Chapter 6: Interest Rates
The difficulty of these questions as seen by students will depend on (1) what was discussed in class and (2)
how
long students have to answer the questions. If time is not an issue, then many of the questions could be
classified as EASY, but under exam conditions with time pressure, many might be regarded as being
CHALLENGING. So, consider the amount of time students have when selecting questions for an exam.
Note that there is some overlap between the True/False and the multiple choice questions, as some T/F
statements are used in the MC questions.
1.
One of the four most fundamental factors that affect the cost of money as discussed in the text is the current
state
of the weather. If the weather is dark and stormy, the cost of money will be higher than if it is bright and
sunny,
other things held constant.
a.
True
b.
False
2.
One of the four most fundamental factors that affect the cost of money as discussed in the text is the expected
rate
of inflation. If inflation is expected to be relatively high, then interest rates will tend to be relatively low,
other things
held constant.
a.
True
b.
False
3.
One of the four most fundamental factors that affect the cost of money as discussed in the text is the risk
inherent in
a given security. The higher the risk, the higher the security’s required return, other things held
constant.
a.
True
b.
False
4.
One of the four most fundamental factors that affect the cost of money as discussed in the text is the time
preference for consumption. The higher the time preference, the lower the cost of money, other things held
constant.
a.
True
b.
False
5.
The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time
preferences for consumption, (3) risk, and (4) inflation.
a.
True
b.
False
6.
The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time
preferences for consumption, (3) risk, and (4) weather conditions.
a.
True
b.
False
7.
The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time
preferences for consumption, (3) risk, and (4) the skill level of the economy’s labor force.
a.
True
b.
False
8.
If the demand curve for funds increased but the supply curve remained constant, we would expect to see the
total
amount of funds supplied and demanded increase and interest rates in general also increase.
a.
True
b.
False
9.
During periods when inflation is increasing, interest rates tend to increase, while interest rates tend to fall when
inflation is declining.
a.
True
b.
False
10.
If investors expect a zero rate of inflation, then the nominal rate of return on a very short-term U.S. Treasury
bond
should be equal to the real risk-free rate, r*.
a.
True
b.
False
11.
If investors expect the rate of inflation to increase sharply in the future, then we should not be surprised to see
an
upward-sloping yield curve.
a.
True
b.
False
12.
The risk that interest rates will increase, and that increase will lead to a decline in the prices of outstanding
bonds, is
called “interest rate risk,” or “price risk.”
a.
True
b.
False
13.
The risk that interest rates will decline, and that decline will lead to a decline in the income provided by a bond
portfolio as interest and maturity payments are reinvested, is called “reinvestment rate risk.”
a.
True
b.
False
14.
The “yield curve” shows the relationship between bonds’ maturities and their yields.
a.
True
b.
False
15.
Because the maturity risk premium is normally positive, the yield curve is normally upward sloping.
a.
True
b.
False
16.
Because the maturity risk premium is normally positive, the yield curve must have an upward slope. If you
measure
the yield curve and find a downward slope, you must have done something wrong.
a.
True
b.
False
17.
If the Treasury yield curve were downward sloping, the yield to maturity on a 10-year Treasury coupon bond
would
be higher than that on a 1-year T-bill.
a.
True
b.
False
18.
If the pure expectations theory is correct, a downward-sloping yield curve indicates that interest rates are
expected
to decline in the future.
a.
True
b.
False
19.
An upward-sloping yield curve is often call a “normal” yield curve, while a downward-sloping yield curve is
called
“abnormal.”
a.
True
b.
False
20.
Since yield curves are based on a real risk-free rate plus the expected rate of inflation, at any given time there
can
be only one yield curve, and it applies to both corporate and Treasury securities.
a.
True
b.
False
21.
Suppose the federal deficit increased sharply from one year to the next, and the Federal Reserve kept the
money
supply constant. Other things held constant, we would expect to see interest rates decline.
a.
True
b.
False
22.
The Federal Reserve tends to take actions to increase interest rates when the economy is very strong and to
decrease rates when the economy is weak.
a.
True
b.
False
23.
One of the four most fundamental factors that affect the cost of money as discussed in the text is the
availability of
production opportunities and their expected rates of return. If production opportunities are
relatively good, then
interest rates will tend to be relatively high, other things held constant.
a.
True
b.
False
Multiple Choice: Conceptual
24.
Assume that inflation is expected to decline steadily in the future, but that the real risk-free rate, r*, will remain
constant. Which of the following statements is CORRECT, other things held constant?
a.
If the pure expectations theory holds, the Treasury yield curve must be downward sloping.
b.
