Chapter 15 – The Term Structure of Interest Rates
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40. What would the yield to maturity be on a four-year zero coupon bond purchased today?
A. 5.80%
B. 7.30%
Difficulty: Moderate
41. Calculate the price at the beginning of year 1 of a 10% annual coupon bond with face
value $1,000 and 5 years to maturity.
A. $1,105
Difficulty: Difficult
42. Given the yield on a 3 year zero-coupon bond is 7.2% and forward rates of 6.1% in year 1
and 6.9% in year 2, what must be the forward rate in year 3?
A. 8.4%
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
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43. An inverted yield curve is one
A. with a hump in the middle.
B. constructed by using convertible bonds.
Difficulty: Easy
44. Investors can use publicly available financial date to determine which of the following?
I) the shape of the yield curve
II) future short-term rates
III) the direction the Dow indexes are heading
IV) the actions to be taken by the Federal Reserve
D. I, III, and IV
E. I, II, III, and IV
Difficulty: Moderate
45. Which of the following combinations will result in a sharply increasing yield curve?
D. increasing expected short rates and constant liquidity premiums
E. constant expected short rates and increasing liquidity premiums
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
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46. The yield curve is a component of
A. the Dow Jones Industrial Average.
B. the consumer price index.
Difficulty: Easy
47. The most recently issued Treasury securities are called
D. off the market.
E. none of the above.
Difficulty: Easy
Suppose that all investors expect that interest rates for the 4 years will be as follows:
Chapter 15 – The Term Structure of Interest Rates
15–20
48. What is the price of 3-year zero coupon bond with a par value of $1,000?
D. $765.55
E. none of the above
Difficulty: Moderate
49. If you have just purchased a 4-year zero coupon bond, what would be the expected rate of
return on your investment in the first year if the implied forward rates stay the same? (Par
value of the bond = $1,000)
D. 10%
E. none of the above
Difficulty: Moderate
50. What is the price of a 2-year maturity bond with a 5% coupon rate paid annually? (Par
value = $1,000)
A. $1,092.97
B. $1,054.24
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
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51. What is the yield to maturity of a 3-year zero coupon bond?
A. 7.00%
B. 9.00%
Difficulty: Moderate
The following is a list of prices for zero coupon bonds with different maturities and par value
of $1,000.
52. What is, according to the expectations theory, the expected forward rate in the third
year?
A. 7.23
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
15–22
53. What is the yield to maturity on a 3-year zero coupon bond?
A. 6.37%
Difficulty: Moderate
54. What is the price of a 4-year maturity bond with a 10% coupon rate paid annually? (Par
value = $1,000)
A. $742.09
B. $1,222.09
Difficulty: Difficult
55. You have purchased a 4-year maturity bond with a 9% coupon rate paid annually. The
bond has a par value of $1,000. What would the price of the bond be one year from now if the
implied forward rates stay the same?
D. $1,042.78
E. none of the above
Difficulty: Difficult
Chapter 15 – The Term Structure of Interest Rates
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56. Given the bond described above, if interest were paid semi-annually (rather than
annually), and the bond continued to be priced at $917.99, the resulting effective annual yield
to maturity would be:
A. Less than 10%
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
15–24
57. What should the purchase price of a 2-year zero coupon bond be if it is purchased at the
beginning of year 2 and has face value of $1,000?
A. $877.54
B. $888.33
Difficulty: Difficult
58. What would the yield to maturity be on a four-year zero coupon bond purchased today?
D. 5.25%
E. none of the above.
Difficulty: Moderate
59. Calculate the price at the beginning of year 1 of an 8% annual coupon bond with face
value $1,000 and 5 years to maturity.
A. $1,105.47
B. $1,131.91
Difficulty: Difficult
Chapter 15 – The Term Structure of Interest Rates
15–25
60. Given the yield on a 3 year zero-coupon bond is 7% and forward rates of 6% in year 1 and
6.5% in year 2, what must be the forward rate in year 3?
