cristiano-zizi
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.
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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 = $$74.07
0.0741 * 1 = 0.0741
2
$$80
$$80/(1.08)
2
= $$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.
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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.
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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.
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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.
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