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Chapter 16 Managing Bond Portfolios
Multiple Choice
Questions
1.
The duration of a bond is
a function of the bond's
A)
coupon rate.
B)
yield to maturity.
C)
time to
maturity.
D)
all of the above.
E)
none of the above.
Answer: D Difficulty:
Easy
Rationale: Duration is calculated by
discounting the bond's cash flows at the bond's
yield to maturity and, except for zero-
coupon bonds, is always less than time to
maturity.
2.
Ceteris paribus, the
duration of a bond is positively correlated with
the bond's
A)
time to maturity.
B)
coupon rate.
C)
yield to maturity.
D)
all of the
above.
E)
none
of the above.
Answer: A
Difficulty: Moderate
Rationale: Duration is negatively
correlated with coupon rate and yield to
maturity.
3.
Holding other factors
constant, the interest-rate risk of a coupon bond
is higher when the
bond's:
A)
term-to-maturity is
lower.
B)
coupon rate is higher.
C)
yield to maturity is
lower.
D)
current yield is higher.
E)
none of the above.
Answer: C Difficulty:
Moderate
Rationale: The longer the maturity, the
greater the interest-rate risk. The lower the
coupon rate, the greater the interest-
rate risk. The lower the yield to maturity, the
greater
the interest-rate risk. These
concepts are reflected in the duration rules;
duration is a
measure of bond price
sensitivity to interest rate changes (interest-
rate risk).
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Chapter 16
Managing Bond Portfolios
4.
The
A)
times the change in interest rate.
B)
times (one plus the
bond's yield to maturity).
C)
divided by (one minus the bond's yield
to maturity).
D)
divided by
(one plus the bond's yield to maturity).
E)
none of the above.
Answer: D Difficulty: Moderate
Rationale: D* = D/(1 + y)
5.
Given the time to
maturity, the duration of a zero-coupon bond is
higher when the
discount rate is
A)
higher.
B)
lower.
C)
equal
to the risk free rate.
D)
The bond's duration is independent of
the discount rate.
E)
none
of the above.
Answer: D Difficulty:
Moderate
Rationale: The
duration of a zero-coupon bond is equal to the
maturity of the bond.
6.
The
interest-rate risk of a bond is
A)
the risk related to the possibility of
bankruptcy of the bond's issuer.
B)
the risk that arises from the
uncertainty of the bond's return caused by changes
in
interest rates.
C)
the unsystematic risk caused by factors
unique in the bond.
D)
A
and B above.
E)
A, B, and C
above.
Answer: B Difficulty:
Moderate
Rationale:
Changing interest rates change the bond's return,
both in terms of the price of
the bond
and the reinvestment of coupon payments.
361
Chapter 16 Managing
Bond Portfolios
7.
Which of the following
two bonds is more price sensitive to changes in
interest rates?
1)
A par value
bond, X, with a 5-year-to-maturity and a 10%
coupon rate.
2)
A
zero-coupon bond, Y, with a 5-year-to-maturity and
a 10% yield-to-maturity.
A)
B)
C)
D)
E)
Bond X because of the
higher yield to maturity.
Bond X
because of the longer time to maturity.
Bond Y because of the longer duration.
Both have the same sensitivity because
both have the same yield to maturity.
None of the above
Answer: C
Difficulty: Moderate
Rationale: Duration is the best measure
of bond price sensitivity; the longer the duration
the higher the price sensitivity.
8.
Holding other factors
constant, which one of the following bonds has the
smallest price
volatility?
A)
5-year, 0% coupon bond
B)
5-year, 12% coupon bond
C)
5 year, 14% coupon bond
D)
5-year, 10% coupon bond
E)
Cannot tell from the
information given.
Answer: C
Difficulty: Moderate
Rationale: Duration (and thus price
volatility) is lower when the coupon rates are
higher.
9.
Which
of the following is
not
true?
A)
Holding other
things constant, the duration of a bond increases
with time to
maturity.
B)
Given time to maturity, the duration of
a zero-coupon decreases with yield to
maturity.
C)
Given time to maturity and yield to
maturity, the duration of a bond is higher when
the coupon rate is lower.
D)
Duration is a better
measure of price sensitivity to interest rate
changes than is time
to maturity.
E)
All of the above.
Answer: B Difficulty: Moderate
Rationale: The duration of
a zero-coupon bond is equal to time to maturity,
and is
independent of yield to
maturity.
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Chapter 16
Managing Bond Portfolios
10.
The duration
of a 5-year zero-coupon bond is
A)
smaller than 5.
