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TBChap 009 - TEST BANK

Financial Institutions (University of Nebraska-Lincoln)

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Chapter 09 Interest Rate Risk II Answer Key

True / False Questions

1. In most countries FIs report their balance sheet using market value accounting.

FALSE

2. Marking-to-market accounting is a market value accounting method that reflects

the purchase prices of assets and liabilities.

FALSE

3. The difference between the changes in the market value of the assets and market
value of liabilities for a given change in interest rates is, by definition, the change
in the FI's net worth.

TRUE

4. Duration measures the average life of a financial asset.

TRUE

5. The economic meaning of duration is the interest elasticity of a financial assets

price.

TRUE

6. Duration considers the timing of all the cash flows of an asset by summing the
product of the cash flows and the time of occurrence.

FALSE

7. A key assumption of Macaulay duration is that the yield curve is flat so that all
cash flows are discounted at the same discount rate.

TRUE

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8. Duration is the weighted-average present value of the cash flows using the timing
of the cash flows as weights.

FALSE

9. In duration analysis, the times at which cash flows are received are weighted by
the relative importance in present value terms of the cash flows arriving at each
point in time.

TRUE

10. Duration normally is less than the maturity for a fixed income asset.

TRUE

11. Duration is equal to maturity when at least some of the cash flows are received
upon maturity of the asset.

FALSE

12. Duration of a fixed-rate coupon bond will always be greater than one-half of the
maturity.

FALSE

13. Duration is related to maturity in a linear manner through the interest rate of the
asset.

FALSE

14. Duration is related to maturity in a nonlinear manner through the current yield to
maturity of the asset.

TRUE

15. Duration of a zero coupon bond is equal to the bond's maturity.

TRUE

16. As interest rates rise, the duration of a consol bond decreases.

TRUE

17. Duration increases with the maturity of a fixed-income asset at a decreasing rate.

TRUE

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18. For a given maturity fixed-income asset, duration decreases as the market yield
increases.

TRUE

19. For a given maturity fixed-income asset, duration increases as the promised
interest payment declines.

FALSE

20. Larger coupon payments on a fixed-income asset cause the present value weights
of the cash flows to be lower in the duration calculation.

FALSE

21. The value for duration describes the percentage increase in the price of an asset
for a given increase in the required yield or interest rate.

FALSE

22. For a given change in required yields, short-duration securities suffer a smaller
capital loss or receive a smaller capital gain than do long-duration securities.

TRUE

23. Investing in a zero-coupon asset with a maturity equal to the desired investment
horizon is one method of immunizing against changes in interest rates.

TRUE

24. Investing in a zero-coupon asset with a maturity equal to the desired investment
horizon removes interest rate risk from the investment management process.

TRUE

25. Buying a fixed-rate asset whose duration is exactly equal to the desired
investment horizon immunizes against interest rate risk.

TRUE

26. Deep discount bonds are semi-annual fixed-rate coupon bonds that sell at a
market price that is less than par value.

FALSE

27. Using a fixed-rate bond to immunize a desired investment horizon means that the
reinvested coupon payments are not affected by changes in market interest rates.

FALSE

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28. An FI can immunize its portfolio by matching the maturity of its asset with its
liabilities.

FALSE

29. The immunization of a portfolio against interest rate risk means that the portfolio
will neither gain nor lose value when interest rates change.

TRUE

30. Perfect matching of the maturities of the assets and liabilities will always achieve
perfect immunization for the equity holders of an FI against interest rate risk.

FALSE

31. Matching the maturities of assets and liabilities is not a perfect method of
immunizing the balance sheet because the timing of the cash flows is likely to
differ between the assets and liabilities.

TRUE

32. The duration of a portfolio of assets can be found by calculating the book value
weighted average of the durations of the individual assets.

FALSE

33. For given changes in interest rates, the change in the market value of net worth of
an FI is equal to the difference between the changes in the market value of the
assets and market value of the liabilities.

TRUE

34. Immunizing the balance sheet of an FI against interest rate risk requires that the
leverage adjusted duration gap (DA-kDL) should be set to zero.

TRUE

35. The smaller the leverage adjusted duration gap, the more exposed the FI is to
interest rate shocks.

FALSE

36. The larger the interest rate shock, the smaller the interest rate risk exposure of an
FI.

FALSE

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37. Setting the duration of the assets higher than the duration of the liabilities will
exactly immunize the net worth of an FI from interest rate shocks.

