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CHAPTER 06—INTEREST RATES
52. Inflation is expected to increase steadily over the next 10 years, there is a positive maturity risk premium on both
Treasury and corporate bonds, and the real risk-free rate of interest is expected to remain constant. Which of the following
statements is CORRECT?
a.
The yield on 10-year Treasury securities must exceed the yield on 7-year Treasury securities.
b.
The yield on any corporate bond must exceed the yields on all Treasury bonds.
c.
The yield on 7-year corporate bonds must exceed the yield on 10-year Treasury bonds.
d.
The stated conditions cannot all be true—they are internally inconsistent.
e.
The Treasury yield curve under the stated conditions would be humped rather than have a consistent positive
or negative slope.
53. Which of the following statements is CORRECT?
a.
Downward-sloping yield curves are inconsistent with the expectations theory.
b.
The actual shape of the yield curve depends only on expectations about future inflation.
c.
If the pure expectations theory is correct, a downward-sloping yield curve indicates that interest rates are
expected to decline in the future.
d.
If the yield curve is upward sloping, the maturity risk premium must be positive and the inflation rate must be
zero.
e.
Yield curves must be either upward or downward sloping—they cannot first rise and then decline.
54. Short Corp just issued bonds that will mature in 10 years, and Long Corp issued bonds that will mature in 20 years.
Both bonds promise to pay a semiannual coupon, they are not callable or convertible, and they are equally liquid. Further
assume that the Treasury yield curve is based only on the pure expectations theory. Under these conditions, which of the
following statements is CORRECT?
a.
If the yield curve for Treasury securities is flat, Short's bond must under all conditions have the same yield as
Long's bonds.
b.
If the yield curve for Treasury securities is upward sloping, Long's bonds must under all conditions have a
higher yield than Short's bonds.
c.
If Long's and Short's bonds have the same default risk, their yields must under all conditions be equal.
CHAPTER 06—INTEREST RATES
d.
If the Treasury yield curve is upward sloping and Short has less default risk than Long, then Short's bonds
must under all conditions have a lower yield than Long's bonds.
e.
If the Treasury yield curve is downward sloping, Long's bonds must under all conditions have the lower yield.
Multiple Choice: Problems
Interest rates are important in finance, and it is important for all students to understand the basics of how they are
determined. However, the chapter really has two aspects that become clear when we try to write test questions and
problems for the chapter. First, the material on the fundamental determinants of interest rates—the real risk-free rate plus
a set of premiums—is logical and intuitive, and easy in a testing sense. However, the second set of material, that dealing
with the yield curve and the relationship between 1-year rates and longer-term rates, is more mathematical and less
intuitive, and test questions dealing with it tend to be more difficult, especially for students who are not good at math.
As a result, problems on the chapter tend to be either relatively easy or relatively difficult, with the difficult ones being
as much exercises in algebra as in finance. In the test bank for prior editions, we tended to use primarily difficult
problems that addressed the problem of forecasting forward rates based on yield curve data. In this edition, we leaned
more toward easy problems that address intuitive aspects of interest rate theory.
We should note one issue that can be confusing if it is not handled carefully—the use of arithmetic versus geometric
averages when bringing inflation into interest rate determination in yield curve related problems. It is easy to explain why
a 2-year rate is an average of two 1-year rates, and it is logical to use a compounding process that is essentially a
geometric average that includes the effects of cross-product terms. It is also easy to explain that average inflation rates
should be calculated as geometric averages. However, when we combine inflation with interest rates, rather than using
the formulation rRF = [(1 + r*)(1 + IP)]0.5 – 1, almost everyone, from Federal Reserve officials down to textbook
authors, uses the approximation rRF = r* + IP. Understandably, this can confuse students when they start working
problems. In both the text and test bank problems we make it clear to students which procedure to use.
Quite a few of the problems are based on this basic equation: r = r* + IP + MRP + DRP + LP. We tell our students to
keep this equation in mind, and that they will have to do some transposing of terms to solve some of the problems.
The other key equation used in the problems is the one for finding the 1-year forward rate, given the current 1-year and
2-year rates: (1 + 2-year rate)2 = (1 + 1-year rate)(1 + X), which converts to X = (1 + 2yr)2/(1 + 1yr) – 1, where X is the
1-year forward rate. This equation, which is used in a number of problems, assumes that the pure expectations theory is
correct and thus the maturity risk premium is zero.