B)
larger than
5.
C)
equal to
5.
D)
equal to
that of a 5-year 10% coupon bond.
E)
none of the above.
Answer: C Difficulty:
Easy
Rationale: Duration of a zero-coupon
bond equals the bond's maturity.
11.
The basic
purpose of immunization is to
A)
eliminate default risk.
B)
produce a
zero net interest-rate risk.
C)
offset price and
reinvestment risk.
D)
A and B.
E)
B and C.
Answer: E Difficulty: Moderate
Rationale: When
a portfolio is immunized, price risk and
reinvestment risk exactly
offset each
other resulting in zero net interest-rate risk.
12.
The duration of a par value bond with a
coupon rate of 8% and a remaining time to
maturity of 5 years is
A)
5 years.
B)
5.4 years.
C)
4.17 years.
D)
4.31 years.
E)
none of the above.
Answer: D Difficulty:
Moderate
Rationale:
Calculations are
shown below.
Yr.
CF
PV of CF@08%
Weight * Yr.
1
$$80
$$80/1.08 =
$$74.07
0.0741 * 1 = 0.0741
2
2
$$80
$$80/(1.08)
= $$68.59
0.0686 * 2 = 0.1372
3
3
$$80
$$80/(1.08)
= $$63.51
0.0635 * 3 = 0.1905
4
4
$$80
$$80/(1.08)
= $$58.80
0.0588 * 4 = 0.2352
5
5
$$1,080
$$1,080/(1.08)
= $$735.03
0.7350 * 5 = 3.6750
Sum
$$1000.00
4.3120
yrs. (duration)
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Chapter 16 Managing Bond Portfolios
13.
The duration of a perpetuity with a
yield of 8% is
A)
13.50 years.
B)
12.11 years.
C)
6.66 years.
D)
cannot be determined.
E)
none of the above.
Answer: A Difficulty:
Easy
Rationale: D = 1.08/0.08 = 13.50 years.
14.
A seven-year par value bond has a
coupon rate of 9% and a modified duration of
A)
7 years.
B)
5.49 years.
C)
5.03 years.
D)
4.87 years.
E)
none of the
above.
Answer: C
Difficulty: Difficult
Rationale:
Calculations are
shown below.
Yr.
CF
PV of CF@9%
Weight * Yr.
1
$$90
$$82.57
0.0826 X 1 = 0.0826
2
$$90
$$75.75
0.0758
X 2 = 0.1516
3
$$90
$$69.50
0.0695 X 3 = 0.2085
4
$$90
$$63.76
0.0638 X 4 = 0.2552
5
$$90
$$58.49
0.0585
X 5 = 0.2925
6
$$90
$$53.66
0.0537 X 6 = 0.3222
7
$$1,090
$$596.26
0.5963 X 7 = 4.1741
Sum
$$1000.00
5.4867
years (duration)
modified
duration = 5.4867 years/1.09 = 5.03 years.
15.
Par value bond XYZ has a modified
duration of 6. Which one of the following
statements regarding the bond is
true
?
A)
If the market yield
increases by 1% the bond's price will decrease by
$$60.
B)
If the
market yield increases by 1% the bond's price will
increase by $$50.
C)
If the market yield
increases by 1% the bond's price will decrease by
$$50.
D)
If the market yield increases by 1% the
bond's price will increase by $$60.
E)
None of the above.
Answer: A Difficulty:
Moderate
Rationale: = -D*-$$60 = -6(0.01) X
$$1,000
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Chapter 16
Managing Bond Portfolios
16.
Which of the
following bonds has the longest duration?
A)
An 8-year
maturity, 0% coupon bond.
B)
An 8-year maturity, 5%
coupon bond.
C)
A 10-year maturity, 5% coupon bond.
D)
A 10-year
maturity, 0% coupon bond.
E)
Cannot tell from the
information given.
Answer:
D Difficulty: Moderate
Rationale: The longer the
maturity and the lower the coupon, the greater the
duration
17.
Which one of the following par value
12% coupon bonds experiences a price change of
$$23 when the market yield changes by 50
basis points?
A)
The bond with a duration of 6 years.
B)
The bond with
a duration of 5 years.
C)
The bond with a duration of 2.7 years.
D)
The bond with
a duration of 5.15 years.
E)
None of the above.
Answer: D Difficulty:
Difficult
Rationale: DP/P = -D X [D(1+y) /
(1+y)]; -.023 = -D X [.005 / 1.12]; D = 5.15.
18.
Which one of the following statements
is
true
concerning the
duration of a perpetuity?
