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Fundamentals of Derivatives Markets (McDonald)
Chapter 6 The Wide World of Futures Contracts
6.1 Multiple Choice Questions
1) Interest rates on the U.S. dollar are 5.4% and euro rates are 4.6%. Given a dollar per euro
spot rate of 0.918, what is the 6–month forward rate ($/E)?
A) 0.912
B) 0.917
C) 0.922
D) 0.934
2) Interest rates on the U.S. dollar are 6.5% and euro rates are 5.5%. The dollar per euro spot
rate is 0.950. What is the arbitrage profit on a required $1 million Euro payment if the
forward rate is 0.980 dollars per Euro and the exchange occurs in one year?
A) $10,000
B) $21,000
C) $28,000
D) $34,000
3) An investor wants to hold 200 euro two years from today. The spot exchange rate is $1.31
per euro. If the euro denominated annual interest rate is 3.0% what is the price of a currency
prepaid forward?
A) $200
B) $206
C) $231
D) $247
4) The current currency spot rate is $1.31 per euro. If dollar denominated interest rates are 3.0%
and euro denominated interest rates are 4.0%, what is the likely dollar per euro exchange
rate for a 2–year forward contract?
A) $1.28
B) $1.30
C) $1.31
D) $1.33
When answering the questions below, refer to the following table of commodity forward and spot prices.
The annual risk free interest rate is 4.0%.
Expiration Pork Bellies Corn Soybeans
Time cents/pound cents/bushel cents/bushel
Today=spot 540 212 430
6 months 560 208 440
12 months 590 203 452
18 months 625 200 445
24 months 655 195 437
5) What is the approximate annualized lease rate on the 12–month corn forward contract?
A) 0.00%
B) 2.25%
C) 4.50%
D) 8.25%
6) What is the approximate annualized lease rate on the 18–month soybean forward contract?
A) 0.69%
B) 1.21%
C) 1.69%
D) 2.31%
7) If hog farmers expect a return of 8.0% on their investment in livestock, what is the
approximate implied increase in pork belly commodity prices over the next 6 months?
A) 3.75%
B) 4.59%
C) 5.26%
D) 6.37%
8) Which of the following terms most accurately describes the forward curve for soybeans over
the next two years?
A) Contango
B) Backwardation
C) Contango and backwardation
D) None of the above
9) Given a lease rate of 7.0% on the 24–month corn forward contract, what is the approximate
potential arbitrage profit per contract?
A) 3.68 cents
B) 4.65 cents
C) 5.84 cents
D) 6.90 cents
10) The lease rate on the 6–month soybean contract is 0.35%. What is the implied annual storage
cost if the cost is continuously paid and proportional?
A) 1.0%
B) 2.0%
C) 3.0%
D) 4.0%
11) The spot price of gasoline is 106 cents per gallon and the annualized risk free interest rate is
4.0%. Given a lease rate of 1.0%, a continuously paid storage rate of 0.5%, and a convenience
yield of 0.75%, what is the no–arbitrage price range of a 1–year forward contract (in cents)?
A) 108.96 to 109.78
B) 107.42 to 108.96
C) 106.00 to 108.96
D) 107.42 to 109.78
12) Nine–month gold futures are trading for $306 per ounce. The spot price is $295 per ounce.
LIBOR during each of the upcoming 4 quarters is listed as 1.04%, 1.22%, 1.30%, and 1.35%,
respectively. Calculate the 9–month lease rate on the futures contract.
A) 2.4%
B) 2.1%
C) 1.3%
D) 0.0%
13) Forward prices for gold, in dollars per ounce, for the next five years are 305, 333, 360, 388,
and 425, respectively. A mine can be opened for 3 years at a cost of $600. Annual mining
costs are a constant $100 and interest rates are 5.0%. When should the mine be opened to
maximize NPV?
A) Year 1
B) Year 2
C) Year 3
D) Never
14) The 6–month futures price for oil is $21 per barrel (or 50 cents per gallon). The 6–month
futures prices for gasoline and heating oil are 80 cents and 69 cents, respectively. What is the
gross margin on a simple 3–2–1 crack spread?
A) $0.79
B) $0.65
C) $0.57
D) $0.42
15) The spot price of corn is $2.23 per bushel. The opportunity cost of capital for an investor is
0.5% per month. If storage costs of $0.04 per bushel per month are factored in, all else being
equal, what is the likely price of a 4–month forward contract?
A) $2.114
B) $2.124
C) $2.212
D) $2.231
16) The spot price of corn is $2.60 per bushel. The opportunity cost of capital for an investor is
0.6% per month. If storage costs of $0.03 per bushel per month are factored in, all else being
equal, what is the future value of storage costs over a 6–month period?
A) $0.1534
B) $0.1684
C) $0.1772
D) $0.1827
17) Oil is selling at a spot price of $42.00 per barrel. Oil can be stored at a cost of $0.42 per barrel
per month. The opportunity cost of capital is 7.2% per year (or 0.6% per month). What is the
gain or loss realized by an oil refinery that floats its exposure and purchases oil on the spot
market in 2 months at a price of $43.00 per barrel, instead of hedging with a forward
contract?
A) $0.35 gain
B) $0.35 loss
C) $1.00 gain
D) $1.00 loss
18) During one winter week, the city of Indianapolis had daily average Fahrenheit temperatures
of 55, 45, 38, 48, 35, 50, and 42 degrees. What is the HDD for this week?
A) 100
B) 122
C) 135
D) 142
19) During one fall week, the city of Indianapolis had daily average Fahrenheit temperatures of
85, 72, 65, 70, 76, 62, and 73 degrees. What is the CDD for this week?
A) 3
B) 35
C) 48
D) 51
20) If the December HDD contract for Chicago is quoted as 994, what is the implied average
HDD for the month of December?
A) 26
B) 32
C) 49
D) 65
21) Housing index and housing futures contracts attempt to track which of the following?
A) Change in value of repeat home sales
B) The value of home improvements
C) New home construction values
D) Value of homes sold in non arms–length transactions
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22) Which of the following is most likely to short a housing futures contract?
A) Home buyer
B) Renter
C) New home builder
D) Real estate broker
6.2
Short Answer Essay Questions
1) Explain how a negative correlation between agricultural production and commodity prices
creates a natural hedge.
2) Give one example of how price discovery functions in the commodity futures market.
3) Why is the cash–and–carry strategy employed in the financial futures market not readily
available in the commodity futures market?
4) What function does the convenience yield serve in setting forward prices and how does this
influence arbitrage opportunities?
5) Explain the steps necessary to take advantage of an arbitrage opportunity, which may exist
between the dollar and yen, when a future yen payment is required.
6.3
Class Discussion Question
1) A review of seasonality forward curves may lead students to adopt a technical analysis
mentality. Ask students to explain why such ideas may pop into their heads. Proceed to
inquire as to why the curves have the appearances they do. An actual numerical example
may be in order. If any still hold fast to their technical roots, insist that they show the profit
numerically after considering all storage and other costs.