Chapter 09 – Derivatives: Futures, Options, and Swaps
Chapter 9
Derivatives: Futures, Options, and Swaps
Conceptual and Analytical Problems
1. An agreement to lease a car can be thought of as a set of derivative contracts.
Describe them. (LO2)
Answer: When someone leases a car, he or she agrees to make a series of fixed
2. How is entering into a forward contract similar to barter? Can you think of costs
associated with forward contracts that are minimized or eliminated with futures
contracts? (LO2)
Answer: As in barter, when you engage in a forward contract, you must establish a
“double coincidence of wants;” that is, you must find someone who “has what you
3. In spring 2002, an electronically traded futures contract on the stock index, called an
E-mini future, was introduced. The contract was one-fifth the size of the standard
futures contract, and could be traded on the 24-hour CME Globex electronic trading
system. Why might someone introduce a futures contract with these properties?
(LO1)
Answer: The size of the contract allows small investors to purchase it. The fact that
4. A hedger buys a futures contract, taking a long position in the wheat futures market.
What are the hedger’s obligations under this contract? Describe the risk that is
hedged in this transaction and give an example of someone who might enter into such
an arrangement. (LO1)
Answer: The hedger has taken the long position, promising to purchase the wheat at a
fixed price on a future date. He is hedging against the risk that the price of wheat will
9-1
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
Chapter 09 – Derivatives: Futures, Options, and Swaps
5. A futures contract on a payment of $250 times the Standard and Poors’ 500 Index is
traded on the Chicago Mercantile Exchange. At an index level of $1,000 or more, the
contract calls for a payment of over $250,000. It is settled by a cash payment
between the buyer and the seller. Who are the hedgers and who are the speculators in
the S&P 500 futures market? (LO1)
Answer: Hedgers are investors who own funds composed of stocks from the S&P
6. Explain why trading derivatives on centralized exchanges rather than in
over-the-counter markets helps to reduce systemic risk. (LO1)
Answer: The presence of a centralized counterparty (CCP) increases transparency, as
The standardization of contracts traded through CCP also increases transparency
7. What are the risks and rewards of writing and buying options? Are there any
circumstances under which you would get involved? Why or why not? (Hint: Think
of a case in which you own shares of the stock on which you are considering writing
a call.) (LO3)
Answer: Because option buyers incur no obligations, their losses are limited to the
price paid for the option. Their potential gains, however, can be large. Sellers must
8. Suppose XYZ Corporation’s stock price rises or falls with equal probability by $20
each month, starting where it ended the previous month. What is the value of a
three-month at-the-money European call option on XYZ’s stock if the stock is priced
at $100 when the option is purchased? (LO3)
9-2
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
Chapter 09 – Derivatives: Futures, Options, and Swaps
Answer:
To calculate the time value of the option, list all the possible outcomes for the stock
Month 1 Month 2 Month 3 Total
+20 +20 +20 +60
+20 +20 -20 +20
Each of the outcomes is equally likely and so occurs 1/8 of the time. Focusing on the
first four where the price goes up,
Time Value of the Option=
15$20$*
8
3
60$*
8
1
Option price = intrinsic value + time value of the option = $0 +$15 = $15
9. *Why might a borrower who wishes to make fixed interest rate payments and who
has access to both fixed- and floating-rate loans still benefit from becoming a party to
a fixed-for-floating interest rate swap? (LO4)
Answer: If the company has a comparative advantage in borrowing in the floating
rate market, it can reduce its overall interest costs by borrowing at a floating interest
10. Concerned about possible disruptions of the supply of oil from the Middle East, the
chief financial officer (CFO) of American Airlines would like to hedge the risk of an
increase in the price of jet fuel. What tools could the CFO use to hedge this risk?
(LO3)
9-3
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
Chapter 09 – Derivatives: Futures, Options, and Swaps
Answer: The CFO could buy oil futures contracts, giving him or her a long position in
11. *How does the existence of derivatives markets enhance an economy’s ability to
grow? (LO1)
Answer: The existence of derivative markets increases the economy’s capacity to
carry risk by facilitating the transfer of risk to those best able to bear it. They allow
12. Credit-default swaps provide a means to insure against default risk and require the
posting of collateral by buyers and sellers. Explain how these “safe-sounding”
derivative products contributed to the 2007-2009 financial crisis? (LO4)
Answer: Credit default swaps (CDS) are traded over the counter and financial
institutions do not report their CDS purchases and sales. This contributed to a lack of
During the 2007-2009 crisis, AIG was a large player in the market for credit default
13. Of the following options, which would you expect to have the highest option price?
(LO3)
a. A European three-month put option on a stock whose market price is $90 where
the strike price is $100. The standard deviation of the stock price over the past
five years has been 15 percent.
b. A European three-month put option on a stock whose market price is $110 where
the strike price is $100. The standard deviation of the stock price over the past
five years has been 15 percent.
c. A European one-month put option on a stock whose market price is $90 where the
strike price is $100. The standard deviation of the stock price over the past five
years has been 15 percent.