If the pure expectations theory holds, the corporate yield curve must be downward sloping.
c.
If there is a positive maturity risk premium, the Treasury yield curve must be upward sloping.
d.
If inflation is expected to decline, there can be no maturity risk premium.
e.
The expectations theory cannot hold if inflation is decreasing.
25.
Which of the following factors would be most likely to lead to an increase in nominal interest rates?
a.
Households reduce their consumption and increase their savings.
b.
A new technology like the Internet has just been introduced, and it increases investment opportunities.
c.
There is a decrease in expected inflation.
d.
The economy falls into a recession.
e.
The Federal Reserve decides to try to stimulate the economy.
26.
Which of the following statements is CORRECT, other things held constant?
a.
If companies have fewer good investment opportunities, interest rates are likely to increase.
b.
If individuals increase their savings rate, interest rates are likely to increase.
c.
If expected inflation increases, interest rates are likely to increase.
d.
Interest rates on all debt securities tend to rise during recessions because recessions increase the possibility
of
bankruptcy, hence the riskiness of all debt securities.
e.
Interest rates on long-term bonds are more volatile than rates on short-term debt securities like T-bills.
27.
Which of the following would be most likely to lead to a higher level of interest rates in the economy?
a.
Households start saving a larger percentage of their income.
b.
Corporations step up their expansion plans and thus increase their demand for capital.
c.
The level of inflation begins to decline.
d.
The economy moves from a boom to a recession.
e.
The Federal Reserve decides to try to stimulate the economy.
28.
Suppose the U.S. Treasury issued $50 billion of short-term securities and sold them to the public. Other things
held
constant, what would be the most likely effect on short-term securities’ prices and interest rates?
a.
Prices and interest rates would both rise.
b.
Prices would rise and interest rates would decline.
c.
Prices and interest rates would both decline.
d.
Prices would decline and interest rates would rise.
e.
There is no reason to expect a change in either prices or interest rates.
29.
Assume that interest rates on 20-year Treasury and corporate bonds are as follows:
T-bond = 7.72% AAA = 8.72% A = 9.64% BBB = 10.18%
The differences in these rates were probably caused primarily by:
a.
Tax effects.
b.
Default and liquidity risk differences.
c.
Maturity risk differences.
d.
Inflation differences.
e.
Real risk-free rate differences.
30.
In the foreseeable future, the real risk-free rate of interest, r*, is expected to remain at 3%, inflation is expected
to
steadily increase, and the maturity risk premium is expected to be 0.1(t − 1)%, where t is the number of
years until
the bond matures. Given this information, which of the following statements is CORRECT?
a.
The yield on 2-year Treasury securities must exceed the yield on 5-year Treasury securities.
b.
The yield on 5-year Treasury securities must exceed the yield on 10-year corporate bonds.
c.
The yield on 5-year corporate bonds must exceed the yield on 8-year Treasury bonds.
d.
The yield curve must be “humped.”
e.
The yield curve must be upward sloping.
31.
If the Treasury yield curve is downward sloping, how should the yield to maturity on a 10-year Treasury
coupon
bond compare to that on a 1-year T-bill?
a.
The yield on a 10-year bond would be less than that on a 1-year bill.
b.
The yield on a 10-year bond would have to be higher than that on a 1-year bill because of the maturity risk
premium.
c.
It is impossible to tell without knowing the coupon rates of the bonds.
d.
The yields on the two securities would be equal.
e.
It is impossible to tell without knowing the relative risks of the two securities.
32.
Assume the following: The real risk-free rate, r*, is expected to remain constant at 3%. Inflation is expected to
be
3% next year and then to be constant at 2% a year thereafter. The maturity risk premium is zero. Given this
information, which of the following statements is CORRECT?
a.
The yield curve for U.S. Treasury securities will be upward sloping.
b.
A 5-year corporate bond must have a lower yield than a 5-year Treasury security.
c.
A 5-year corporate bond must have a lower yield than a 7-year Treasury security.
d.
The real risk-free rate cannot be constant if inflation is not expected to remain constant.
e.
This problem assumed a zero maturity risk premium, but that is probably not valid in the real world.
33.
Which of the following statements is CORRECT?
a.
If the maturity risk premium (MRP) is greater than zero, the Treasury bond yield curve must be upward
sloping.
b.
If the maturity risk premium (MRP) equals zero, the Treasury bond yield curve must be flat.
c.
If inflation is expected to increase in the future and the maturity risk premium (MRP) is greater than zero,
the
Treasury bond yield curve must be upward sloping.
d.
If the expectations theory holds, the Treasury bond yield curve will never be downward sloping.
e.
