracts call for delivery of an 8 percent
coupon (paid annually), 20-year maturity T-bond.
A. 398 contracts long
B. 524 contracts short
C. 1048 contracts short
D. 398 contracts short
E. None of these is correct
0.9864485 × $50 M = $49,322,425; $50,000,000 − $49,322,425 = $677,575 loss on bonds;
$100.00 − $82.97 = $17.03 × 100 = $1703 gain on futures; $677,575/$1,703 = 398 contracts
short.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Risk management
24. A swap
A. obligates two counterparties to exchange cash flows at one or more future dates.
B. allows participants to restructure their balance sheets.
C. allows a firm to convert outstanding fixed rate debt to floating rate debt.
D. obligates two counterparties to exchange cash flows at one or more future dates and allows
participants to restructure their balance sheets.
E. obligates two counterparties to exchange cash flows at one or more future dates, allows
participants to restructure their balance sheets, and allows a firm to convert outstanding fixed
rate debt to floating rate debt.
A firm can enter into agreement to pay a floating rate and receive a fixed rate. Swaps involve
an exchange of cash flows rather than securities.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-30
Chapter 23 - Futures, Swaps, and Risk Management
25. Credit risk in the swap market
A. is extensive.
B. is limited to the difference between the values of the fixed rate and floating rate
obligations.
C. is equal to the total value of the payments that the floating rate payer was obligated to
make.
D. is extensive and is equal to the total value of the payments that the floating rate payer was
obligated to make.
E. None of these is correct.
Swaps obligate two counterparties to exchange cash flows at one or more future dates. Swaps
allow firms to restructure balance sheets, and the firm is obligated only for the difference
between the fixed and floating rates.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
26. Trading in stock index futures
A. now exceeds buying and selling of shares in most markets.
B. reduces transactions costs as compared to trading in stocks.
C. increases leverage as compared to trading in stocks.
D. generally results in faster execution than trading in stocks.
E. All of these are correct.
Trading in stock index futures now exceeds buying and selling of shares in most markets,
reduces transactions costs as compared to trading in stocks, increases leverage as compared to
trading in stocks, and generally results in faster execution than trading in stocks.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
23-31
Chapter 23 - Futures, Swaps, and Risk Management
27. Commodity futures pricing
A. must be related to spot prices.
B. includes cost of carry.
C. converges to spot prices at maturity.
D. All of these are correct.
E. None of these is correct.
Commodity futures are similar to other types of futures contracts but the cost of carrying must
be considered. The cost of carrying includes interest costs, storage costs, and allowance for
spoilage.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
28. Arbitrage proofs in futures market pricing relationships
A. rely on the CAPM.
B. demonstrate how investors can exploit misalignments.
C. incorporate transactions costs.
D. All of these are correct.
E. None of these is correct.
No-arbitrage relationships are stronger than arguments such as the CAPM, but may be less
precise if transactions or storage costs are not known.
AACSB: Analytic
Bloom's: Remember
Difficulty: Challenge
Topic: Risk management
23-32
Chapter 23 - Futures, Swaps, and Risk Management
29. One reason swaps are desirable is that
A. they are free of credit risk.
B. they have no transactions costs.
C. they increase interest rate volatility.
D. they increase interest rate risk.
E. they offer participants easy ways to restructure their balance sheets.
For example, a firm can change a floating-rate obligation into a fixed-rate obligation and vice
versa.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
30. Which two indices had the lowest correlation between them during the 2001-2006
period?
A. S&P and DJIA; the correlation was 0.957
B. S&P and NASDAQ; the correlation was 0.899
C. DJIA and Russell 2000 the correlation was 0.758
D. S&P and NYSE; the correlation was 0.973
E. NYSE and DJIA; the correlation was 0.931
The correlations are shown in Table 23.2.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-33
Chapter 23 - Futures, Swaps, and Risk Management
31. Which two indices had the highest correlation between them during the 2001-2006
period?
