Hull: Options, Futures, and Other Derivatives, Ninth Edition
Chapter 5: Determination of Forward and Futures Prices
Multiple Choice Test Bank: Questions with Answers
1. Which of the following is a consumption asset?
A. The S&P 500 index
B. The Canadian dollar
C. Copper
D. IBM stock
Answer: C
A, B, and D are investment assets (held by at least some investors purely for investment
purposes). C is a consumption asset.
2. An investor shorts 100 shares when the share price is $50 and closes out the position six months
later when the share price is $43. The shares pay a dividend of $3 per share during the six
months. How much does the investor gain?
A. $1,000
B. $400
C. $700
D. $300
Answer: B
The investor gains $7 per share because he or she sells at $50 and buys at $43. However, the
investor has to pay the $3 per share dividend. The net profit is therefore 7−3 or $4 per share.
100 shares are involved. The total gain is therefore $400.
3. The spot price of an investment asset that provides no income is $30 and the risk-free rate for all
maturities (with continuous compounding) is 10%. What is the three-year forward price?
A. $40.50
B. $22.22
C. $33.00
D. $33.16
Answer: A
The 3-year forward price is the spot price grossed up for 3 years at the risk-free rate. It is 30e0.1×3
=$40.50.
4. The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with
continuous compounding. The asset provides an income of $2 at the end of the first year and at
the end of the second year. What is the three-year forward price?
A. $19.67
B. $35.84
C. $45.15
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, Hull: Options, Futures, and Other Derivatives, Ninth Edition
Chapter 5: Determination of Forward and Futures Prices
Multiple Choice Test Bank: Questions with Answers
D. $40.50
Answer: B
The present value of the income is 2e-0.1×1+2e-0.1×2= $3.447. The three year forward price is
obtained by subtracting the present value of the income from the current stock price and then
grossing up the result for three years at the risk-free rate. It is (30−3.447)e0.1×3 = $35.84.
5. An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are
5% and 7% (both expressed with continuous compounding). What is the six-month forward rate?
A. 0.7070
B. 0.7177
C. 0.7249
D. 0.6930
Answer: D
The six-month forward rate is 0.7000e−(0.05−0.07)×0.5=0.6930.
6. Which of the following is true?
A. The convenience yield is always positive or zero.
B. The convenience yield is always positive for an investment asset.
C. The convenience yield is always negative for a consumption asset.
D. The convenience yield measures the average return earned by holding futures contracts.
Answer: A
The convenience yield measures the benefit of owning an asset rather than having a
forward/futures contract on an asset. For an investment asset it is always zero. For a
consumption asset it is greater than or equal to zero.
7. A short forward contract that was negotiated some time ago will expire in three months and has
a delivery price of $40. The current forward price for three-month forward contract is $42. The
three month risk-free interest rate (with continuous compounding) is 8%. What is the value of
the short forward contract?
A. +$2.00
B. −$2.00
C. +$1.96
D. −$1.96
Answer: D
The contract gives one the obligation to sell for $40 when a forward price negotiated today
would give one the obligation to sell for $42. The value of the contract is the present value of −
$2 or −2e-0.08×0.25 = −$1.96.
/
Chapter 5: Determination of Forward and Futures Prices
Multiple Choice Test Bank: Questions with Answers
1. Which of the following is a consumption asset?
A. The S&P 500 index
B. The Canadian dollar
C. Copper
D. IBM stock
Answer: C
A, B, and D are investment assets (held by at least some investors purely for investment
purposes). C is a consumption asset.
2. An investor shorts 100 shares when the share price is $50 and closes out the position six months
later when the share price is $43. The shares pay a dividend of $3 per share during the six
months. How much does the investor gain?
A. $1,000
B. $400
C. $700
D. $300
Answer: B
The investor gains $7 per share because he or she sells at $50 and buys at $43. However, the
investor has to pay the $3 per share dividend. The net profit is therefore 7−3 or $4 per share.
100 shares are involved. The total gain is therefore $400.
3. The spot price of an investment asset that provides no income is $30 and the risk-free rate for all
maturities (with continuous compounding) is 10%. What is the three-year forward price?
A. $40.50
B. $22.22
C. $33.00
D. $33.16
Answer: A
The 3-year forward price is the spot price grossed up for 3 years at the risk-free rate. It is 30e0.1×3
=$40.50.
4. The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with
continuous compounding. The asset provides an income of $2 at the end of the first year and at
the end of the second year. What is the three-year forward price?
A. $19.67
B. $35.84
C. $45.15
/
, Hull: Options, Futures, and Other Derivatives, Ninth Edition
Chapter 5: Determination of Forward and Futures Prices
Multiple Choice Test Bank: Questions with Answers
D. $40.50
Answer: B
The present value of the income is 2e-0.1×1+2e-0.1×2= $3.447. The three year forward price is
obtained by subtracting the present value of the income from the current stock price and then
grossing up the result for three years at the risk-free rate. It is (30−3.447)e0.1×3 = $35.84.
5. An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are
5% and 7% (both expressed with continuous compounding). What is the six-month forward rate?
A. 0.7070
B. 0.7177
C. 0.7249
D. 0.6930
Answer: D
The six-month forward rate is 0.7000e−(0.05−0.07)×0.5=0.6930.
6. Which of the following is true?
A. The convenience yield is always positive or zero.
B. The convenience yield is always positive for an investment asset.
C. The convenience yield is always negative for a consumption asset.
D. The convenience yield measures the average return earned by holding futures contracts.
Answer: A
The convenience yield measures the benefit of owning an asset rather than having a
forward/futures contract on an asset. For an investment asset it is always zero. For a
consumption asset it is greater than or equal to zero.
7. A short forward contract that was negotiated some time ago will expire in three months and has
a delivery price of $40. The current forward price for three-month forward contract is $42. The
three month risk-free interest rate (with continuous compounding) is 8%. What is the value of
the short forward contract?
A. +$2.00
B. −$2.00
C. +$1.96
D. −$1.96
Answer: D
The contract gives one the obligation to sell for $40 when a forward price negotiated today
would give one the obligation to sell for $42. The value of the contract is the present value of −
$2 or −2e-0.08×0.25 = −$1.96.
/