FALSE

38. Immunization of an FIs net worth requires the duration of the liabilities to be
adjusted for the amount of leverage on the balance sheet.

TRUE

39. The leverage adjusted duration of a typical depository institution is positive.

TRUE

40. One method of changing the positive leverage adjusted duration gap for the
purpose of immunizing the net worth of a typical depository institution is to
increase the duration of the assets and to decrease the duration of the liabilities.

FALSE

41. Attempts to satisfy the objectives of shareholders and regulators requires the bank
to use the same duration match in the protection of net worth from interest rate
risk.

FALSE

42. Immunizing the net worth ratio requires that the duration of the assets be set
equal to the duration of the liabilities.

TRUE

43. The cost in terms of both time and money to restructure the balance sheet of large
and complex FIs has decreased over time.

TRUE

44. Immunizing net worth from interest rate risk using duration matching requires that
the duration match must be realigned periodically as the maturity horizon
approaches.

TRUE

45. The rate of change in duration values is less than the rate of change in maturity.

TRUE

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46. As the investment horizon approaches, the duration of an unrebalanced portfolio

that originally was immunized will be less than the time remaining to the
investment horizon.

FALSE

47. The use of duration to predict changes in bond prices for given changes in interest
rate changes will always underestimate the amount of the true price change.

FALSE

48. The fact that the capital gain effect for rate decreases is greater than the capital
loss effect for rate increases is caused by convexity in the yield-price relationship.

TRUE

49. Convexity is a desirable effect to a portfolio manager because it is easy to

measure and price.

FALSE

50. All fixed-income assets exhibit convexity in their price-yield relationships.

TRUE

51. The greater is convexity, the more insurance a portfolio manager has against
interest rate increases and the greater potential gain from rate decreases.

TRUE

52. The error from using duration to estimate the new price of a fixed-income security
will be less as the amount of convexity increases.

FALSE

Multiple Choice Questions

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53. Which of the following is indicated by high numerical value of the duration of an
asset?

A. Low sensitivity of an asset price to interest rate

shocks.
B. High interest inelasticity of a
bond.
C. High sensitivity of an asset price to interest rate
shocks.
D. Lack of sensitivity of an asset price to interest rate
shocks.
E. Smaller capital loss for a given change in
interest rates.

54. For small change in interest rates, market prices of bonds move in an inversely
proportional manner according to the size of the

A. equit
y.
B. asset
value.
C. liability
value.
D. duration
value.
E. Answers A and B
only.

55. Which of the following statements about leverage adjusted duration gap is true?

A. It is equal to the duration of the assets minus the duration of the

liabilities.
B. Larger the gap in absolute terms, the more exposed the FI is to interest
rate shocks.
C. It reflects the degree of maturity mismatch in an FI's
balance sheet.
D. It indicates the dollar size of the potential
net worth.
E. Its value is equal to duration divided by
(1 + R).

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56. The larger the size of an FI, the larger the _________ from any given interest rate
shock.

A. duration
mismatch
B. immunization
effect
C. net worth
exposure
D. net interest
income
E. risk of
bankruptcy

57. The duration of all floating rate debt instruments is

A. equal to the time to

maturity.
B. less than the time to repricing of the
instrument.
C. time interval between the purchase of the security
and its sale.
D. equal to time to repricing of the
instrument.
E. infinit
y.

58. Managers can achieve the results of duration matching by using these to hedge
interest rate risk.

A. Rate sensitive
assets.
B. Rate sensitive
liabilities.
C. Coupon
bonds.
D. Consol
bonds.
E. Derivative
s.

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59. Immunizing the balance sheet to protect equity holders from the effects of interest
rate risk occurs when

A. the maturity gap is

zero.
B. the repricing gap is
zero.
C. the duration gap is
zero.
D. the effect of a change in the level of interest rates on the value of the assets of
the FI is exactly offset by the effect of the same change in interest rates on the
liabilities of the FI.
E. after-the-fact analysis demonstrates that immunization
coincidentally occurred.

60. The duration of a consol bond is

A. less than its

maturity.
B. infinit
y.
C. 30
years.
D. more than its
maturity.
E. given by the formula D = 1/
(1-R).

