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Chapter 11 - Managing Bond Portfolios

Chapter 11
Managing Bond Portfolios

Multiple Choice Questions

1. All other things equal, which of the following has the longest duration?
A. A 30 year bond with a 10% coupon
B. A 20 year bond with a 9% coupon
C. A 20 year bond with a 7% coupon
D. A 10 year zero coupon bond

2. All other things equal, which of the following has the shortest duration?
A. A 30 year bond with a 10% coupon
B. A 20 year bond with a 9% coupon
C. A 20 year bond with a 7% coupon
D. A 10 year zero coupon bond

3. A pension fund must pay out \$1 million next year, \$2 million the following year and then
\$3 million the year after that. If the discount rate is 8% what is the duration of this set of
payments?
A. 2.00 years
B. 2.15 years
C. 2.29 years
D. 2.53 years

4. All other things equal, which of the following has the longest duration?
A. A 20 year bond with a 10% coupon yielding 10%
B. A 20 year bond with a 10% coupon yielding 11%
C. A 20 year zero coupon bond yielding 10%
D. A 20 year zero coupon bond yielding 11%

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Chapter 11 - Managing Bond Portfolios

5. The duration of a perpetuity varies _______ with interest rates.
A. directly
B. inversely
C. convexly
D. randomly

6. Because of convexity, when interest rates change the actual bond price will ____________
the bond price predicted by duration.
A. always be higher than
B. sometimes be higher than
C. always be lower than
D. sometimes be lower than

7. You find a 5 year AA Xerox bond priced to yield 6%. You find a similar risk 5 year Canon
bond priced to yield 6.5%. To take advantage of this you should do which of the following?
A. Short the Canon bond and buy the Xerox bond
B. Buy the Canon bond and short the Xerox bond
C. Short both the Canon bond and the Xerox bond
D. Buy both the Canon bond and the Xerox bond

8. A forecast of bond returns based largely on a prediction of the yield curve at the end of the
investment horizon is called a _________.
A. contingent immunization
B. dedication strategy
C. duration analysis
D. horizon analysis

9. A bond's price volatility _________ at a/an _________ rate as maturity increases.
A. increases; increasing
B. increases; decreasing
C. decreases; increasing
D. decreases; decreasing

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10. As a result of bond convexity an increase in a bond's price when yield to maturity falls is
________ the price decrease resulting from an increase in yield of equal magnitude.
A. greater than
B. equivalent to
C. smaller than

11. All else equal, bond price volatility is greater for __________.
A. higher coupon rates
B. lower coupon rates
C. shorter maturity
D. lower default risk

12. ______________ is an important characteristic of the relationship between bond prices
and yields.
A. Convexity
B. Concavity
C. Complexity
D. Linearity

13. Bond prices are _______ sensitive to changes in yield when the bond is selling at a
_______ initial yield to maturity.
A. more; lower
B. more; higher
C. less; lower
D. equally; higher or lower

14. The pioneer of the duration concept was _________.
A. Eugene Fama
B. John Herzog
C. Frederick Macaulay
D. Harry Markowitz

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15. A portfolio manager sells treasury bonds and buys corporate bonds because the spread
between corporate and Treasury bond yields is higher than its historical average. This is an
example of __________ swap.
A. a pure yield pick up
B. a rate anticipation
C. a substitution

16. The duration of a 5-year zero coupon bond is ____ years.
A. 4.5
B. 5.0
C. 5.5
D. 3.5

17. A portfolio manager believes interest rates will drop and decides to sell short duration
bonds and buy long duration bonds. This is an example of __________ swap.
A. a pure yield pick up
B. a rate anticipation
C. a substitution

18. Target date immunization would primarily be of interest to _________.
A. banks
B. mutual funds
C. pension funds
D. individual investors

19. Duration is a concept that is useful in assessing a bond's _________.
A. credit risk
B. liquidity risk
C. price volatility
D. convexity risk

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20. A pension fund has an average duration of its liabilities equal to 15 years. The fund is
looking at 5 year maturity zero coupon bonds and 4% yield perpetuities to immunize its
interest rate risk. How much of its portfolio should it allocate to the zero coupon bonds to
immunize if there are no other assets funding the plan?
A. 52%
B. 48%
C. 33%
D. 25%

21. You own a bond that has a duration of 6 years. Interest rates are currently 7% but you
believe the Fed is about to increase interest rates by 25 basis points. Your predicted price
change on this bond is ________.
A. +1.40%
B. -1.40%
C. -2.51%
D. +2.51%

22. Given its time to maturity the duration of a zero coupon bond is _________.
A. higher when the discount rate is higher
B. higher when the discount rate is lower
C. lowest when the discount rate is equal to the risk free rate
D. the same regardless of the discount rate

23. An increase in a bond's yield to maturity results in a price decline that is ________ the
price increase resulting from a decrease in yield of equal magnitude.
A. greater than
B. equivalent to
C. smaller than

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24. All other things equal, a bond's duration is _________.
A. higher when the yield to maturity is higher
B. lower when the yield to maturity is higher
C. the same at all yield rates
D. indeterminable when the yield to maturity is high

25. A bank has an average duration of its liabilities equal to 2 years. The bank's average
duration of its assets is 3.5 years. The bank's market value of equity is at risk if
_______________________.
A. interest rates fall
C. interest rates rise
D. the price of all fixed income securities rises

26. All other things equal, a bond's duration is _________.
A. higher when the coupon rate is higher
B. lower when the coupon rate is higher
C. the same when the coupon rate is higher
D. indeterminate when the coupon rate is high