A. S&P and DJIA; the correlation was 0.957
B. S&P and Russell 2000 the correlation was 0.899
C. DJIA and Russell 2000 the correlation was 0.758
D. S&P and NYSE; the correlation was 0.973
E. NYSE and DJIA; the correlation was 0.931
The correlations are shown in Table 23.2.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
32. The value of a futures contract for storable commodities can be determined by the
_______ and the model __________ consistent with parity relationships.
A. CAPM, will be
B. CAPM, will not be
C. APT, will not be
D. APT, will be
E. CAPM and APT; will be
Both the CAPM and the APT can be used for this purpose and both will be consistent with
parity relationships.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
23-34
Chapter 23 - Futures, Swaps, and Risk Management
33. In the equation Profits = a + b*($/₤ exchange rate), b is a measure of
A. the firm's beta when measured in terms of the foreign currency.
B. the ratio of the firm's beta in terms of dollars to the firm's beta in terms of pounds.
C. the sensitivity of profits to the exchange rate.
D. the sensitivity of the exchange rate to profits.
E. the frequency with which the exchange rate changes.
The slope of a line that plots profits vs. exchange rates gives the average amount by which
profits will change for each unit change in the exchange rate.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
34. Hedging one commodity by using a futures contract on another commodity is called
A. surrogate hedging.
B. cross hedging.
C. alternative hedging.
D. correlative hedging.
E. proxy hedging.
Cross-hedging is used in some cases because no futures contract exists for the item you want
to hedge. The two commodities should be highly correlated.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
You are given the following information about a portfolio you are to manage. For the longterm you are bullish, but you think the market may fall over the next month.
23-35
Chapter 23 - Futures, Swaps, and Risk Management
35. If the anticipated market value materializes, what will be your expected loss on the
portfolio?
A. 14.29%
B. 16.67%
C. 15.43%
D. 8.57%
E. 6.42%
The change would represent a drop of (1200 − 1400)/1400 = 14.3% in the index. Given the
portfolio's beta, your portfolio would be expected to lose 0.6*14.3% = 8.57%
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
36. What is the dollar value of your expected loss?
A. $142,900
B. $16,670
C. $85,700
D. $30,000
E. $64,200
The dollar value equals the loss of 8.57% times the $1 million portfolio value = $85,700.
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Topic: Risk management
23-36
Chapter 23 - Futures, Swaps, and Risk Management
37. For a 200-point drop in the S&P500, by how much does the value of the futures position
change?
A. $200,000
B. $50,000
C. $250,000
D. $500,000
E. $100,000
The change is 200 points times the $250 multiplier, which equals $50,000.
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Topic: Risk management
38. How many contracts should you buy or sell to hedge your position? Allow fractions of
contracts in your answer.
A. sell 1.714
B. buy 1.714
C. sell 4.236
D. buy 4.236
E. sell 11.235
The number of contracts equals the hedge ratio = Change in portfolio value / Profit on one
futures contract = $85,700/$50,000 = 1.714. You should sell the contract because as the
market falls the value of the futures contract will rise and will offset the decline in the
portfolio's value.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
23-37
Chapter 23 - Futures, Swaps, and Risk Management
39. You sold S&P 500 Index futures contract at a price of 950 and closed your position when
the index futures was 947, you incurred:
A. a loss of $1,500.
B. a gain of $1,500.
C. a loss of $750.
D. a gain of $750.
E. None of these is correct.
($950 − $947) = $3 × 250 = $750.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
40. You took a short position in three S&P 500 futures contracts at a price of 900 and closed
the position when the index futures was 885, you incurred:
A. a gain of $11,250.
B. a loss of $11,250.
C. a loss of $8,000.
D. a gain of $8,000.
E. None of these is correct.
($900 − $885) = $15 × 250 × 3 = $11,250.
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Topic: Risk management
23-38
Chapter 23 - Futures, Swaps, and Risk Management
41. Suppose that the risk-free rates in the United States and in the Canada are 3% and 5%,
respectively. The spot exchange rate between the dollar and the Canadian dollar (C$) is
$0.80/C$. What should the futures price of the C$ for a one-year contract be to prevent
arbitrage opportunities, ignoring transactions costs.
A. $1.00/ C$
B. $1.70/ C$
C. $0.88/ C$
D. $0.78/ C$
E. $1.22/ C$
$0.80(1.03/1.05) = $0.78/ C$.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
42. Suppose that the risk-free rates in the United States and in the Canada are 5% and 3%,
respectively. The spot exchange rate between the dollar and the Canadian dollar (C$) is
$0.80/C$. What should the futures price of the C$ for a one-year contract be to prevent
arbitrage opportunities, ignoring transactions costs.
A. $1.00/ C$
B. $0.82/ C$
C. $0.88/ C$
D. $0.78/ C$
E. $1.22/ C$
$0.80(1.05/1.03) = $0.82/ C$.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
23-39
Chapter 23 - Futures, Swaps, and Risk Management
43. Suppose that the risk-free rates in the United States and in the United Kingdom are 6%
and 4%, respectively. The spot exchange rate between the dollar and the pound is $1.60/BP.