A)
The duration of 15% yield
perpetuity that pays $$100 annually is longer than
that of a
15% yield perpetuity that
pays $$200 annually.
B)
The duration of a 15% yield perpetuity
that pays $$100 annually is shorter than that
of a 15% yield perpetuity that pays
$$200 annually.
C)
The duration of a 15% yield perpetuity
that pays $$100 annually is equal to that of
15% yield perpetuity that pays $$200
annually.
D)
the duration of a perpetuity cannot be
calculated.
E)
None of the above.
Answer: C Difficulty: Easy
Rationale:
Duration of a perpetuity = (1 + y)/y; thus, the
duration of a perpetuity is
determined
by the yield and is independent of the cash flow.
365
Chapter 16 Managing
Bond Portfolios
19.
The two
components of interest-rate risk are
A)
price risk and default
risk.
B)
reinvestment risk and systematic risk.
C)
call risk and
price risk.
D)
price risk and reinvestment risk.
E)
none of the
above.
Answer: D
Difficulty: Easy
Rationale: Default, systematic, and
call risks are not part of interest-rate risk.
Only
price and reinvestment risks are
part of interest-rate risk.
20.
The duration
of a coupon bond
A)
does not change after the bond is
issued.
B)
can
accurately predict the price change of the bond
for any interest rate change.
C)
will decrease as the
yield to maturity decreases.
D)
all of the above are
true.
E)
none
of the above is true.
Answer: E Difficulty: Easy
Rationale:
Duration changes as interest rates and time to
maturity change, can only
predict price
changes accurately for small interest rate
changes, and increases as the
yield to
maturity decreases.
21.
Indexing of bond
portfolios is difficult because
A)
the number of bonds
included in the major indexes is so large that it
would be
difficult to purchase them in
the proper proportions.
B)
many bonds are thinly traded so it is
difficult to purchase them at a fair market price.
C)
the composition of bond indexes is
constantly changing.
D)
all of the above are true.
E)
both A and B are true.
Answer: D Difficulty:
Moderate
Rationale: All of the above are true
statements about bond indexes.
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Chapter 16 Managing Bond Portfolios
22.
You have an obligation to pay $$1,488 in
four years and 2 months. In which bond would
you invest your $$1,000 to accumulate
this amount, with relative certainty, even if the
yield on the bond declines to 9.5%
immediately after you purchase the bond?
A)
a
6-year; 10% coupon par value bond
B)
a 5-year; 10% coupon par
value bond
C)
a
5-year; zero-coupon bond
D)
a 4-year; 10% coupon par
value bond
E)
none of the above
Answer: B Difficulty: Difficult
Rationale: When
duration = horizon date, one is immunized, or
protected, against one
interest rate
change. The zero has D = 5. Since the other
bonds have the same coupon
and yield,
solve for the closest value of T that gives D =
4.2 years. 4.2 = (1.10))/.10 -
[(1.10)
+ T(.10-.10)] / = 1.1; .68 (1.10) T - .68 + .68 =
1.1; .68 (1.10) T = 1.1; (1.10) T =
1.6176; T [ln (1.10)] = ln (1.6176); T
= 5.05 years, so choose the 5-year 10% coupon
bond.
23.
Duration measures
A)
weighted
average time until a bond's half-life.
B)
weighted
average time until cash flow payment.
C)
the time required to
recoup one's investment, assuming the bond was
purchased for
$$1,000.
D)
A and C.
E)
B and C.
Answer: E Difficulty: Moderate
Rationale: B
and C are true, as one receives coupon payments
throughout the life of the
bond (for
coupon bonds); thus, duration is less than time to
maturity (except for zeros).
24.
Duration
A)
assesses the time element of bonds in
terms of both coupon and term to maturity.
B)
allows structuring a portfolio to avoid
interest-rate risk.
C)
is a direct comparison between bond
issues with different levels of risk.
D)
A and B.
E)
A and C.
Answer: D Difficulty:
Moderate
Rationale: Duration is a weighted
average of when the cash flows of a bond are
received;
thus both coupon and time to
maturity are considered. If the duration of the
portfolio
equals the investor's horizon
date, the investor is protected against interest
rate changes.
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Chapter 16
Managing Bond Portfolios
25.
Identify the
bond that has the longest duration (no
calculations necessary).
A)
20-year maturity with an
8% coupon.
B)
20-year maturity with a 12% coupon.
C)
15-year
maturity with a 0% coupon.
D)
10-year maturity with a
15% coupon.