27. Banks and other financial institutions can best manage interest rate risk by
_____________.
A. maximizing the duration of assets and minimizing the duration of liabilities
B. minimizing the duration of assets and maximizing the duration of liabilities
C. matching the durations of their assets and liabilities
D. matching the maturities of their assets and liabilities

28. In the context of a bond portfolio, price risk and reinvestment rate risk exactly cancel out
at a time horizon equal to ____.
A. the average bond maturity in the portfolio
B. the duration of the portfolio
C. the difference between the shortest duration and longest duration of the individual bonds in
the portfolio
D. the average of the shortest duration and longest duration of the bonds in the portfolio

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29. Bond portfolio immunization techniques balance ________ and ________ risk.
A. price; reinvestment
B. price; liquidity
C. credit; reinvestment
D. credit; liquidity

30. You have purchased a Guaranteed Investment contracts (GICs) from an insurance firm
that promises to pay you a 5% compound rate of return per year for 6 years. If you pay
\$10,000 for the GIC today and receive no interest along the way you will get __________ in 6
years (to the nearest dollar).
A. \$12,565
B. \$13,000
C. \$13,401
D. \$13,676

31. The duration of a portfolio of bonds can be calculated as _______________.
A. the coupon weighted average of the durations of the individual bonds in the portfolio
B. the yield weighted average of the durations of the individual bonds in the portfolio
C. the value weighed average of the durations of the individual bonds in the portfolio
D. averages of the durations of the longest and shortest duration bonds in the portfolio

32. Pension fund managers can generally best bring about an effective reduction in their
interest rate risk by holding ___________________.
A. long maturity bonds
B. long duration bonds
C. short maturity bonds
D. short duration bonds

33. Which of the following is not a type of bond swap used in active portfolio management?
B. Substitution swap
C. Rate anticipation swap
D. Asset-liability swap

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34. The exchange of one bond for a bond with similar attributes but more attractively priced is
called ______________.
A. a substitution swap
C. rate anticipation swap
D. pure yield pickup swap

35. Rank the interest sensitivity of the following from most sensitive to an interest rate change
to the least sensitive.
I. 8% coupon, noncallable 20 year maturity, par bond
II. 9% coupon, currently callable 20 year maturity, premium bond
III. Zero coupon, 30 year maturity bond
A. I, II, III
B. II, III, I
C. III, I, II
D. III, II, I

36. A bond swap made in response to forecasts of interest rate changes is called ______.
A. a substitution swap
C. rate anticipation swap
D. pure yield pickup swap

37. Moving to higher yield bonds, usually with longer maturities is called ________.
A. a substitution swap
C. rate anticipation swap
D. pure yield pickup swap

38. In a pure yield pickup swap, ________ bonds are exchanged for _________ bonds.
A. longer duration; shorter duration
B. shorter duration; longer duration
C. high coupon; high yield
D. low yield; high yield

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39. The duration rule always ________ the value of a bond following a change in its yield.
A. under-estimates
B. provides an unbiased estimate of
C. over-estimates
D. The estimated price may be biased either upward or downward, depending on whether the

40. Where Y = yield to maturity, the duration of a perpetuity would be _________.
A. Y
B. Y/(1 + Y)
C. 1/Y
D. (1 + Y)/Y

41. A bond currently has a price of \$1,050. The yield on the bond is 6.00%. If the yield
increases 25 basis points, the price of the bond will go down to \$1,030. The duration of this
bond is ____ years.
A. 7.46
B. 8.08
C. 9.02
D. 10.11

42. A bond has a current price of \$1,030. The yield on the bond is 8.00%. If the yield changes
from 8.00% to 8.10%, the price of the bond will go down to \$1,025.88. The modified duration
of this bond is _________.
A. 4.32
B. 4.00
C. 3.25
D. 3.75

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43. A bank has \$50 million in assets, \$47 million in liabilities and \$3 million in shareholders'
equity. If the duration of its liabilities are 1.3 and the bank wants to immunize its net worth
against interest rate risk and thus set the duration of equity equal to zero, it should select
assets with an average duration of _________.
A. 1.22
B. 1.50
C. 1.60
D. 2.00

44. A perpetuity pays \$100 each and every year forever. The duration of this perpetuity will
be __________ if its yield is 9%.
A. 7
B. 9
C. 9.39
D. 12.11

A bond pays annual interest. Its coupon rate is 9%. Its value at maturity is \$1,000. It matures
in four years. Its yield to maturity is currently 6%.

45. The duration of this bond is _______ years.
A. 2.44
B. 3.23
C. 3.56
D. 4.10

46. The modified duration of this bond is ______ years.
A. 4.00
B. 3.56
C. 3.36
D. 3.05

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47. A bond has a maturity of 12 years, a duration of 9.5 years at a promised yield rate of 8%.
What is the bond's modified duration?
A. 12 years
B. 11.1 years
C. 9.5 years
D. 8.8 years

48. A 20-year maturity bond pays interest of \$90 once per year and has a face value of \$1,000.
Its yield to maturity is 10%. Over the upcoming year, you expect interest rates to decline and
that the yield to maturity on this bond will only be 8% a year from now. Using horizon
analysis, the return you expect to earn by holding this bond over the upcoming year is
_________.
A. 10.0%
B. 12.0%
C. 21.6%
D. 29.6%

49. A bond with a 9-year duration is worth \$1,080.00 and its yield to maturity is 8%. If the
yield to maturity falls to 7.84%, you would predict that the new value of the bond will be
_________.
A. \$1,035
B. \$1,036
C. \$1,094
D. \$1,124