Answer: Option Price = Intrinsic value + Time value of the option
9-4
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
Chapter 09 – Derivatives: Futures, Options, and Swaps
We know that a put option is in the money if the strike price is higher than the market
Looking at the time value of the option, all three options have the same standard
deviation.
Option A has a longer time to expiration than Option C, so with the same intrinsic
14. What kind of an option should you purchase if you anticipate selling $1 million of
Treasury bonds in one year’s time and wish to hedge against the risk of interest rates
rising? (LO3)
Answer: You could purchase a put option that gives you (as the holder) the right but
15. You sell a bond futures contract and, one day later, the clearinghouse informs you that
it had credited funds to your margin account. What happened to interest rates over
that day? (LO2)
Answer: Interest rates have risen. This reduced the price of the bonds and so as the
16. You are completely convinced that the price of copper is going to rise significantly
over the next year and want to take as large a position as you can in the market but
have limited funds. How could you use the futures market to leverage your position?
(LO2)
Answer: You should buy as many one-year copper futures contracts as you can afford.
This will depend on the margin payment required. As the margin payment is a
9-5
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
Chapter 09 – Derivatives: Futures, Options, and Swaps
17. Suppose you have $8,000 to invest and you follow the strategy you devised in
question 16 to leverage your exposure to the copper market. Copper is selling at $3 a
pound and the margin requirement for a futures contract for 25,000 pounds of copper
is $8,000. (LO2)
a. Calculate your return if copper prices rise to $3.10 a pound.
b. How does this compare with the return you would have made if you have
simply purchased $8000 worth of copper and sold it a year later?
c. Compare the risk involved in each of these strategies.
Answer:
a) With $8,000, you can afford to purchase one copper futures contract. At $3 a
pound, this is worth $75,000. The contract specifies that you will take delivery of
b) If you purchased copper directly at $3 a pound, you could have afforded 2,667
c) Speculating in the futures market can bring high returns (in this case returns
almost ten times as large), but, as usual, these high returns come at the cost of
18. * The table below shows the yields on the fixed and floating borrowing choices
available to three firms. Firms A and B want to be exposed to a floating interest rate
while Firm C would prefer to pay a fixed interest rate. Which pair(s) of firms (if any)
should borrow in the market they do not want and then enter into a fixed-for-floating
interest-rate swap. (LO4)
Fixed Rate Floating Rate
Firm A 7% LIBOR+50 bps
Firm B 12% LIBOR+150 bps
Firm C 10% LIBOR+150 bps
Note: LIBOR, which stands for the London Interbank Offered Rate, is a floating
interest rate.
9-6
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
Chapter 09 – Derivatives: Futures, Options, and Swaps
Answer: Possible pairs: A and C or B and C. (As A and B both want floating, they
won’t engage in a fixed-for-floating swap with each other.)
Next, look at who has the comparative advantage in which market.
A versus C:
A has a 3% advantage over C in the fixed rate market and a 1% advantage in the
B versus C:
19. Suppose you were the manager of a bank that raised most of its funds from short-term
variable-rate deposits and used these funds to make fixed-rate mortgage loans.
Should you be more concerned about rises or falls in short-term interest rates? How
could you use interest-rate swaps to hedge against the interest-rate risk you face?
(LO4)
Answer: Given that you make interest payments based on short-term interest rates and
You could hedge against this risk by entering into a fixed-for-floating interest rate
swap where you make payments based on a fixed interest rate and receive payments
20. *Basis swaps are swaps where, instead of one payment stream being based on a fixed
interest rate, both payment streams are based on different floating interest rates. Why
might anyone be interested in entering a floating-for-floating interest rate swap? (You
should assume that both payment flows are denominated in the same currency.)
(LO4)
Answer: In a basis swap, the two payment streams are referenced from different
9-7
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
Chapter 09 – Derivatives: Futures, Options, and Swaps
9-8
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.