What should the futures price of the pound for a one-year contract be to prevent arbitrage
opportunities, ignoring transactions costs.
A. $1.60/BP
B. $1.70/BP
C. $1.66/Bp
D. $1.63/BP
E. $1.57/BP
$1.60(1.06/1.04) = $1.63/BP.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
You are given the following information about a portfolio you are to manage. For the longterm you are bullish, but you think the market may fall over the next month.
44. If the anticipated market value materializes, what will be your expected loss on the
portfolio?
A. 7.58%
B. 6.52%
C. 15.43%
D. 8.57%
E. 6.42%
The change would represent a drop of (915-990)/990=7.58% in the index. Given the
portfolio's beta, your portfolio would be expected to lose 0.86*7.58%=6.52%
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
23-40
Chapter 23 - Futures, Swaps, and Risk Management
45. What is the dollar value of your expected loss?
A. $142,900
B. $65,200
C. $85,700
D. $30,000
E. $64,200
The dollar value equals the loss of 6.52% times the $1 million portfolio value = $65,200.
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Topic: Risk management
46. For a 75-point drop in the S&P500, by how much does the futures position change?
A. $200,000
B. $50,000
C. $250,000
D. $500,000
E. $18,750
The change is 75 points times the $250 multiplier, which equals $18,750.
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Topic: Risk management
23-41
Chapter 23 - Futures, Swaps, and Risk Management
47. How many contracts should you buy or sell to hedge your position? Allow fractions of
contracts in your answer.
A. sell 3.477
B. buy 3.477
C. sell 4.236
D. buy 4.236
E. sell 11.235
The number of contracts equals the hedge ratio = Change in portfolio value / Profit on one
futures contract = $65,200/$18,750 = 3.477. You should sell the contract because as the
market falls the value of the futures contract will rise and will offset the decline in the
portfolio's value.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Risk management
48. Covered interest arbitrage ____________.
A. ensures that currency futures prices are set correctly
B. ensures that commodity futures prices are set correctly
C. ensures that interest rate futures prices are set correctly
D. ensures that currency futures prices are set correctly and ensures that commodity futures
prices are set correctly
E. None of these is correct
Covered interest arbitrage ensures that currency futures prices are set correctly.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-42
Chapter 23 - Futures, Swaps, and Risk Management
49. A hedge ratio can be computed as ____________.
A. profit derived from one futures position for a given change in the exchange rate divided by
the change in value of the unprotected position for the same exchange rate
B. the change in value of the unprotected position for a given change in the exchange rate
divided by the profit derived from one futures position for the same exchange rate
C. profit derived from one futures position for a given change in the exchange rate plus the
change in value of the unprotected position for the same exchange rate
D. the change in value of the unprotected position for a given change in the exchange rate
plus by the profit derived from one futures position for the same exchange rate
E. None of these is correct
A hedge ratio can be computed as the change in value of the unprotected position for a given
change in the exchange rate divided by the profit derived from one futures position for the
same exchange rate.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
50. E-Minis typically have a value of ____________ percent of the standard contract and exist
for ____________.