50. When interest rates increase, the duration of a 20-year bond selling at a premium
_________.
A. increases
B. decreases
C. remains the same
D. increases at first, then declines

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51. Duration facilitates the comparison of bonds with differing ___________.
A. default risk
B. conversion ratios
C. maturities
D. yields to maturity

52. The historical yield spread between the AA bond and the AAA bond has been 25 basis
its historical levels you should ________________________.
A. buy the AA and short the AAA
B. buy both the AA and the AAA
C. buy the AAA and short the AA
D. short both the AA and the AAA

53. The duration of a bond normally increases with an increase in _________.
I. term-to-maturity
II. yield-to-maturity.
III. coupon rate
A. I only
B. I and II only
C. II and III only
D. I, II and III

54. A fixed income portfolio manager sets a minimum acceptable rate of return on the bond
portfolio at 5% per year over the next 4 years. The portfolio is currently worth \$10 million.
One year later interest rates are at 6%. What is the portfolio value trigger point at this time
that would require him to immunize the portfolio?
A. \$12,155,063
B. \$10,205,625
C. \$9,627,948
D. \$10,500,000

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55. Compute the duration of an 8%, 5-year corporate bond with a par value of \$1000 if yield
to maturity of 10%.
A. 3.92
B. 4.28
C. 4.55
D. 5.00

56. Compute the modified duration of a 9% coupon, 3-year corporate bond with a yield to
maturity of 12%.
A. 2.45
B. 2.75
C. 2.88
D. 3.00

57. An 8%, 30-year bond has a yield-to-maturity of 10% and a modified duration of 8.0 years.
If the market yield drops by 15 basis points, there will be a __________ in the bond's price.
A. 1.15% decrease
B. 1.20% increase
C. 1.53% increase
D. 2.43% decrease

58. To create a portfolio with a duration of 4 years using a 5 year zero-coupon bond and a 3
year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest
________ of the portfolio value in the zero-coupon bond.
A. 50%
B. 55%
C. 60%
D. 75%

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59. Which of the following set of conditions will result in a bond with the greatest price
volatility?
A. A high coupon and a short maturity.
B. A high coupon and a long maturity.
C. A low coupon and a short maturity.
D. A low coupon and a long maturity.

60. An investor who expects declining interest rates would maximize their capital gain by
purchasing a bond that has a ___ coupon and a ___ term to maturity.
A. low; long
B. high; short
C. high; long
D. zero; long

61. If you choose a zero coupon bond with a maturity that matches your investment horizon
which of the following statements is/are correct?
I. You will have no interest rate risk on this bond.
II. Absent default, you can be sure you will earn the promised yield rate.
III. The duration of your bond is less than the time to your investment horizon.
A. I only
B. I and II only
C. II and III only
D. I, II and III

62. As compared with equivalent maturity bonds selling at par, deep discount bonds will have
________.
A. greater reinvestment risk
B. greater price volatility
C. less call protection
D. shorter average maturity

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Steel Pier Company has issued bonds that pay semiannually with the following
characteristics:

63. The modified duration for the Steel Pier bond is ______.
A. 6.15 years
B. 5.95 years
C. 6.49 years
D. 9.09 years

64. If the bond's coupon was smaller than 10%, the modified duration would be _____
compared to the original modified duration.
A. larger
B. unchanged
C. smaller
D. There is not enough information to determine the direction of change

65. If the maturity of the bond was less than 10 years, the modified duration would be _____
compared to the original modified duration.
A. larger
B. unchanged
C. smaller
D. There is not enough information to determine the direction of change

66. If the yield to maturity decreases to 8.045% the expected percentage change in the price of
the bond using Macauley's duration would be ____, while the expected percentage change in
the price of the bond using modified duration would be ____.
A. 11%, 12%
B. 12%, 11%
C. 12%, 12%
D. 11%, 11%

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67. A 20 year maturity corporate bond has a 6.5% coupon rate (the coupons are paid
annually). The bond currently sells for \$925.50. A bond market analyst forecasts that in five
years yield rates on these bonds will be at 7.0%. You believe that you will be able to reinvest
the coupons earned over the next five years at a 6% rate of return. What is your expected
annual compound rate of return if you plan on selling the bond in five years?
A. 7.37%
B. 7.56%
C. 8.12%
D. 8.54%

68. When bonds sell above par, what is the relationship of price sensitivity to rising interest
rates?
A. Price volatility increases at an increasing rate
B. Price volatility increases at a decreasing rate
C. Price volatility decreases at a decreasing rate
D. Price volatility decreases at an increasing rate

69. A zero coupon bond is selling at a deep discount price of \$430.00. It matures in 13 years.
If the yield to maturity of the bond is 6.7%, what is the duration of the bond?
A. 6.7 years
B. 8.0 years
C. 10 years
D. 13 years

70. You have an investment that in today's dollars returns 15% of your investment in year 1,
12% in year two, 9% in year 3 and the remainder in year 4. What is the duration of this
investment?
A. 4 years
B. 3.50 years
C. 3.22 years
D. 2.95 years

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71. If an investment returns a higher percentage of your money back sooner it will ______.
A. be less price volatile
B. have a higher credit rating
C. be less liquid
D. have a higher modified duration

72. Which one of the following statements correctly describes the weights used in the
Macaulay duration calculation? The weight in year t is equal to ____________.
A. the dollar amount of the investment received in year t
B. the percentage of the future value of the investment received in year t
C. the present value of the dollar amount of the investment received in year t
D. the percentage of the total present value of the investment received in year t