E)
12-year maturity with a 12% coupon.
Answer: C Difficulty:
Moderate
Rationale: The lower the coupon, the
longer the duration. The zero-coupon bond is the
ultimate low coupon bond, and thus
would have the longest duration.
26.
When
interest rates decline, the duration of a 10-year
bond selling at a premium
A)
increases.
B)
decreases.
C)
remains the same.
D)
increases at
first, then declines.
E)
decreases at first, then increases.
Answer: A Difficulty:
Moderate
Rationale: The relationship between
interest rates and duration is an inverse one.
27.
An 8%, 30-year corporate bond was
recently being priced to yield 10%. The Macaulay
duration for the bond is 10.20 years.
Given this information, the bond's modified
duration would be________.
A)
8.05
B)
9.44
C)
9.27
D)
11.22
E)
none of the above
Answer: C Difficulty:
Easy
Rationale: D* = D/(1 + y); D* =
10.2/(1.1) = 9.27
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Chapter 16 Managing Bond Portfolios
28.
An 8%, 15-year bond has a yield to
maturity of 10% and duration of 8.05 years. If
the
market yield changes by 25 basis
points, how much change will there be in the
bond's
price?
A)
1.85%
B)
2.01%
C)
3.27%
D)
6.44%
E)
none of the above
Answer: A Difficulty:
Moderate
Rationale:
ΔP/P =
(
-8.05 X 0.0025)/1.1 = 1.85%
29.
One way that banks can reduce the
duration of their asset portfolios is through the
use of
A)
fixed rate mortgages.
B)
adjustable rate
mortgages.
C)
certificates of deposit.
D)
short-term borrowing.
E)
none of the
above.
Answer: B
Difficulty: Easy
Rationale: One of the gap management
strategies practiced by banks is the issuance of
adjustable rate mortgages, which reduce
the interest rate sensitivity of their asset
portfolios.
30.
The duration of a bond
normally increases with an increase in
A)
term to
maturity.
B)
yield to maturity.
C)
coupon rate.
D)
all of the above.
E)
none of the
above.
Answer: A
Difficulty: Moderate
Rationale: The relationship between
duration and term to maturity is a direct one; the
relationship between duration and yield
to maturity and to coupon rate is
negative.
369
Chapter 16 Managing Bond Portfolios
31.
Which one of the following is an
incorrect
statement
concerning duration?
A)
The higher the yield to maturity, the
greater the duration
B)
The higher the coupon, the shorter the
duration.
C)
The difference in duration is small
between two bonds with different coupons each
maturing in more than 15 years.
D)
The duration
is the same as term to maturity only in the case
of zero-coupon bonds.
E)
All of the statements are correct.
Answer: A Difficulty:
Moderate
Rationale: The relationship between
duration and yield to maturity is an inverse one;
as
is the relationship between duration
and coupon rate. The difference in the durations
of
longer-term bonds of varying coupons
(high coupon vs. zero) is considerable. Duration
equals term to maturity only with
zeros.
32.
Immunization is not a strictly passive
strategy because
A)
it requires choosing an asset portfolio
that matches an index.
B)
there is likely to be a gap between the
values of assets and liabilities in most
portfolios.
C)
it requires frequent rebalancing as
maturities and interest rates change.
D)
durations of
assets and liabilities fall at the same rate.
E)
none of the
above.
Answer: C
Difficulty: Moderate
Rationale: As time passes the durations
of assets and liabilities fall at different rates,
requiring portfolio rebalancing.
Further, every change in interest rates creates
changes
in the durations of portfolio
assets and liabilities.
33.
Contingent immunization
A)
is a mixed-
active passive bond portfolio management strategy.
B)
is a strategy
whereby the portfolio may or may not be immunized.
C)
is a strategy
whereby if and when some trigger point value of
the portfolio is
reached, the portfolio
is immunized to insure an minimum required return.
D)
A
and B.
E)
A, B,
and C.
Answer: E
Difficulty: Easy
Rationale: Contingent immunization
insures a minimum average rate of return over
time by immunizing the portfolio if and
when the value of the portfolio reaches the
trigger point required to insure that
rate of return. Thus, the strategy is a
combination
active/passive strategy;
but the portfolio will be immunized only if
necessary.
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Chapter 16 Managing Bond Portfolios
34.
Some of the problems with immunization
are
A)
duration
assumes that the yield curve is flat.
B)
duration assumes that if
shifts in the yield curve occur, these shifts are
parallel.
C)
immunization is valid for one interest
rate change only.