61. Immunization of a portfolio implies that changes in _____ will not affect the value of
the portfolio.

A. book value of
assets
B. maturi
ty
C. market
prices
D. interest
rates
E. duratio
n

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62. When does "duration" become a less accurate predictor of expected change in
security prices?

A. As interest rate shocks increase in

size.
B. As interest rate shocks decrease in
size.
C. When maturity distributions of an FI's assets and liabilities are
considered.
D. As inflation
decreases.
E. When the leverage adjustment is
incorporated.

63. An FI has financial assets of $800 and equity of $50. If the duration of assets is
1.21 years and the duration of all liabilities is 0.25 years, what is the leverage-
adjusted duration gap?

A. 0.9000
years.
B. 0.9600
years.
C. 0.9756
years.
D. 0.8844
years.
E. Cannot be
determined.

Leverage-adjusted duration gap

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64. Calculate the duration of a two-year corporate bond paying 6 percent interest
annually, selling at par. Principal of $20,000,000 is due at the end of two years.

A. 2
years.
B. 1.91
years.
C. 1.94
years.
D. 1.49
years.
E. 1.75
years.

65. Calculate the duration of a two-year corporate loan paying 6 percent interest
annually, selling at par. The $30,000,000 loan is 100 percent amortizing with
annual payments.

A. 2
years.
B. 1.89
years.
C. 1.94
years.
D. 1.49
years.
E. 1.73
years.

Fully amortizing loan cash flows:

Macaulay's Duration

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66. Calculate the modified duration of a two-year corporate loan paying 6 percent
interest annually. The $40,000,000 loan is 100 percent amortizing, and the current
yield is 9 percent annually.

A. 2
years.
B. 1.91
years.
C. 1.94
years.
D. 1.49
years.
E. 1.36
years.

Fully amortizing loan cash flows:

Fair Market Value

Macaulay's Duration

Modified Duration

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67. Which of the following statements is true?

A. The optimal duration gap is

zero.
B. Duration gap measures the impact of changes in interest rates on the market
value of equity.
C. The shorter the maturity of the FI's securities, the greater the FI's interest rate
risk exposure.
D. The duration of all floating rate debt instruments is equal to the time
to maturity.
E. The duration of equity is equal to the duration of assets minus the duration
of liabilities.

68. An FI purchases a $9.982 million pool of commercial loans at par. The loans have
an interest rate of 8 percent, a maturity of five years, and annual payments of
principal and interest that will exactly amortize the loan at maturity. What is the
duration of this asset?

A. 4.12
years.
B. 3.07
years.
C. 2.50
years.
D. 2.85
years.
E. 5.00
years.

Fully amortizing loan cash flows:

Macaulay's Duration

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69. A $1,000 six-year Eurobond has an 8 percent coupon, is selling at par, and
contracts to make annual payments of interest. The duration of this bond is 4.99
years. What will be the new price using the duration model if interest rates
increase to 8.5 percent?

A. $23.1
0.
B. $976.9
0.
C. $977.2
3.
D. $1,023.1
0.
E. -
$23.10
.

Modified Duration

Dollar Duration

Change in Price

New Price

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70. An FI purchases at par value a $100,000 Treasury bond paying 10 percent interest
with a 7.5 year duration. If interest rates rise by 4 percent, calculate the bond's
new value.
Recall that Treasury bonds pay interest semiannually. Use the duration valuation
equation.

A. $28,57
2
B. $20,86
4
C. $15,00
0
D. $22,64
2
E. $71,42
8

Modified Duration, semi-annual

Dollar Duration

Change in Price

New Price

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71. What is the duration of an 8 percent annual payment two-year note that currently
sells at par?

A. 2
years.
B. 1.75
years.
C. 1.93
years.
D. 1.5
years.
E. 1.97
years.

Macaulay's Duration

72. What is the duration of a 5-year par value zero coupon bond yielding 10 percent
annually?

A. 0.50
years.
B. 2.00
years.
C. 4.40
years.
D. 5.00
years.
E. 4.05
years.

Macaulay's Duration

The duration of a zero coupon bond is equal to its maturity.