73. The duration is independent of the coupon rate only for which one of the following?
A. Discount bonds
C. Perpetuities
D. Short term bonds

74. You have an investment horizon of 6 years. You choose to hold a bond with a duration of
10 years. Your realized rate of return will be larger than the promised yield on the bond if
___________________.
A. interest rates increase
B. interest rates stay the same
C. interest rates fall
D. one can't tell with the information given

75. A bond portfolio manager notices a hump in the yield curve at the five year point. How
might a bond manager take advantage of this event?
A. Buy the 5 year bonds and short the surrounding maturity bonds
B. Buy the 5 year bonds and buy the surrounding maturity bonds
C. Short the 5 year bonds and short the surrounding maturity bonds
D. Short the 5 year bonds and buy the surrounding maturity bonds

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76. Market economists all predict a rise in interest rates. An astute bond manager wishing to
maximize her capital gain might employ which strategy?
A. Switch from low duration to high duration bonds.
B. Switch from high duration to low duration bonds.
D. Switch from low coupon to high coupon bonds.

77. You have an investment horizon of 6 years. You choose to hold a bond with a duration of
4 years. Your realized rate of return will be larger than the promised yield on the bond if
___________________.
A. interest rates increase
B. interest rates stay the same
C. interest rates fall
D. one can't tell with the information given

78. What strategy might an insurance company employ to ensure that it will be able to meet
the obligations of annuity holders?
A. Cash flow matching
B. Index tracking
C. Yield pickup swaps
D. Substitution swap

79. You have an investment horizon of 6 years. You choose to hold a bond with a duration of
6 years and continue to match your investment horizon and duration throughout your holding
period. Your realized rate of return will be the same as the promised yield on the bond if
I. interest rates increase
II. interest rates stay the same
III. interest rates fall
A. I only
B. II only
C. I and II only
D. I, II and III

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80. Immunization of coupon paying bonds is not a passive strategy because
I. the portfolio must be rebalanced every time interest rates change
II. the portfolio must be rebalanced over time even if interest rates don't change
III. convexity implies duration based immunization strategies don't work
A. I only
B. I and II only
C. II only
D. I, II and III

81. Advantages of cash flow matching and dedicated strategies include ______.
I. once the cash flows are matched there is no need for rebalancing
II. cash flow matching typically earns a higher rate of return than active bond portfolio
management
III. financial institution's liabilities often exceed the maturity of available bonds, making cash
matching even more desirable
A. I only
B. II only
C. I and III only
D. I, II and III

82. Convexity implies that duration predictions _______.
I. underestimate the % increase in bond price when the yield falls
II. underestimate the % decrease in bond price when the yield rises
III. overestimates the % increase in bond price when the yield falls
IV. overestimates the % decrease in bond price when the yield rises
A. I and III only
B. II and IV only
C. I and IV only
D. II and III only

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83. You have a 25 year maturity 10% coupon, 10% yield bond with duration of 10 years and a
convexity of 135.50. If interest rate were to fall 125 basis points your predicted new price for
the bond (including convexity) is _________.
A. \$1098.45
B. \$1104.56
C. \$1113.41
D. \$1124.20

84. You have a 15 year maturity 4% coupon, 6% yield bond with duration of 10.5 years and a
convexity of 128.75. The bond is currently priced at \$805.76. If interest rate were to increase
200 basis points your predicted new price for the bond (including convexity) is _________.
A. \$638.85
B. \$642.54
C. \$666.88
D. \$705.03

85. Convexity of a bond is ___________.
A. the same as horizon analysis
B. the rate of change of the price-yield curve divided by bond price
C. a measure of bond duration
D. none of the above

Chapter 11 Managing Bond Portfolios Answer Key

Multiple Choice Questions

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1. All other things equal, which of the following has the longest duration?
A. A 30 year bond with a 10% coupon
B. A 20 year bond with a 9% coupon
C. A 20 year bond with a 7% coupon
D. A 10 year zero coupon bond

Difficulty: Medium

2. All other things equal, which of the following has the shortest duration?
A. A 30 year bond with a 10% coupon
B. A 20 year bond with a 9% coupon
C. A 20 year bond with a 7% coupon
D. A 10 year zero coupon bond

Difficulty: Medium

3. A pension fund must pay out \$1 million next year, \$2 million the following year and then
\$3 million the year after that. If the discount rate is 8% what is the duration of this set of
payments?
A. 2.00 years
B. 2.15 years
C. 2.29 years
D. 2.53 years

Difficulty: Hard

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4. All other things equal, which of the following has the longest duration?
A. A 20 year bond with a 10% coupon yielding 10%
B. A 20 year bond with a 10% coupon yielding 11%
C. A 20 year zero coupon bond yielding 10%
D. A 20 year zero coupon bond yielding 11%

Difficulty: Medium

5. The duration of a perpetuity varies _______ with interest rates.
A. directly
B. inversely
C. convexly
D. randomly

Difficulty: Medium

6. Because of convexity, when interest rates change the actual bond price will ____________
the bond price predicted by duration.
A. always be higher than
B. sometimes be higher than
C. always be lower than
D. sometimes be lower than

Difficulty: Easy

7. You find a 5 year AA Xerox bond priced to yield 6%. You find a similar risk 5 year Canon
bond priced to yield 6.5%. To take advantage of this you should do which of the following?
A. Short the Canon bond and buy the Xerox bond
B. Buy the Canon bond and short the Xerox bond
C. Short both the Canon bond and the Xerox bond
D. Buy both the Canon bond and the Xerox bond