55. Suppose 1-year T-bills currently yield 7.00% and the future inflation rate is expected to be constant at 3.20% per year.
What is the real risk-free rate of return, r*? Disregard any cross-product terms, i.e., if averaging is required, use the
arithmetic average.
a.
3.80%
b.
3.99%
c.
4.19%
d.
4.40%
e.
4.62%
CHAPTER 06—INTEREST RATES
56. Suppose the real risk-free rate is 3.50% and the future rate of inflation is expected to be constant at 2.20%. What rate
of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-
product terms, i.e., if averaging is required, use the arithmetic average.
a.
5.14%
b.
5.42%
c.
5.70%
d.
5.99%
e.
6.28%
57. Suppose the real risk-free rate is 2.50% and the future rate of inflation is expected to be constant at 4.10%. What rate
of return would you expect on a 5-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-
product terms, i.e., if averaging is required, use the arithmetic average.
a.
5.38%
b.
5.66%
c.
5.96%
d.
6.27%
e.
6.60%
CHAPTER 06—INTEREST RATES
58. The real risk-free rate is 3.05%, inflation is expected to be 2.75% this year, and the maturity risk premium is zero.
Ignoring any cross-product terms, what is the equilibrium rate of return on a 1-year Treasury bond?
a.
5.51%
b.
5.80%
c.
6.09%
d.
6.39%
e.
6.71%
59. Suppose the real risk-free rate is 3.00%, the average expected future inflation rate is 2.25%, and a maturity risk
premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the number of years to maturity. What
rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is NOT valid?
Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.
a.
5.08%
b.
5.35%
c.
5.62%
d.
5.90%
e.
6.19%
CHAPTER 06—INTEREST RATES
60. Suppose the real risk-free rate is 4.20%, the average expected future inflation rate is 3.10%, and a maturity risk
premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the number of years to maturity, hence
the pure expectations theory is NOT valid. What rate of return would you expect on a 4-year Treasury security? Disregard
cross-product terms, i.e., if averaging is required, use the arithmetic average.
a.
6.60%
b.
6.95%
c.
7.32%
d.
7.70%
e.
8.09%
61. The real risk-free rate is 3.55%, inflation is expected to be 3.15% this year, and the maturity risk premium is zero.
Taking account of the cross-product term, i.e., not ignoring it, what is the equilibrium rate of return on a 1-year Treasury
bond?
a.
5.840%
b.
6.148%
c.
6.471%
d.
6.812%
e.
7.152%
CHAPTER 06—INTEREST RATES
62. Suppose the yield on a 10-year T-bond is currently 5.05% and that on a 10-year Treasury Inflation Protected Security
(TIPS) is 2.15%. Suppose further that the MRP on a 10-year T-bond is 0.90%, that no MRP is required on a TIPS, and
that no liquidity premium is required on any T-bond. Given this information, what is the expected rate of inflation over
the next 10 years? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.
a.
1.81%
b.
1.90%
c.
2.00%
d.
2.10%
e.
2.21%
63. Suppose the rate of return on a 10-year T-bond is 6.55%, the expected average rate of inflation over the next 10 years
is 2.0%, the MRP on a 10-year T-bond is 0.9%, no MRP is required on a TIPS, and no liquidity premium is required on
any Treasury security. Given this information, what should the yield be on a 10-year TIPS? Disregard cross-product
terms, i.e., if averaging is required, use the arithmetic average.
a.
2.97%
b.
3.13%
c.
3.29%
d.
3.47%
e.
3.65%
CHAPTER 06—INTEREST RATES
64. Suppose 10-year T-bonds have a yield of 5.30% and 10-year corporate bonds yield 6.75%. Also, corporate bonds have
a 0.25% liquidity premium versus a zero liquidity premium for T-bonds, and the maturity risk premium on both Treasury
and corporate 10-year bonds is 1.15%. What is the default risk premium on corporate bonds?
a.
1.08%
b.
1.20%
c.
1.32%
d.
1.45%
e.
1.60%
65. If 10-year T-bonds have a yield of 6.2%, 10-year corporate bonds yield 8.5%, the maturity risk premium on all 10-
year bonds is 1.3%, and corporate bonds have a 0.4% liquidity premium versus a zero liquidity premium for T-bonds,
what is the default risk premium on the corporate bond?
a.