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73. Calculating modified duration involves

A. dividing the value of duration by the change in the market

interest rate.
B. dividing the value of duration by 1 plus the
interest rate.
C. dividing the value of duration by discounted change in
interest rates.
D. multiplying the value of duration by discounted change in
interest rates.
E. dividing the value of duration by the
curvature effect.

First Duration, a securities dealer, has a leverage-adjusted duration gap of 1.21

years, $60 million in assets, 7 percent equity to assets ratio, and market rates are
8 percent.

74. What is the impact on the dealer's market value of equity per $100 of assets if the
change in all interest rates is an increase of 0.5 percent [i.e., ΔR = 0.5 percent]

A. +
$336,111
.
B. -
$0.605
.
C. -
$336,111
.
D. +
$0.605.
E. -
$363,000
.

Change in the market value of equity, leverage-adjusted duration gap

∆E = -1.21 × $60,000,000 × (0.005 ÷ 1.08) = -$336,111

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75. What conclusions can you draw from the duration gap in your answer to the
previous question?

A. The market value of the dealer's equity decreases slightly if

interest rates fall.
B. The market value of the dealer's equity becomes negative if interest
rates rise.
C. The market value of the dealer's equity decreases slightly if interest
rates rise.
D. The market value of the dealer's equity becomes negative if
interest rates fall.
E. The dealer has no interest rate risk
exposure.

Consider a one-year maturity, $100,000 face value bond that pays a 6 percent
fixed coupon annually.

76. What is the price of the bond if market interest rates are 7 percent?

A. $99,050.1
5.
B. $99,457.9
4.
C. $99,249.6
2.
D. $100,000.0
0.
E. $99,065.4
2.

$100,000 face value, 6% annual coupon, 1 year maturity, 7% rate

$100,000 face
value, 6% annual coupon, 1-year maturity, 5% rate

Percent
change in price in rates increase from 6.0 percent to 6.5 percent

Percent ∆P = (P1 - P0) ÷ P0

%∆P = (99,530.52 - 100,000) ÷ 100,000 = -0.004695

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Consider a six-year maturity, $100,000 face value bond that pays a 5 percent fixed
coupon annually.

77. What is the price of the bond if market interest rates are 4 percent?

A. $105,816.4
4.
B. $105,287.6
7.
C. $105,242.1
4.
D. $100,000.0
0.
E. $106,290.5
6.

$100,000 face value, 5% annual coupon, 6 year maturity, 4% rate

78. What is the price of the bond if market interest rates are 6 percent?

A. $95,082.6
8.
B. $95,769.5
5.
C. $95,023.0
0.
D. $100,000.0
0.
E. $96,557.8
7.

$100,000 face value, 5% annual coupon, 6 year maturity, 6% rate

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79. What is the percentage price change for the bond if interest rates decline 50 basis
points from the original 5 percent?

A. -2.106
percent.
B. +2.579
percent.
C. +0.000
percent.
D. +3.739
percent.
E. +2.444
percent.

Percent change in price in rates decrease from 5.0 percent to 4.5 percent

Percent ∆P = (P1 - P0) ÷ P0

%∆P = (102,578.94 - 100,000) ÷ 100,000 = +0.025789

First Duration Bank has the following assets and liabilities on its balance sheet

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80. What is the duration of the commercial loans?

A. 1.00
years.
B. 2.00
years.
C. 1.73
years.
D. 1.91
years.
E. 1.50
years.

Duration of commercial loans

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81. What is the FI's leverage-adjusted duration gap?

A. 0.91
years.
B. 0.83
years.
C. 0.73
years.
D. 0.50
years.
E. 0
years.

Leverage-adjusted duration.

Duration of the CDs first

1-year T-bills will also have a duration of 1

Duration of the assets is a weighted average
DA = (400/500) × 1.9114 + (100/500) × 1.000 = 1.52912 + 0.200 = 1.72912
Finally, leverage-adjusted duration

82. What is the FI's interest rate risk exposure?

A. Exposed to increasing
rates.
B. Exposed to decreasing
rates.
C. Perfectly
balanced.
D. Exposed to long-term rate
changes.
E. Insufficient
information.

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The following information is about current spot rates for Second Duration Savings'
assets (loans) and liabilities (CDs). All interest rates are fixed and paid annually.