Difficulty: Medium

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8. A forecast of bond returns based largely on a prediction of the yield curve at the end of the
investment horizon is called a _________.
A. contingent immunization
B. dedication strategy
C. duration analysis
D. horizon analysis

Difficulty: Easy

9. A bond's price volatility _________ at a/an _________ rate as maturity increases.
A. increases; increasing
B. increases; decreasing
C. decreases; increasing
D. decreases; decreasing

Difficulty: Easy

10. As a result of bond convexity an increase in a bond's price when yield to maturity falls is
________ the price decrease resulting from an increase in yield of equal magnitude.
A. greater than
B. equivalent to
C. smaller than

Difficulty: Medium

11. All else equal, bond price volatility is greater for __________.
A. higher coupon rates
B. lower coupon rates
C. shorter maturity
D. lower default risk

Difficulty: Easy

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12. ______________ is an important characteristic of the relationship between bond prices
and yields.
A. Convexity
B. Concavity
C. Complexity
D. Linearity

Difficulty: Medium

13. Bond prices are _______ sensitive to changes in yield when the bond is selling at a
_______ initial yield to maturity.
A. more; lower
B. more; higher
C. less; lower
D. equally; higher or lower

Difficulty: Easy

14. The pioneer of the duration concept was _________.
A. Eugene Fama
B. John Herzog
C. Frederick Macaulay
D. Harry Markowitz

Difficulty: Easy

15. A portfolio manager sells treasury bonds and buys corporate bonds because the spread
between corporate and Treasury bond yields is higher than its historical average. This is an
example of __________ swap.
A. a pure yield pick up
B. a rate anticipation
C. a substitution

Difficulty: Easy

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16. The duration of a 5-year zero coupon bond is ____ years.
A. 4.5
B. 5.0
C. 5.5
D. 3.5

Difficulty: Easy

17. A portfolio manager believes interest rates will drop and decides to sell short duration
bonds and buy long duration bonds. This is an example of __________ swap.
A. a pure yield pick up
B. a rate anticipation
C. a substitution

Difficulty: Easy

18. Target date immunization would primarily be of interest to _________.
A. banks
B. mutual funds
C. pension funds
D. individual investors

Difficulty: Easy

19. Duration is a concept that is useful in assessing a bond's _________.
A. credit risk
B. liquidity risk
C. price volatility
D. convexity risk

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

20. A pension fund has an average duration of its liabilities equal to 15 years. The fund is
looking at 5 year maturity zero coupon bonds and 4% yield perpetuities to immunize its
interest rate risk. How much of its portfolio should it allocate to the zero coupon bonds to
immunize if there are no other assets funding the plan?
A. 52%
B. 48%
C. 33%
D. 25%

Durperpetuity =   = 26 years
15 = (wz)(5) + (1 - wz) 26; wz = 52.38%

Difficulty: Hard

21. You own a bond that has a duration of 6 years. Interest rates are currently 7% but you
believe the Fed is about to increase interest rates by 25 basis points. Your predicted price
change on this bond is ________.
A. +1.40%
B. -1.40%
C. -2.51%
D. +2.51%

%P = (-6)           = -1.40%

Difficulty: Medium

22. Given its time to maturity the duration of a zero coupon bond is _________.
A. higher when the discount rate is higher
B. higher when the discount rate is lower
C. lowest when the discount rate is equal to the risk free rate
D. the same regardless of the discount rate

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

23. An increase in a bond's yield to maturity results in a price decline that is ________ the
price increase resulting from a decrease in yield of equal magnitude.
A. greater than
B. equivalent to
C. smaller than

Difficulty: Medium

24. All other things equal, a bond's duration is _________.
A. higher when the yield to maturity is higher
B. lower when the yield to maturity is higher
C. the same at all yield rates
D. indeterminable when the yield to maturity is high

Difficulty: Medium

25. A bank has an average duration of its liabilities equal to 2 years. The bank's average
duration of its assets is 3.5 years. The bank's market value of equity is at risk if
_______________________.
A. interest rates fall
C. interest rates rise
D. the price of all fixed income securities rises

Difficulty: Medium

26. All other things equal, a bond's duration is _________.
A. higher when the coupon rate is higher
B. lower when the coupon rate is higher
C. the same when the coupon rate is higher
D. indeterminate when the coupon rate is high

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

27. Banks and other financial institutions can best manage interest rate risk by
_____________.
A. maximizing the duration of assets and minimizing the duration of liabilities
B. minimizing the duration of assets and maximizing the duration of liabilities
C. matching the durations of their assets and liabilities
D. matching the maturities of their assets and liabilities

Difficulty: Medium

28. In the context of a bond portfolio, price risk and reinvestment rate risk exactly cancel out
at a time horizon equal to ____.
A. the average bond maturity in the portfolio
B. the duration of the portfolio
C. the difference between the shortest duration and longest duration of the individual bonds in
the portfolio
D. the average of the shortest duration and longest duration of the bonds in the portfolio

Difficulty: Easy

29. Bond portfolio immunization techniques balance ________ and ________ risk.
A. price; reinvestment
B. price; liquidity
C. credit; reinvestment
D. credit; liquidity

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

30. You have purchased a Guaranteed Investment contracts (GICs) from an insurance firm
that promises to pay you a 5% compound rate of return per year for 6 years. If you pay
\$10,000 for the GIC today and receive no interest along the way you will get __________ in 6
years (to the nearest dollar).
A. \$12,565
B. \$13,000
C. \$13,401
D. \$13,676