1.90%
b.
2.09%
c.
2.30%
d.
2.53%
e.
2.78%
CHAPTER 06—INTEREST RATES
66. Koy Corporation's 5-year bonds yield 7.00%, and 5-year T-bonds yield 5.15%. The real risk-free rate is r* = 3.0%, the
inflation premium for 5-year bonds is IP = 1.75%, the liquidity premium for Koy's bonds is LP = 0.75% versus zero for T-
bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t − 1) × 0.1%, where t = number of
years to maturity. What is the default risk premium (DRP) on Koy's bonds?
a.
0.60%
b.
1.10%
c.
1.50%
d.
2.25%
e.
3.00%
67. Keys Corporation's 5-year bonds yield 6.20% and 5-year T-bonds yield 4.40%. The real risk-free rate is r* = 2.5%, the
inflation premium for 5-year bonds is IP = 1.50%, the liquidity premium for Keys' bonds is LP = 0.5% versus zero for T-
bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t − 1) × 0.1%, where t = number of
years to maturity. What is the default risk premium (DRP) on Keys' bonds?
a.
1.17%
b.
1.30%
c.
1.43%
d.
1.57%
CHAPTER 06—INTEREST RATES
e.
1.73%
68. Kay Corporation's 5-year bonds yield 6.20% and 5-year T-bonds yield 4.40%. The real risk-free rate is r* = 2.5%, the
inflation premium for 5-year bonds is IP = 1.50%, the default risk premium for Kay's bonds is DRP = 1.30% versus zero
for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t − 1) × 0.1%, where t =
number of years to maturity. What is the liquidity premium (LP) on Kay's bonds?
a.
0.36%
b.
0.41%
c.
0.45%
d.
0.50%
e.
0.55%
CHAPTER 06—INTEREST RATES
69. Niendorf Corporation's 5-year bonds yield 8.00%, and 5-year T-bonds yield 4.80%. The real risk-free rate is r* =
2.75%, the inflation premium for 5-year bonds is IP = 1.65%, the default risk premium for Niendorf's bonds is DRP =
1.20% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t − 1) ×
0.1%, where t = number of years to maturity. What is the liquidity premium (LP) on Niendorf's bonds?
a.
1.31%
b.
1.46%
c.
1.62%
d.
1.80%
e.
2.00%
70. Kern Corporation's 5-year bonds yield 7.30% and 5-year T-bonds yield 4.10%. The real risk-free rate is r* = 2.5%, the
default risk premium for Kern's bonds is DRP = 1.90% versus zero for T-bonds, the liquidity premium on Kern's bonds is
LP = 1.3%, and the maturity risk premium for all bonds is found with the formula MRP = (t − 1) × 0.1%, where t =
number of years to maturity. What is the inflation premium (IP) on all 5-year bonds?
a.
1.20%
b.
1.32%
c.
1.45%
d.
1.60%
e.
1.68%
CHAPTER 06—INTEREST RATES
71. Crockett Corporation's 5-year bonds yield 6.35%, and 5-year T-bonds yield 4.75%. The real risk-free rate is r* =
3.60%, the default risk premium for Crockett's bonds is DRP = 1.00% versus zero for T-bonds, the liquidity premium on
Crockett's bonds is LP = 0.90% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the
formula MRP = (t − 1) × 0.1%, where t = number of years to maturity. What inflation premium (IP) is built into 5-year
bond yields?
a.
0.68%
b.
0.75%
c.
0.83%
d.
0.91%
e.
1.00%
CHAPTER 06—INTEREST RATES
72. Kelly Inc's 5-year bonds yield 7.50% and 5-year T-bonds yield 4.90%. The real risk-free rate is r* = 2.5%, the default
risk premium for Kelly's bonds is DRP = 0.40%, the liquidity premium on Kelly's bonds is LP = 2.2% versus zero on T-
bonds, and the inflation premium (IP) is 1.5%. What is the maturity risk premium (MRP) on all 5-year bonds?
a.
0.73%
b.
0.81%
c.
0.90%
d.
0.99%
e.
1.09%
73. Kop Corporation's 5-year bonds yield 6.50%, and T-bonds with the same maturity yield 4.40%. The default risk
premium for Kop's bonds is DRP = 0.40%, the liquidity premium on Kop's bonds is LP = 1.70% versus zero on T-bonds,
the inflation premium (IP) is 1.50%, and the maturity risk premium (MRP) on 5-year bonds is 0.40%. What is the real
risk-free rate, r*?
a.