A. 50; individual stocks and commodities
B. 50; stock indexes and foreign currencies
C. 40; stock indexes and commodities
D. 20; individual stocks and commodities
E. 20; stock indexes and foreign currencies
E-Minis typically have a value of 20 percent of the standard contract and exist for stock
indexes and foreign currencies.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
23-43
Chapter 23 - Futures, Swaps, and Risk Management
51. The most common short term interest rate used in the swap market is
A. the U.S. discount rate
B. the U.S. prime rate
C. the U.S. fed funds rate
D. LIBOR
E. None of these is correct
None of the listed answers are common short term interest rates used in the swap market.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Risk management
52. If interest rate parity holds
A. covered interest arbitrage opportunities will exist
B. covered interest arbitrage opportunities will not exist
C. arbitragers will be able to make risk-free profits
D. covered interest arbitrage opportunities will exist and arbitragers will be able to make riskfree profits
E. covered interest arbitrage opportunities will not exist and arbitragers will be able to make
risk-free profits
If interest rate parity holds covered interest arbitrage opportunities will not exist.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
23-44
Chapter 23 - Futures, Swaps, and Risk Management
53. If interest rate parity does not hold
A. covered interest arbitrage opportunities will exist
B. covered interest arbitrage opportunities will not exist
C. arbitragers will be able to make risk-free profits
D. covered interest arbitrage opportunities will exist and arbitragers will be able to make riskfree profits
E. covered interest arbitrage opportunities will not exist and arbitragers will be able to make
risk-free profits
If interest rate parity holds covered interest arbitrage opportunities will not exist.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
54. If covered interest arbitrage opportunities do not exist
A. interest rate parity does not hold
B. interest rate parity holds
C. arbitragers will be able to make risk-free profits
D. interest rate parity does not hold and arbitragers will be able to make risk-free profits
E. interest rate parity holds and arbitragers will be able to make risk-free profits
If interest rate parity holds covered interest arbitrage opportunities will not exist.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
23-45
Chapter 23 - Futures, Swaps, and Risk Management
55. If covered interest arbitrage opportunities exist
A. interest rate parity does not hold
B. interest rate parity holds
C. arbitragers will be able to make risk-free profits
D. interest rate parity does not hold and arbitragers will be able to make risk-free profits
E. interest rate parity holds and arbitragers will be able to make risk-free profits
If interest rate parity holds covered interest arbitrage opportunities will not exist.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Risk management
Short Answer Questions
56. Why are commodity futures prices different from other futures prices? Explain the
difference and give an example of a commodity and the factors involved.
The price of a futures contract for a commodity that must be stored is given by F0 = P0*(1 + rf
+ c), where P0 is the spot price of the commodity, rf is the risk-free rate that applies to the
opportunity cost of holding the commodity, and c is the carrying cost.
Commodity futures have an extra cost integrated into their price—carrying costs can be
significant. Carrying costs can include interest costs, storage costs, insurance costs, and an
allowance for spoilage of goods in storage. These costs should be considered on a net basis:
costs minus the benefits of carrying the commodity, such as protection against running out of
stock.
An example is a contract on corn. If the producer doesn't sell the corn now, it will need to be
stored for future delivery. There will be explicit costs like insurance and the marginal cost of
silo usage, including the resources used to keep the corn at its proper moisture level. There
may be some spoilage of the corn. An implicit cost is the opportunity cost of not investing the
funds that would have been earned if the corn had been sold in the spot market.
Feedback: This question tests whether the student recognizes the important difference in
commodities contracts due to carrying costs.
AACSB: Reflective Thinking
Bloom's: Understand
Difficulty: Intermediate
Topic: Risk management
23-46
Chapter 23 - Futures, Swaps, and Risk Management
57. Suppose that the risk-free rate is 4% and the market risk premium is 6%. You are
interested in a cocoa futures contract. The beta of cocoa is −0.291.
- What is the required annual rate of return on the cocoa contract?
- You plan to hold the contract for three months, then take delivery of the cocoa. At that time
you expect the spot price of cocoa to be $900 per ton. What is the present value of this threemonth deferred claim?
What would the proper price be for this contract?
The required rate of return is given by the CAPM. E(r) = 4%+ (−.291)*6% = 2.254%.
The present value of the deferred claim is $900/(1.02254)0.25 = $895.
The proper price for the contract would be determined by setting the present value of the
commitment to pay F0 dollars in three months to $895. F0/(1.04)0.25 = $895. F0 = $903.82.
Feedback: This question gives the student a chance to apply the CAPM to a storable
commodity and to recognize the present value relationships that must hold.
AACSB: Reflective Thinking
Bloom's: Apply
Difficulty: Challenge
Topic: Risk management
58. Explain how a firm that has issued $1 million of long-term bonds with a fixed 6% interest
rate can convert its fixed-rate debt into floating-rate debt. Give two numerical examples that
show the possible outcomes, one favorable and one unfavorable.
The firm can enter a swap arrangement, committing to pay .06*$1 million = $60,000 in
exchange for receiving payments equal to $1 million times the LIBOR rate. If the LIBOR rate
is 5, the cash inflow would be $1 million*.05 = $50,000. The net cash flow would be $10,000
in this case, which is unfavorable. If the LIBOR rate is 8%, the firm will have a cash inflow of
$1 million*.08 = $80,000. The net cash flow in this case is $20,000, which is favorable.
Feedback: This is a basic question about the mechanics of a swap agreement.
AACSB: Reflective Thinking
Bloom's: Understand
Difficulty: Basic
Topic: Risk management
23-47