(10,000)(1.05)6 = \$13,401

Difficulty: Easy

31. The duration of a portfolio of bonds can be calculated as _______________.
A. the coupon weighted average of the durations of the individual bonds in the portfolio
B. the yield weighted average of the durations of the individual bonds in the portfolio
C. the value weighed average of the durations of the individual bonds in the portfolio
D. averages of the durations of the longest and shortest duration bonds in the portfolio

Difficulty: Medium

32. Pension fund managers can generally best bring about an effective reduction in their
interest rate risk by holding ___________________.
A. long maturity bonds
B. long duration bonds
C. short maturity bonds
D. short duration bonds

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

33. Which of the following is not a type of bond swap used in active portfolio management?
B. Substitution swap
C. Rate anticipation swap
D. Asset-liability swap

Difficulty: Easy

34. The exchange of one bond for a bond with similar attributes but more attractively priced is
called ______________.
A. a substitution swap
C. rate anticipation swap
D. pure yield pickup swap

Difficulty: Easy

35. Rank the interest sensitivity of the following from most sensitive to an interest rate change
to the least sensitive.
I. 8% coupon, noncallable 20 year maturity, par bond
II. 9% coupon, currently callable 20 year maturity, premium bond
III. Zero coupon, 30 year maturity bond
A. I, II, III
B. II, III, I
C. III, I, II
D. III, II, I

Difficulty: Hard

36. A bond swap made in response to forecasts of interest rate changes is called ______.
A. a substitution swap
C. rate anticipation swap
D. pure yield pickup swap

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

37. Moving to higher yield bonds, usually with longer maturities is called ________.
A. a substitution swap
C. rate anticipation swap
D. pure yield pickup swap

Difficulty: Easy

38. In a pure yield pickup swap, ________ bonds are exchanged for _________ bonds.
A. longer duration; shorter duration
B. shorter duration; longer duration
C. high coupon; high yield
D. low yield; high yield

Difficulty: Easy

39. The duration rule always ________ the value of a bond following a change in its yield.
A. under-estimates
B. provides an unbiased estimate of
C. over-estimates
D. The estimated price may be biased either upward or downward, depending on whether the

Difficulty: Medium

40. Where Y = yield to maturity, the duration of a perpetuity would be _________.
A. Y
B. Y/(1 + Y)
C. 1/Y
D. (1 + Y)/Y

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

41. A bond currently has a price of \$1,050. The yield on the bond is 6.00%. If the yield
increases 25 basis points, the price of the bond will go down to \$1,030. The duration of this
bond is ____ years.
A. 7.46
B. 8.08
C. 9.02
D. 10.11

P =                 = -0.019

P = -0.019 = -Dur              ; Dur = 8.08

Difficulty: Medium

42. A bond has a current price of \$1,030. The yield on the bond is 8.00%. If the yield changes
from 8.00% to 8.10%, the price of the bond will go down to \$1,025.88. The modified duration
of this bond is _________.
A. 4.32
B. 4.00
C. 3.25
D. 3.75

P =                      = -0.004

P = -0.004 = -Dur               ; Dur = 4.32

DurMOD =             =4

Difficulty: Hard

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Chapter 11 - Managing Bond Portfolios

43. A bank has \$50 million in assets, \$47 million in liabilities and \$3 million in shareholders'
equity. If the duration of its liabilities are 1.3 and the bank wants to immunize its net worth
against interest rate risk and thus set the duration of equity equal to zero, it should select
assets with an average duration of _________.
A. 1.22
B. 1.50
C. 1.60
D. 2.00

(50,000,000)(DA) = (47,000,000) (1.3); DA = 1.22

Difficulty: Medium

44. A perpetuity pays \$100 each and every year forever. The duration of this perpetuity will
be __________ if its yield is 9%.
A. 7
B. 9
C. 9.39
D. 12.11

Difficulty: Medium

A bond pays annual interest. Its coupon rate is 9%. Its value at maturity is \$1,000. It matures
in four years. Its yield to maturity is currently 6%.

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Chapter 11 - Managing Bond Portfolios

45. The duration of this bond is _______ years.
A. 2.44
B. 3.23
C. 3.56
D. 4.10

Duration = 3.56

Difficulty: Hard

46. The modified duration of this bond is ______ years.
A. 4.00
B. 3.56
C. 3.36
D. 3.05

DurMOD = 3.56/1.06 = 3.36 years

Difficulty: Hard

47. A bond has a maturity of 12 years, a duration of 9.5 years at a promised yield rate of 8%.
What is the bond's modified duration?
A. 12 years
B. 11.1 years
C. 9.5 years
D. 8.8 years

DurMOD = 9.5/1.08 = 8.8 years

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

48. A 20-year maturity bond pays interest of \$90 once per year and has a face value of \$1,000.
Its yield to maturity is 10%. Over the upcoming year, you expect interest rates to decline and
that the yield to maturity on this bond will only be 8% a year from now. Using horizon
analysis, the return you expect to earn by holding this bond over the upcoming year is
_________.
A. 10.0%
B. 12.0%
C. 21.6%
D. 29.6%

(use financial calculator to calculate PV10%, 20 and
PV8%, 19)

Difficulty: Hard

49. A bond with a 9-year duration is worth \$1,080.00 and its yield to maturity is 8%. If the
yield to maturity falls to 7.84%, you would predict that the new value of the bond will be
_________.
A. \$1,035
B. \$1,036
C. \$1,094
D. \$1,124