Because long-term bonds are riskier than short-term bonds, yields on long-term Treasury bonds will always
be
higher than yields on short-term T-bonds.
34.
A bond trader observes the following information:
•
The Treasury yield curve is downward sloping.
•
Empirical data indicate that a positive maturity risk premium applies to both Treasury and
corporate bonds.
•
Empirical data also indicate that there is no liquidity premium for Treasury securities but that
a positive
liquidity premium is built into corporate bond yields.
On the basis of this information, which of the following statements is most CORRECT?
a.
A 10-year corporate bond must have a higher yield than a 5-year Treasury bond.
b.
A 10-year Treasury bond must have a higher yield than a 10-year corporate bond.
c.
A 5-year corporate bond must have a higher yield than a 10-year Treasury bond.
d.
The corporate yield curve must be flat.
e.
Since the Treasury yield curve is downward sloping, the corporate yield curve must also be downward
sloping.
35.
The real risk-free rate is expected to remain constant at 3% in the future, a 2% rate of inflation is expected for
the
next 2 years, after which inflation is expected to increase to 4%, and there is a positive maturity risk
premium that
increases with years to maturity. Given these conditions, which of the following statements is
CORRECT?
a.
The yield on a 2-year T-bond must exceed that on a 5-year T-bond.
b.
The yield on a 5-year Treasury bond must exceed that on a 2-year Treasury bond.
c.
The yield on a 7-year Treasury bond must exceed that of a 5-year corporate bond.
d.
The conditions in the problem 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.
36.
Which of the following statements is CORRECT?
a.
The yield on a 3-year Treasury bond cannot exceed the yield on a 10-year Treasury bond.
b.
The yield on a 2-year corporate bond should always exceed the yield on a 2-year Treasury bond.
c.
The yield on a 3-year corporate bond should always exceed the yield on a 2-year corporate bond.
d.
The yield on a 10-year AAA-rated corporate bond should always exceed the yield on a 5-year AAA-rated
corporate bond.
e.
The following represents a “possibly reasonable” formula for the maturity risk premium on bonds: MRP =
−0.1%(t), where t is the years to maturity.
37.
Which of the following statements is CORRECT?
a.
The yield on a 2-year corporate bond should always exceed the yield on a 2-year Treasury bond.
b.
The yield on a 3-year corporate bond should always exceed the yield on a 2-year corporate bond.
c.
The yield on a 3-year Treasury bond should always exceed the yield on a 2-year Treasury bond.
d.
If inflation is expected to increase, then the yield on a 2-year bond should exceed that on a 3-year bond.
e.
The real risk-free rate should increase if people expect inflation to increase.
38.
Which of the following statements is CORRECT?
a.
If inflation is expected to increase in the future, and if the maturity risk premium (MRP) is greater than zero,
then the Treasury yield curve will have an upward slope.
b.
If the maturity risk premium (MRP) is greater than zero, then the yield curve must have an upward slope.
c.
Because long-term bonds are riskier than short-term bonds, yields on long-term Treasury bonds will always
be
higher than yields on short-term T-bonds.
d.
If the maturity risk premium (MRP) equals zero, the yield curve must be flat.
e.
The yield curve can never be downward sloping.
39.
Assume that the current corporate bond yield curve is upward sloping. Under this condition, then we could be
sure
that
a.
Inflation is expected to decline in the future.
b.
The economy is not in a recession.
c.
Long-term bonds are a better buy than short-term bonds.
d.
Maturity risk premiums could help to explain the yield curve’s upward slope.
e.
Long-term interest rates are more volatile than short-term rates.
40.
Which of the following statements is CORRECT?
a.
The higher the maturity risk premium, the higher the probability that the yield curve will be inverted.
b.
The most likely explanation for an inverted yield curve is that investors expect inflation to increase.
c.
The most likely explanation for an inverted yield curve is that investors expect inflation to decrease.
d.
If the yield curve is inverted, short-term bonds have lower yields than long-term bonds.
e.
Inverted yield curves can exist for Treasury bonds, but because of default premiums, the corporate yield
curve can never be inverted.
41.
Assume that the current corporate bond yield curve is upward sloping, or normal. Under this condition, we
could be
sure that
a.
Long-term interest rates are more volatile than short-term rates.
b.
Inflation is expected to decline in the future.
c.
The economy is not in a recession.
d.
Long-term bonds are a better buy than short-term bonds.
e.
Maturity risk premiums could help to explain the yield curve’s upward slope.
42.
Assuming that the term structure of interest rates is determined as posited by the pure expectations theory,
which of
the following statements is CORRECT?
a.
