Fundamentals of Derivatives Markets (McDonald)
Chapter 7 Interest Rate Forwards and Futures
7.1 Multiple Choice Questions
1) The price of a 3–year zero coupon government bond is 85.16. The price of a similar 4–year
bond is 79.81. What is the yield to maturity (effective annual yield) on the 4–year bond?
A) 4.6%
B) 5.5%
C) 5.8%
D) 6.7%
2) The price of a 3–year zero coupon government bond is 85.16. The price of a similar 4–year
bond is 78.81. What is the yield to maturity (effective annual yield) on the 3–year bond?
A) 4.6%
B) 5.5%
C) 5.8%
D) 6.7%
3) The price of a 3–year zero coupon government bond is 85.16. The price of a similar 4–year
bond is 78.81. What is the 1–year implied forward rate from year 3 to year 4?
A) 4.6%
B) 5.5%
C) 5.8%
D) 6.7%
4) The prices of 1, 2, 3, and 4–year zero coupon government bonds are 95.42, 90.36, 85.16, and
78.81, respectively. What is the implied 2–year forward rate between years 2 and 4?
A) 4.8%
B) 5.2%
C) 5.5%
D) 6.4%
5) The prices of 1, 2, 3, and 4–year zero coupon government bonds are 95.42, 90.36, 85.16, and
78.81, respectively. What is the par coupon on a 4–year coupon bond selling at par?
A) 5.02%
B) 5.43%
C) 5.81%
D) 6.06%
6) The prices of 1, 2, 3, and 4–year zero coupon government bonds are 95.42, 90.36, 85.16, and
78.81, respectively. What is the continuously compounded 3–year zero yield?
A) 5.35%
B) 5.85%
C) 6.12%
D) 6.40%
7) The annual coupon rate on a 1–year treasury bond is 5.5%. The coupon on a 2–year treasury
bond is 5.8%. What is the implied YTM on a hypothetical 2–year zero coupon treasury bond?
A) 5.45%
B) 5.50%
C) 5.75%
D) 5.81%
8) The annual coupon rate on a 1–year treasury bond is 5.5%. The coupon on a 2–year treasury
bond is 5.8%. What is the continuously compounded yield on a 2–year zero coupon bond?
A) 5.55%
B) 5.65%
C) 5.75%
D) 5.85%
9) A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6–month loan. If
settled at the time of borrowing, what amount would the borrower pay or receive on a
$500,000 loan if the prevailing 6–month interest rate is 2.9%?
A) $1,000 payment
B) $1,000 receipt
C) $972 payment
D) $972 receipt
10) A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6–month loan. If
settled in arrears, what amount would the borrower pay or receive on an $800,000 loan if the
prevailing 6–month interest rate is 3.6%?
A) $4,000 payment
B) $4,000 receipt
C) $1,729 payment
D) $1,729 receipt
11) Two months from today you plan to borrow $3 million for 6 months at LIBOR. You hedge
your interest rate risk with a euro dollar futures contract priced at 93.6. If settled in arrears,
what is your payment if the 6–month LIBOR is 2.5% in two months?
A) $8,500
B) $10,500
C) $13,500
D) $15,500
12) Given a 3–year, 8.0% annual coupon bond with a par value of $1,000, what is the bond’s
Macaulay duration if the yield to maturity is 9.5%?
A) 2.779
B) 2.634
C) 2.535
D) 2.442
13) A 4–year bond with a price of 100.696 exists. The duration on the bond is 3.674. If the yield
rises from 5.8% to 6.2%, what is the new bond price as estimated by the duration?
A) $98.40
B) $99.30
C) $100.60
D) $101.40
14) Compute the conversion factor on a semi–annual 6.8% coupon bond, which matures in
exactly 5
2
1
years.
A) 1.037
B) 1.046
C) 1.052
D) 1.068
15) The conversion factor on a deliverable bond is 1.03 and the bond price is 100.50. The
observed futures price is 97.5 and the YTM is 5.8%. What is invoice less market price on the
security?
A) +0.08
B) –0.08
C) –0.02
D) +0.02
16) You wish to create a synthetic forward rate agreement in which you would lock in a return
between 150 and 310 days. The price of a 150–day zero coupon bond is 0.9823 and the price
of 310–day zero coupon bond is 0.9634. What is the approximate yield on the synthetic FRA?
A) 1.8%
B) 2.0%
C) 2.9%
D) 3.8%
17) You wish to create a synthetic forward rate agreement in which you would lock in a return
between 150 and 310 days. The price of a 150–day zero coupon bond is 0.9823 and the price
of 310–day zero coupon bond is 0.9634. What are the transactions used to create this
instrument?
A) Borrow one 150–day bond and invest in 1.02 of the 310–day bonds
B) Borrow two 150–day bonds and invest in 0.98 of the 310–day bonds
C) Lend one of the 150–day bonds and borrow1.02 of the 310–day bonds
D) Lend two of the 150–day bonds and borrow 0.98 of the 310–day bonds
18) The price of a 6–month T–bill is 96.73. You wish to enter into a repurchase agreement that
provides for your purchase of a $100,000 bond in 10 days at a price of 97.02. What is the
implied 10 day repo rate in this transaction?
A) 0.10%
B) 0.20%
C) 0.30%
D) 0.40%
19) An investor holds a bond with a duration of 7.2 years. The only available security with
which to hedge has a duration of 1.8 years. Given comparable par values, how many of the
hedge security will be shorted to properly create a hedge?
A) 1
B) 2
C) 3
D) 4
20) The change in a bond price for a unit change in the prevailing yield is calculated as $198.54.
What is the price value of a basis point on this bond?
A) $0.019854
B) $0.19854
C) $1.9854
D) $19.854
21) Which is the more precise measurement of bond price sensitivity?
A) Convexity
B) Duration
C) Maturity
D) Yield
22) Which of the following items will a short bond futures position be most interested in at
expiration of the futures contract?
A) Cash and carry
B) Cheapest to deliver
C) Conversion factor
D) Implied Repo rate
23) Which of the following formulas is used to determine the cheapest to deliver?
A) Invoice price – market price
B) Market price x accrued interest
C) Futures price x accrued interest
D) Futures price – invoice price
7.2
Short Answer Essay Questions
1) What is the pure yield curve and why is it common to present coupon–based yield curves in
practice?
2) Explain the expectations hypothesis and its ability to accurately forecast interest rates.
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3) Explain the process of creating a synthetic Forward Rate Agreement.
4) What is the rationale behind cheapest–to–deliver calculations and why do we perform such
calculations?
5) Why can repos be used to simulate borrowing?
7.3 Class Discussion Question
1) How is duration calculated? What is the nature and use of duration? How does duration
compare to the linear concept of the bond price and interest rate relationship? Is duration
better than convexity or worse? Duration is considered common knowledge in the fixed
income world and should be discussed at length.