Difficulty: Hard

50. When interest rates increase, the duration of a 20-year bond selling at a premium
_________.
A. increases
B. decreases
C. remains the same
D. increases at first, then declines

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

51. Duration facilitates the comparison of bonds with differing ___________.
A. default risk
B. conversion ratios
C. maturities
D. yields to maturity

Difficulty: Easy

52. The historical yield spread between the AA bond and the AAA bond has been 25 basis
its historical levels you should ________________________.
A. buy the AA and short the AAA
B. buy both the AA and the AAA
C. buy the AAA and short the AA
D. short both the AA and the AAA

Difficulty: Medium

53. The duration of a bond normally increases with an increase in _________.
I. term-to-maturity
II. yield-to-maturity.
III. coupon rate
A. I only
B. I and II only
C. II and III only
D. I, II and III

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

54. A fixed income portfolio manager sets a minimum acceptable rate of return on the bond
portfolio at 5% per year over the next 4 years. The portfolio is currently worth \$10 million.
One year later interest rates are at 6%. What is the portfolio value trigger point at this time
that would require him to immunize the portfolio?
A. \$12,155,063
B. \$10,205,625
C. \$9,627,948
D. \$10,500,000

Minimum terminal value = (\$10 mill.)(1.05)4 = \$12,155,062.50
Trigger point value = \$12,155,062.50/1.063 = \$10,205,625

Difficulty: Hard

55. Compute the duration of an 8%, 5-year corporate bond with a par value of \$1000 if yield
to maturity of 10%.
A. 3.92
B. 4.28
C. 4.55
D. 5.00

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

56. Compute the modified duration of a 9% coupon, 3-year corporate bond with a yield to
maturity of 12%.
A. 2.45
B. 2.75
C. 2.88
D. 3.00

Difficulty: Medium

57. An 8%, 30-year bond has a yield-to-maturity of 10% and a modified duration of 8.0 years.
If the market yield drops by 15 basis points, there will be a __________ in the bond's price.
A. 1.15% decrease
B. 1.20% increase
C. 1.53% increase
D. 2.43% decrease

(P/P) = - 8.0 (0.0015) = - 0.012

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

58. To create a portfolio with a duration of 4 years using a 5 year zero-coupon bond and a 3
year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest
________ of the portfolio value in the zero-coupon bond.
A. 50%
B. 55%
C. 60%
D. 75%

Difficulty: Hard

59. Which of the following set of conditions will result in a bond with the greatest price
volatility?
A. A high coupon and a short maturity.
B. A high coupon and a long maturity.
C. A low coupon and a short maturity.
D. A low coupon and a long maturity.

Difficulty: Easy

60. An investor who expects declining interest rates would maximize their capital gain by
purchasing a bond that has a ___ coupon and a ___ term to maturity.
A. low; long
B. high; short
C. high; long
D. zero; long

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

61. If you choose a zero coupon bond with a maturity that matches your investment horizon
which of the following statements is/are correct?
I. You will have no interest rate risk on this bond.
II. Absent default, you can be sure you will earn the promised yield rate.
III. The duration of your bond is less than the time to your investment horizon.
A. I only
B. I and II only
C. II and III only
D. I, II and III

Difficulty: Easy

62. As compared with equivalent maturity bonds selling at par, deep discount bonds will have
________.
A. greater reinvestment risk
B. greater price volatility
C. less call protection
D. shorter average maturity

Difficulty: Easy

Steel Pier Company has issued bonds that pay semiannually with the following
characteristics:

11-40
Chapter 11 - Managing Bond Portfolios

63. The modified duration for the Steel Pier bond is ______.
A. 6.15 years
B. 5.95 years
C. 6.49 years
D. 9.09 years

DurMOD = 6.76/1.10 = 6.15 years

Difficulty: Medium

64. If the bond's coupon was smaller than 10%, the modified duration would be _____
compared to the original modified duration.
A. larger
B. unchanged
C. smaller
D. There is not enough information to determine the direction of change

Difficulty: Easy

65. If the maturity of the bond was less than 10 years, the modified duration would be _____
compared to the original modified duration.
A. larger
B. unchanged
C. smaller
D. There is not enough information to determine the direction of change

Difficulty: Easy

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Chapter 11 - Managing Bond Portfolios

66. If the yield to maturity decreases to 8.045% the expected percentage change in the price of
the bond using Macauley's duration would be ____, while the expected percentage change in
the price of the bond using modified duration would be ____.
A. 11%, 12%
B. 12%, 11%
C. 12%, 12%
D. 11%, 11%

%P =                                   ; %P is the same using DurMOD

Difficulty: Hard

67. A 20 year maturity corporate bond has a 6.5% coupon rate (the coupons are paid
annually). The bond currently sells for \$925.50. A bond market analyst forecasts that in five
years yield rates on these bonds will be at 7.0%. You believe that you will be able to reinvest
the coupons earned over the next five years at a 6% rate of return. What is your expected
annual compound rate of return if you plan on selling the bond in five years?
A. 7.37%
B. 7.56%
C. 8.12%
D. 8.54%

FV5coupons =

P5Bond =
Total Future Value5 = \$366.41 + \$954.46 = \$1,320.87
PV0 = \$925.50
(\$925.50)(1 + r)5 = \$1,320.87; r = 7.37%

Difficulty: Hard

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Chapter 11 - Managing Bond Portfolios

68. When bonds sell above par, what is the relationship of price sensitivity to rising interest
rates?
A. Price volatility increases at an increasing rate
B. Price volatility increases at a decreasing rate
C. Price volatility decreases at a decreasing rate
D. Price volatility decreases at an increasing rate

Difficulty: Medium

69. A zero coupon bond is selling at a deep discount price of \$430.00. It matures in 13 years.
If the yield to maturity of the bond is 6.7%, what is the duration of the bond?
A. 6.7 years
B. 8.0 years
C. 10 years
D. 13 years

Duration of a zero-coupon bond is equal to its maturity.