A. 7.2%
B. 8.6%
Difficulty: Moderate
61. What should the purchase price of a 1-year zero coupon bond be if it is purchased today
and has face value of $1,000?
A. $966.37
B. $912.87
Difficulty: Difficult
Chapter 15 – The Term Structure of Interest Rates
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62. What should the purchase price of a 2-year zero coupon bond be if it is purchased today
and has face value of $1,000?
A. $966.87
Difficulty: Difficult
63. What should the purchase price of a 3-year zero coupon bond be if it is purchased today
and has face value of $1,000?
A. $887.42
B. $871.12
Difficulty: Difficult
64. What should the purchase price of a 4-year zero coupon bond be if it is purchased today
and has face value of $1,000?
A. $887.42
Difficulty: Difficult
Chapter 15 – The Term Structure of Interest Rates
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65. What should the purchase price of a 5-year zero coupon bond be if it is purchased today
and has face value of $1,000?
D. $756.02
E. $766.32
Difficulty: Difficult
66. What is the yield to maturity of a 1-year bond?
D. 5.5%
E. 5.8%
Difficulty: Moderate
67. What is the yield to maturity of a 5-year bond?
A. 4.6%
B. 4.9%
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
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68. What is the yield to maturity of a 4-year bond?
A. 4.69%
B. 4.95%
Difficulty: Moderate
69. What is the yield to maturity of a 3-year bond?
A. 4.6%
Difficulty: Moderate
70. What is the yield to maturity of a 2-year bond?
A. 4.6%
B. 4.9%
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
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Short Answer Questions
71. Discuss the three theories of the term structure of interest rates. Include in your discussion
the differences in the theories, and the advantages/disadvantages of each.
The expectations hypothesis is the most commonly accepted theory of term structure. The
theory states that the forward rate equals the market consensus expectation of future short-
term rates. Thus, yield to maturity is determined solely by current and expected future one-
period interest rates. An upward sloping, or normal, yield curve would indicate that investors
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
15–30
72. Term structure of interest rates is the relationship between what variables? What is
assumed about other variables? How is term structure of interest rates depicted graphically?
Term structure of interest rates is the relationship between yield to maturity and term to
maturity, all else equal. The “all else equal” refers to risk class. Term structure of interest rates
is depicted graphically by the yield curve, which is usually a graph of U.S. governments of
Difficulty: Moderate
73. Although the expectations of increases in future interest rates can result in an upward
sloping yield curve; an upward sloping yield curve does not in and of itself imply the
expectations of higher future interest rates. Explain.
The effects of possible liquidity premiums confound any simple attempt to extract expectation
from the term structure. That is, the upward sloping yield curve may be due to expectations of
interest rate increases, or due to the requirement of a liquidity premium, or both. The liquidity
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
15–31
74. Explain what the following terms mean: spot rate, short rate, and forward rate. Which of
these is (are) observable today?
From the answer to Concept Check 2, on page 516: “The n-period spot rate is the yield to
maturity on a zero-coupon bond with a maturity of n periods. The short rate for period n is the
one-period interest rate that will prevail in period n. The forward rate for period n is the short
rate that would satisfy a “break-even condition” equating the total returns on two n-period
Difficulty: Moderate
Chapter 15 – The Term Structure of Interest Rates
15–32
75. Answer the following questions that relate to bonds.
– A 2-year zero-coupon bond is selling for $890.00. What is the yield to maturity of this bond?
– The price of a 1-year zero coupon bond is $931.97. What is the yield to maturity of this
bond?
– Calculate the forward rate for the second year.
– How can you construct a synthetic one-year forward loan (you are agreeing now to loan in
one year)? State the strategy and show the corresponding cash flows. Assume that you can
purchase and sell fractional portions of bonds. Show all calculations and discuss the meaning
of the transactions.
Calculations are shown in the table below.
– Calculations for YTM of the 2-year zero: N=2, PV=-890.00, PMT=0, FV=1000, CPT
I6.0.
Difficulty: Difficult