83. If rates do not change, the balance sheet position that maximizes the FI's returns
is
165 1-year 2-year

A. a positive spread of 15 basis points by selling 1-year CDs to finance 2-

year CDs.
B. a positive spread of 100 basis points by selling 1-year CDs to finance 1-
year loans.
C. a positive spread of 85 basis points by financing the purchase of a 1-year loan
with a 2-year CD.
D. a positive spread of 165 basis points by selling 1-year CDs to finance 2-
year loans.
E. a positive spread of 150 basis points by selling 2-year CDs to finance 2-
year loans.

84. What is the interest rate risk exposure of the optimal transaction in the previous
question over the next 2 years?

A. The risk that interest rates will rise since the FI must purchase a 2-year CD
in one year.
B. The risk that interest rates will rise since the FI must sell a 1-year CD in
one year.
C. The risk that interest rates will fall since the FI must sell a 2-year loan
in one year.
D. The risk that interest rates will fall since the FI must buy a 1-year loan
in one year.
E. There is no interest rate risk
exposure.

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85. What is the duration of the two-year loan (per $100 face value) if it is selling at
par?

A. 2.00
years
B. 1.92
years
C. 1.96
years
D. 1.00
year
E. 0.91
years

86. If the FI finances a $500,000 2-year loan with a $400,000 1-year CD and equity,
what is the leveraged adjusted duration gap of this position? Use your answer to
the previous question.

A. +1.25
years
B. +1.12
years
C. -1.12
years
D. +0.92
years
E. -1.25
years

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87. Use the duration model to approximate the change in the market value (per $100
face value) of two-year loans if interest rates increase by 100 basis points.

A. -
$1.75
6
B. -
$1.77
5
C. +
$98.24
D. -
$1.00
0
E. +
$1.924

Modified Duration

Dollar Duration

Change in Price

Based on an 18-month, 8 percent (semiannual) coupon Treasury note selling at

par.

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88. What is the duration of this Treasury note?

A. 1.500
years.
B. 1.371
years.
C. 1.443
years.
D. 2.882
years.
E. 1.234
years.

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89. If interest rates increase by 20 basis points (i.e., ΔR = 20 basis points), use the
duration approximation to determine the approximate price change for the
Treasury note.

A. $0.00
0.
B. $0.2775 per $100 face
value.
C. $2.775 per $100 face
value.
D. $0.2672 per $100 face
value.
E. $2.672 per $100 face
value.

Modified Duration

Dollar Duration

Change in Price

Third Duration Investments has the following assets and liabilities on its balance
sheet. The two-year Treasury notes are zero coupon assets. Interest payments on
all other assets and liabilities occur at maturity. Assume 360 days in a year.

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90. What is the duration of the assets?

A. 0.708
years.
B. 0.354
years.
C. 0.350
years.
D. 0.955
years.
E. 0.519
years.

91. What is the duration of the liabilities?

A. 0.708
years.
B. 0.354
years.
C. 0.350
years.
D. 0.955
years.
E. 0.519
years.

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92. What is the leverage-adjusted duration gap?

A. 0.605
years.
B. 0.956
years.
C. 0.360
years.
D. 0.436
years.
E. 0.189
years.

Consider a five-year, 8 percent annual coupon bond selling at par of $1,000.

93. What is the duration of this bond?

A. 5
years.
B. 4.31
years.
C. 3.96
years.
D. 5.07
years.
E. Not enough information to
answer.

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94. If interest rates increase by 20 basis points, what is the approximate change in the
market price using the duration approximation?

A. -
$7.98
5
B. -
$7.94
1
C. -
$3.99
0
D. +
$3.990
E. +
$7.949

Modified Duration

Dollar Duration

Change in Price

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95. Using present value bond valuation techniques, calculate the exact price of the
bond after the interest rate increase of 20 basis points.

A. $1,007.9
4.
B. $992.0
2.
C. $992.0
6.
D. $996.0
1.
E. $1,003.9
9.

∆P = 922.06 - 1,000 = -$7.94

Compare to duration estimate of change -$7.985

The numbers provided by Fourth Bank of Duration are in thousands of dollars.

Notes: All Treasury bills have six months until maturity. One-year Treasury notes
are priced at par and have a coupon of 7 percent paid semiannually. Treasury
bonds have an average duration of 4.5 years and the loan portfolio has a duration
of 7 years. Time deposits have a 1-year duration and the Fed funds duration is
0.003 years. Fourth Bank of Duration assigns a duration of zero (0) to demand
deposits.