Difficulty: Easy

70. You have an investment that in today's dollars returns 15% of your investment in year 1,
12% in year two, 9% in year 3 and the remainder in year 4. What is the duration of this
investment?
A. 4 years
B. 3.50 years
C. 3.22 years
D. 2.95 years

Dur = (15%)(1) + (12%)(2) + (9%)(3) + (64%)(4) = 3.22 years

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

71. If an investment returns a higher percentage of your money back sooner it will ______.
A. be less price volatile
B. have a higher credit rating
C. be less liquid
D. have a higher modified duration

Difficulty: Easy

72. Which one of the following statements correctly describes the weights used in the
Macaulay duration calculation? The weight in year t is equal to ____________.
A. the dollar amount of the investment received in year t
B. the percentage of the future value of the investment received in year t
C. the present value of the dollar amount of the investment received in year t
D. the percentage of the total present value of the investment received in year t

Difficulty: Hard

73. The duration is independent of the coupon rate only for which one of the following?
A. Discount bonds
C. Perpetuities
D. Short term bonds

Difficulty: Medium

74. You have an investment horizon of 6 years. You choose to hold a bond with a duration of
10 years. Your realized rate of return will be larger than the promised yield on the bond if
___________________.
A. interest rates increase
B. interest rates stay the same
C. interest rates fall
D. one can't tell with the information given

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

75. A bond portfolio manager notices a hump in the yield curve at the five year point. How
might a bond manager take advantage of this event?
A. Buy the 5 year bonds and short the surrounding maturity bonds
B. Buy the 5 year bonds and buy the surrounding maturity bonds
C. Short the 5 year bonds and short the surrounding maturity bonds
D. Short the 5 year bonds and buy the surrounding maturity bonds

Difficulty: Medium

76. Market economists all predict a rise in interest rates. An astute bond manager wishing to
maximize her capital gain might employ which strategy?
A. Switch from low duration to high duration bonds.
B. Switch from high duration to low duration bonds.
D. Switch from low coupon to high coupon bonds.

Difficulty: Medium

77. You have an investment horizon of 6 years. You choose to hold a bond with a duration of
4 years. Your realized rate of return will be larger than the promised yield on the bond if
___________________.
A. interest rates increase
B. interest rates stay the same
C. interest rates fall
D. one can't tell with the information given

Difficulty: Medium

78. What strategy might an insurance company employ to ensure that it will be able to meet
the obligations of annuity holders?
A. Cash flow matching
B. Index tracking
C. Yield pickup swaps
D. Substitution swap

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

79. You have an investment horizon of 6 years. You choose to hold a bond with a duration of
6 years and continue to match your investment horizon and duration throughout your holding
period. Your realized rate of return will be the same as the promised yield on the bond if
I. interest rates increase
II. interest rates stay the same
III. interest rates fall
A. I only
B. II only
C. I and II only
D. I, II and III

Difficulty: Medium

80. Immunization of coupon paying bonds is not a passive strategy because
I. the portfolio must be rebalanced every time interest rates change
II. the portfolio must be rebalanced over time even if interest rates don't change
III. convexity implies duration based immunization strategies don't work
A. I only
B. I and II only
C. II only
D. I, II and III

Difficulty: Medium

81. Advantages of cash flow matching and dedicated strategies include ______.
I. once the cash flows are matched there is no need for rebalancing
II. cash flow matching typically earns a higher rate of return than active bond portfolio
management
III. financial institution's liabilities often exceed the maturity of available bonds, making cash
matching even more desirable
A. I only
B. II only
C. I and III only
D. I, II and III

Difficulty: Medium

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Chapter 11 - Managing Bond Portfolios

82. Convexity implies that duration predictions _______.
I. underestimate the % increase in bond price when the yield falls
II. underestimate the % decrease in bond price when the yield rises
III. overestimates the % increase in bond price when the yield falls
IV. overestimates the % decrease in bond price when the yield rises
A. I and III only
B. II and IV only
C. I and IV only
D. II and III only

Difficulty: Hard

83. You have a 25 year maturity 10% coupon, 10% yield bond with duration of 10 years and a
convexity of 135.50. If interest rate were to fall 125 basis points your predicted new price for
the bond (including convexity) is _________.
A. \$1098.45
B. \$1104.56
C. \$1113.41
D. \$1124.20

PV0 = \$1,000

%P =
PNew = (\$1,000)(1 + 0.1242) = \$1,124.20

Difficulty: Hard

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Chapter 11 - Managing Bond Portfolios

84. You have a 15 year maturity 4% coupon, 6% yield bond with duration of 10.5 years and a
convexity of 128.75. The bond is currently priced at \$805.76. If interest rate were to increase
200 basis points your predicted new price for the bond (including convexity) is _________.
A. \$638.85
B. \$642.54
C. \$666.88
D. \$705.03

PV0 = \$805.76

%P =
PNew = (\$805.76)(1 + -0.1724) = \$666.88

Difficulty: Hard

85. Convexity of a bond is ___________.
A. the same as horizon analysis
B. the rate of change of the price-yield curve divided by bond price
C. a measure of bond duration
D. none of the above

Difficulty: Medium

11-48

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