In equilibrium, long-term rates must be equal to short-term rates.
b.
An upward-sloping yield curve implies that future short-term rates are expected to decline.
c.
The maturity risk premium is assumed to be zero.
d.
Inflation is expected to be zero.
e.
Consumer prices as measured by an index of inflation are expected to rise at a constant rate.
43.
Assume that the rate on a 1-year bond is now 6%, but all investors expect 1-year rates to be 7% one year from
now
and then to rise to 8% two years from now. Assume also that the pure expectations theory holds, hence the
maturity
risk premium equals zero. Which of the following statements is CORRECT?
a.
The yield curve should be downward sloping, with the rate on a 1-year bond at 6%.
b.
The interest rate today on a 2-year bond should be approximately 6%.
c.
The interest rate today on a 2-year bond should be approximately 7%.
d.
The interest rate today on a 3-year bond should be approximately 7%.
e.
The interest rate today on a 3-year bond should be approximately 8%.
44.
The real risk-free rate of interest is expected to remain constant at 3% for the foreseeable future. However,
inflation
is expected to increase steadily over the next 30 years, so the Treasury yield curve has an upward
slope. Assume
that the pure expectations theory holds. You are also considering two corporate bonds, one with
a 5-year maturity
and one with a 10-year maturity. Both have the same default and liquidity risks. Given these
assumptions, which of
these statements is CORRECT?
a.
Since the pure expectations theory holds, the 10-year corporate bond must have the same yield as the 5-year
corporate bond.
b.
Since the pure expectations theory holds, all 5-year Treasury bonds must have higher yields than all 10-year
Treasury bonds.
c.
Since the pure expectations theory holds, all 10-year corporate bonds must have the same yield as 10-year
Treasury bonds.
d.
The 10-year Treasury bond must have a higher yield than the 5-year corporate bond.
e.
The 10-year corporate bond must have a higher yield than the 5-year corporate bond.
45.
If the pure expectations theory of the term structure is correct, which of the following statements would be
CORRECT?
a.
An upward-sloping yield curve would imply that interest rates are expected to be lower in the future.
b.
If a 1-year Treasury bill has a yield to maturity of 7% and a 2-year Treasury bill has a yield to maturity of
8%,
this would imply the market believes that 1-year rates will be 7.5% one year from now.
c.
The yield on a 5-year corporate bond should always exceed the yield on a 3-year Treasury bond.
d.
Interest rate (price) risk is higher on long-term bonds, but reinvestment rate risk is higher on short-term
bonds.
e.
Interest rate (price) risk is higher on short-term bonds, but reinvestment rate risk is higher on long-term
bonds.
46.
Assuming the pure expectations theory is correct, which of the following statements is CORRECT?
a.
If 2-year Treasury bond rates exceed 1-year rates, then the market must expect interest rates to rise.
b.
If both 2-year and 3-year Treasury rates are 7%, then 5-year rates must also be 7%.
c.
If 1-year rates are 6% and 2-year rates are 7%, then the market expects 1-year rates to be 6.5% in one year.
d.
Reinvestment rate risk is higher on long-term bonds, and interest rate (price) risk is higher on short-term
bonds.
e.
Interest rate (price) risk and reinvestment rate risk are relevant to investors in corporate bonds, but these
concepts do not apply to Treasury bonds.
47.
If the pure expectations theory holds, which of the following statements is CORRECT?
a.
The yield curve for both Treasury and corporate bonds should be flat.
b.
The yield curve for Treasury securities would be flat, but the yield curve for corporate securities might be
downward sloping.
c.
The yield curve for Treasury securities cannot be downward sloping.
d.
The maturity risk premium would be zero.
e.
If 2-year bonds yield more than 1-year bonds, an investor with a 2-year time horizon would almost certainly
end up with more money if he or she bought 2-year bonds.
48.
Which of the following statements is CORRECT?
a.
The yield on a 3-year Treasury bond cannot exceed the yield on a 10-year Treasury bond.
b.
The real risk-free rate is higher for corporate than for Treasury bonds.
c.
Most evidence suggests that the maturity risk premium is zero.
d.
Liquidity premiums are higher for Treasury than for corporate bonds.
e.
The pure expectations theory states that the maturity risk premium for long-term Treasury bonds is zero and
that differences in interest rates across different Treasury maturities are driven by expectations about future
interest rates.
49.
Which of the following statements is CORRECT?
a.
The maturity premiums embedded in the interest rates on U.S. Treasury securities are due primarily to the
fact that the probability of default is higher on long-term bonds than on short-term bonds.
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.
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.
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
future.
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.
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.