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96. What is the duration of the bank's Treasury portfolio?

A. 1.07
years.
B. 1.00
year.
C. 0.98
years.
D. 0.92
years.
E. Insufficient
information.

Duration of 1-year Treasury note ($55,000,000, semi-annual coupon)

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97. What is the bank's leverage adjusted duration gap?

A. 6.73
years
B. 0.29
years
C. 6.44
years
D. 6.51
years
E. 0
years.

a. Find weighted average duration for all assets and liabilities

b. Find weighted average duration of liabilities

c. Find leverage-adjusted duration gap

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98. If the relative change in interest rates is a decrease of 1 percent, calculate the
impact on the bank's market value of equity using the duration approximation.
(That is, ΔR/(1 + R) = -1 percent)

A. The bank's market value of equity increases by

$325,550.
B. The bank's market value of equity decreases by
$325,550.
C. The bank's market value of equity increases by
$336,500.
D. The bank's market value of equity decreases by
$336,500.
E. There is no change in the bank's market value of
equity.

Change in the market value of equity, leverage-adjusted duration gap

∆E = -6.51 × $5,000,000 × (-0.01) = +$325,500

A bond is scheduled to mature in five years. Its coupon rate is 9 percent with
interest paid annually. This $1,000 par value bond carries a yield to maturity of 10
percent.

99. What is the bond's current market price?

A. $962.0
9.
B. $961.3
9.
C. $1,00
0.
D. $1,038.9
0.
E. $995.0
5.

$1,000 face value, 9% annual coupon, 5 year maturity, 10% rate

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100. What is the duration of the bond?

A. 4.677
years.
B. 5.000
years.
C. 4.674
years.
D. 4.328
years.
E. 4.223
years

101. Calculate the percentage change in this bond's price if interest rates on
comparable risk securities decline to 7 percent. Use the duration valuation
equation.

A. +8.58
percent
B. +12.76
percent
C. -12.75
percent
D. +11.80
percent
E. +11.52
percent

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102. Calculate the percentage change in this bond's price if interest rates on
comparable risk securities increase to 11 percent. Use the duration valuation
equation.

A. +4.25
percent
B. -4.25
percent
C. +8.58
percent
D. -3.93
percent
E. -3.84
percent

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103. Calculate the duration of the assets to four decimal places.

A. 2.5375
years.
B. 4.3750
years.
C. 1.7500
years.
D. 3.0888
years.
E. 2.5000
years.

104. Calculate the duration of the liabilities to four decimal places.

A. 2.05
years.
B. 1.75
years.
C. 2.22
years.
D. 2.125
years.
E. 2.50
years.

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105. Calculate the leverage-adjusted duration gap to four decimal places and state the
FI's interest rate risk exposure of this institution.

A. +1.0308 years; exposed to interest rate

increases.
B. -0.3232 years; exposed to interest rate
increases.
C. +0.8666 years; exposed to interest rate
increases.
D. +0.4875 years; exposed to interest rate
increases.
E. -1.3232 years; exposed to interest rate
decreases.

The institution is exposed to increasing interest rates because the market value of
assets will decline faster than the market value of liabilities.

106. If all interest rates decline 90 basis points (ΔR/(1 + R) = -90 basis points), what is
the change in the market value of equity?

A. -$4.4300
million
B. +$3.9255
million
C. +$4.3875
million
D. +$2.5506
million
E. +$0.0227
million

Change in the market value of equity, leverage-adjusted duration gap

∆E = -0.4875 × $1,000,000,000 × (-0.009) = +$4,378,500

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U.S. Treasury quotes from the WSJ on Oct. 15, 2003:

107. What is the duration of the above Treasury note? Use the asked price to calculate
the duration. Recall that Treasuries pay interest semiannually.

A. 3.86
years.
B. 1.70
years.
C. 2.10
years.
D. 1.90
years.
E. 3.40
years.

In addition to paying interest semi-annually, also recall that Treasuries are quoted
on 32nds, so 102:8 = 102 + (8/32) = 102.25

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108. If yields increase by 10 basis points, what is the approximate price change on the
$100,000 Treasury note? Use the duration approximation relationship.

