Chapter 06: Interest Rates
b.
Reinvestment rate risk is lower, other things held constant, on long-term than on short-term bonds.
c.
The pure expectations theory of the term structure states that borrowers generally prefer to borrow on a long–
term basis while savers generally prefer to lend on a short-term basis, and as a result, the yield curve is
normally upward sloping.
d.
If the maturity risk premium were zero and interest rates were expected to decrease in the future, then the yield
curve for U.S. Treasury securities would, other things held constant, have an upward slope.
e.
Liquidity premiums are generally higher on Treasury than on corporate bonds.
Multiple Choice
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50. If the pure expectations theory is correct (that is, the maturity risk premium is zero), which of the following is
CORRECT?
a.
An upward-sloping Treasury yield curve means that the market expects interest rates to decline in the future.
b.
A 5-year T-bond would always yield less than a 10-year T-bond.
c.
The yield curve for corporate bonds may be upward sloping even if the Treasury yield curve is flat.
d.
The yield curve for stocks must be above that for bonds, but both yield curves must have the same slope.
e.
If the maturity risk premium is zero for Treasury bonds, then it must be negative for corporate bonds.
Multiple Choice
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51. Which of the following statements is CORRECT?
a.
Even if the pure expectations theory is correct, there might at times be an inverted Treasury yield curve.
b.
If the yield curve is inverted, short-term bonds have lower yields than long-term bonds.
c.
The higher the maturity risk premium, the higher the probability that the yield curve will be inverted.
d.
Inverted yield curves can exist for Treasury bonds, but because of default premiums, the corporate yield curve
cannot become inverted.
e.
The most likely explanation for an inverted yield curve is that investors expect inflation to increase in the
Chapter 06: Interest Rates
future.
a
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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.
a
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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.
c
MODERATE
Comprehensive
Chapter 06: Interest Rates
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 corvertible, 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.
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.
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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
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Chapter 06: Interest Rates
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)] – 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 6.00% 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.
b.
c.
d.
e.
e
7.00%
Inflation
6.00%
1.00%
b.
c.
d.
e.
EASY
Problems
56. Suppose the real risk-free rate is 3.50% and the future rate of inflation is expected to be constant at 4.80%. 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.
b.
c.
Chapter 06: Interest Rates
d.
e.
3.50%
Inflation
4.80%
8.30%
b.
c.
d.
e.
EASY
57. Suppose the real risk-free rate is 2.50% and the future rate of inflation is expected to be constant at 7.00%. 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.
9.50%
b.
11.59%
c.
7.70%
d.
7.41%
e.
8.46%
a
2.50%
Inflation
7.00%
9.50%
b.
c.
d.
e.
EASY
Chapter 06: Interest Rates
58. The real risk-free rate is 3.05%, inflation is expected to be 3.60% this year, and the maturity risk premium is zero.
Ignoring any cross-product terms, i.e., if averaging is required, use the arithmetic average, what is the equilibrium rate of
return on a 1-year Treasury bond?
a.
b.
c.
d.
e.
3.05%
3.60%
b.
c.
d.
e.
EASY
59. Suppose the real risk-free rate is 3.00%, the average expected future inflation rate is 5.90%, 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.
9.27%
b.
8.91%
c.
7.29%
d.
9.00%
e.
10.35%
a.
3.00%
Chapter 06: Interest Rates
Inflation
5.90%
MRP
0.10%
b.
c.
d.
e.
EASY
60. Suppose the real risk-free rate is 4.20%, the average expected future inflation rate is 2.50%, 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.
b.
c.
d.
e.
b.
c.
d.
e.
EASY
Chapter 06: Interest Rates
61. The real risk-free rate is 3.55%, inflation is expected to be 3.60% 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? (Round your final answer to 3 decimal places.)
a.
8.224%
b.
7.059%
c.
6.914%
d.
7.278%
e.
8.442%
3.55%
3.60%
7.150%
b.
c.
d.
e.
EASY
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 1.80%. 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.
b.
c.
d.
e.
c
Chapter 06: Interest Rates
63. Suppose the rate of return on a 10-year T-bond is 6.90%, 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.
b.
c.
d.
e.
10-year T-bond yield
6.90%
2.00%
0.90%
b.
c.
d.
e.
MODERATE
10-year T-bond yield
5.05%
10-year TIPS yield = r*
1.80%
0.90%
b.
c.
d.
e.
MODERATE
Chapter 06: Interest Rates
64. Suppose 10-year T-bonds have a yield of 5.30% and 10-year corporate bonds yield 6.65%. 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.
b.
c.
d.
e.
5.30%
6.65%
0.25%
1.10%
b.
c.
d.
e.
MODERATE
65. If 10-year T-bonds have a yield of 6.2%, 10-year corporate bonds yield 7.9%, 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.
b.
c.
d.
e.
Chapter 06: Interest Rates
0.40%
7.90%
1.70%
1.30%
b.
c.
d.
e.
MODERATE
66. Koy Corporation’s 5-year bonds yield 8.00%, 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.
b.
c.
d.
e.
3.00%
MRP
c.
Chapter 06: Interest Rates
e.
MODERATE
6-5 What Determines the Shape of the Yield Curve?
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67. Keys Corporation’s 5-year bonds yield 5.10% 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.
b.
c.
d.
e.
Maturity
Included in both bonds
2.5%
Included in both bonds
1.5%
Included in Keys only
0.50%
b.
c.
d.
e.
6-5 What Determines the Shape of the Yield Curve?
QUESTION TYPE:
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