2.04%
b.
2.14%
c.
2.26%
d.
2.38%
e.
2.50%
CHAPTER 06—INTEREST RATES
74. 5-year Treasury bonds yield 5.5%. The inflation premium (IP) is 1.9%, and the maturity risk premium (MRP) on 5-
year T-bonds is 0.4%. There is no liquidity premium on these bonds. What is the real risk-free rate, r*?
a.
2.59%
b.
2.88%
c.
3.20%
d.
3.52%
e.
3.87%
75. Suppose 1-year T-bills currently yield 7.00% and the future inflation rate is expected to be constant at 3.20% per year.
What is the real risk-free rate of return, r*? The cross-product term should be considered, i.e., if averaging is required, use
the geometric average.
a.
3.68%
b.
3.87%
c.
4.06%
d.
4.26%
e.
4.48%
CHAPTER 06—INTEREST RATES
76. Suppose the real risk-free rate is 3.50% and the future rate of inflation is expected to be constant at 2.20%. What rate
of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is valid? Include cross-
product terms, i.e., if averaging is required, use the geometric average.
a.
5.21%
b.
5.49%
c.
5.78%
d.
6.07%
e.
6.37%
77. Suppose the real risk-free rate is 3.00%, the average expected future inflation rate is 2.25%, and a maturity risk
premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the years to maturity. What rate of return
would you expect on a 1-year Treasury security, assuming the pure expectations theory is NOT valid? Include the cross-
product term, i.e., if averaging is required, use the geometric average.
a.
5.15%
b.
5.42%
c.
5.69%
d.
5.97%
e.
6.27%
CHAPTER 06—INTEREST RATES
78. Suppose the interest rate on a 1-year T-bond is 5.0% and that on a 2-year T-bond is 7.0%. Assuming the pure
expectations theory is correct, what is the market's forecast for 1-year rates 1 year from now?
a.
7.36%
b.
7.75%
c.
8.16%
d.
8.59%
e.
9.04%
79. Suppose 1-year Treasury bonds yield 4.00% while 2-year T-bonds yield 5.10%. Assuming the pure expectations
theory is correct, and thus the maturity risk premium for T-bonds is zero, what is the yield on a 1-year T-bond expected to
be one year from now?
a.
5.90%
b.
6.21%
c.
6.52%
d.
6.85%
e.
7.19%
CHAPTER 06—INTEREST RATES
80. Suppose the real risk-free rate is 3.25%, the average future inflation rate is 4.35%, and a maturity risk premium of
0.07% per year to maturity applies to both corporate and T-bonds, i.e., MRP = 0.07%(t), where t is the number of years to
maturity. Suppose also that a liquidity premium of 0.50% and a default risk premium of 0.90% apply to A-rated corporate
bonds but not to T-bonds. How much higher would the rate of return be on a 10-year A-rated corporate bond than on a 5-
year Treasury bond? Here we assume that the pure expectations theory is NOT valid. Disregard cross-product terms, i.e.,
if averaging is required, use the arithmetic average.
a.
1.75%
b.
1.84%
c.
1.93%
d.
2.03%
e.
2.13%
81. Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2.50%, a maturity premium of 0.20% per
year to maturity applies, i.e., MRP = 0.20%(t), where t is the number of years to maturity. Suppose also that a liquidity
premium of 0.50% and a default risk premium of 1.35% applies to A-rated corporate bonds. What is the difference in the
yields on a 5-year A-rated corporate bond and on a 10-year Treasury bond? Here we assume that the pure expectations
theory is NOT valid, and disregard any cross-product terms, i.e., if averaging is required, use the arithmetic average.
a.
0.77%
b.
0.81%
CHAPTER 06—INTEREST RATES
c.
0.85%
d.
0.89%
e.
0.94%
82. Suppose the interest rate on a 1-year T-bond is 5.00% and that on a 2-year T-bond is 6.00%. Assume that the pure
expectations theory is NOT valid, and the MRP is zero for a 1-year T-bond but 0.40% for a 2-year bond. What is the yield
on a 1-year T-bond expected to be one year from now?
a.
5.32%
b.
5.60%
c.
5.89%
d.
6.20%
e.
6.51%
CHAPTER 06—INTEREST RATES