A. +
$179.39
B. +
$16.05
C. -
$1,605.0
5
D. -
$16.0
5
E. +
$160.51

Note no semi-annual adjustment needed. Duration is measured in years.

∆P = $179.39

The numbers provided are in millions of dollars and reflect market values:

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109. The short-term debt consists of 4-year bonds paying an annual coupon of 4
percent and selling at par. What is the duration of the short-term debt?

A. 3.28
years.
B. 3.53
years.
C. 3.78
years.
D. 4.03
years.
E. 4.28
years.

110. What is the weighted average duration of the assets of the FI?

A. 7.25
years.
B. 7.75
years.
C. 8.25
years.
D. 8.75
years.
E. 9.25
years.

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111. What is the weighted average duration of the liabilities of the FI?

A. 5.00
years.
B. 5.35
years.
C. 5.70
years.
D. 6.05
years.
E. 6.40
years.

112. What is the leverage-adjusted duration gap of the FI?

A. 3.61
years.
B. 3.74
years.
C. 4.01
years.
D. 4.26
years.
E. 4.51
years.

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113. A risk manager could restructure assets and liabilities to reduce interest rate
exposure for this example by

A. increasing the average duration of its assets to

9.56 years.
B. decreasing the average duration of its assets to
4.00 years.
C. increasing the average duration of its liabilities to
6.78 years.
D. increasing the average duration of its liabilities to
9.782 years.
E. increasing the leverage ratio, k,
to 1.

To completely immunize against interest rate changes, set the leverage adjusted
duration to zero.

DL = 8.246 × (830 ÷ 700) = 9.78 years. Option C is the only selection that
immunizes against interest rate risk.

114. The shortcomings of this strategy are the following except

A. duration changes as the time to maturity changes, making it difficult to

maintain a continuous hedge.
B. estimation of duration is difficult for some accounts such as demand deposits
and passbook savings account.
C. it ignores convexity which can be distorting for large changes in
interest rates.
D. it is difficult to compute market values for many assets and
liabilities.
E. it does not assume a flat term structure, so its estimation is
imprecise.

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115. What is the effect of a 100 basis point increase in interest rates on the market
value of equity of the FI? Use the duration approximation relationship. Assume r =
4 percent.

A. -27.56
million.
B. -28.01
million.
C. -29.85
million.
D. -31.06
million.
E. -33.76
million.

Change in the market value of equity, leverage-adjusted duration gap

∆E = -3.74 × $830,000,000 × (+0.0096) = -$29,848,000 approximate

The following is an FI's balance sheet ($millions).

Notes to Balance Sheet:

Munis are 2-year 6 percent annual coupon municipal notes selling at par. Loans are
floating rates, repriced quarterly. Spot discount yields for 91-day Treasury bills are
3.75 percent. CDs are 1-year pure discount certificates of deposit paying 4.75
percent.

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116. What is the duration of the municipal notes (the value of x)?

A. 1.94
years.
B. 2.00
years.
C. 1.00
years.
D. 1.81
years.
E. 0.97
years.

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117. What is this bank's interest rate risk exposure, if any?

increase positive +0.21

A. The bank is exposed to decreasing interest rates because it has a negative

duration gap of -0.21 years.
B. The bank is exposed to increasing interest rates because it has a negative
duration gap of -0.21 years.
C. The bank is exposed to increasing interest rates because it has a positive
duration gap of +0.21 years.
D. The bank is exposed to decreasing interest rates because it has a positive
duration gap of +0.21 years.
E. The bank is not exposed to interest rate changes since it is running a
matched book.

Weighted Average Duration of Assets

Weighted Average Duration of Liabilities

Leverage-Adjusted Duration Gap

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118. What will be the impact, if any, on the market value of the bank's equity if all
interest rates increase by 75 basis points? (i.e., ΔR/(1 + R) = 0.0075)

decrease 426825
A. The market value of equity will decrease by
$15,750.
B. The market value of equity will increase by
$15,750.
C. The market value of equity will decrease by
$426,825.
D. The market value of equity will increase by
$426,825.
E. There will be no impact on the market value of
equity.

Change in the market value of equity, leverage-adjusted duration gap

∆E = -0.21 × $271,000,000 × (0.0075) = -$426,825

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