D)
durations and horizon dates change by
the same amounts with the passage of time.
E)
A, B, and C.
Answer: E Difficulty: Moderate
Rationale:
Durations and horizon dates change with the
passage of time, but not by the
same
amounts.
35.
If a bond portfolio manager believes
A)
in market
efficiency, he or she is likely to be a passive
portfolio manager.
B)
that he or she can accurately predict
interest rate changes, he or she is likely to be
an
active portfolio manager.
C)
that he or
she can identify bond market anomalies, he or she
is likely to be a passive
portfolio
manager.
D)
A
and B.
E)
A, B,
and C.
Answer: D
Difficulty: Moderate
Rationale: If one believes that one can
predict bond market anomalies, one is likely to
be an active portfolio manager.
36.
According to experts, most pension
funds are underfunded because
A)
their liabilities are of
shorter duration than their assets.
B)
their assets are of
shorter duration than their liabilities.
C)
they
continually adjust the duration of their
liabilities.
D)
they continually adjust the duration of
their assets.
E)
they are too heavily invested in
stocks.
Answer: B
Difficulty: Moderate
37.
Cash flow matching on a
multiperiod basis is referred to as a
A)
immunization.
B)
contingent
immunization.
C)
dedication.
D)
duration matching.
E)
rebalancing.
Answer: C Difficulty: Easy
Rationale: Cash
flow matching on a multiperiod basis is referred
to as a dedication
strategy.
371
Chapter 16 Managing
Bond Portfolios
38.
Immunization
through duration matching of assets and
liabilities may be ineffective or
inappropriate because
A)
conventional duration
strategies assume a flat yield curve.
B)
duration matching can
only immunize portfolios from parallel shifts in
the yield
curve.
C)
immunization only
protects the nominal value of terminal liabilities
and does not
allow for inflation
adjustment.
D)
both A and C are true.
E)
all of the above are
true.
Answer: E
Difficulty: Easy
Rationale: All of the above are correct
statements about the limitations of immunization
through duration matching.
39.
The
curvature of the price-yield curve for a given
bond is referred to as the bond's
A)
modified duration.
B)
immunization.
C)
sensitivity.
D)
convexity.
E)
tangency.
Answer: D Difficulty:
Easy
Rationale: Convexity measures the rate
of change of the slope of the price-yield curve,
expressed as a fraction of the bond's
price.
40.
Consider a bond selling at par with
modified duration of 10.6 years and convexity of
210. A 2 percent decrease in yield
would cause the price to increase by 21.2%,
according to the duration rule. What
would be the percentage price change according to
the duration-with-convexity rule?
A)
21.2%
B)
25.4%
C)
17.0%
D)
10.6%
E)
none of the
above.
Answer: B
Difficulty: Difficult
Rationale:
?
P/P =
-D*
?
y + (1/2) * Convexity *
(
?
y)
2
;
= -10.6 * -.02 + (1/2) * 210 *
(.02)
2
= .212 +
.042 = .254 (25.4%)
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Chapter 16 Managing Bond Portfolios
41.
A
substitution
swap
is an exchange of bonds undertaken
to
A)
change
the credit risk of a portfolio.
B)
extend the duration of a
portfolio.
C)
reduce the duration of a portfolio.
D)
profit from
apparent mispricing between two bonds.
E)
adjust for
differences in the yield spread.
Answer: D Difficulty: Moderate
Rationale: A
substitution swap is an example of bond price
arbitrage, undertaken when
the
portfolio manager attempts to profit from apparent
mispricing.
42.
A
rate anticipation
swap
is an exchange of bonds undertaken
to
A)
shift
portfolio duration in response to an anticipated
change in interest rates.
B)
shift between corporate
and government bonds when the yield spread is out
of line
with historical values.
C)
profit from
apparent mispricing between two bonds.
D)
change the
credit risk of the portfolio.
E)
increase return by
shifting into higher yield bonds.
Answer: A Difficulty: Moderate
Rationale: A
rate anticipation swap is pegged to interest rate
forecasting, and involves
increasing
duration when rates are expected to fall and vice-
versa.
43.
An analyst who selects a particular
holding period and predicts the yield curve at the
end
of that holding period is engaging
in
A)
a rate
anticipation swap.
B)
immunization.
C)
horizon analysis.
D)
an
intermarket spread swap.
E)
none of the above.
Answer: C Difficulty:
Easy
Rationale: Horizon analysis involves
selecting a particular holding period and
predicting the yield curve at the end
of that holding period. The holding period return
for the bond can then be predicted.
373
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