Test Bank Chapter 9 Interest Rate Risk Ii - Financial Institutions 10e Complete Test Bank by Anthony Saunders. DOCX document preview.
Chapter 09 Interest Rate Risk II
KEY
1. In most countries FIs report their balance sheet using market value accounting.
2. Market value accounting reflects economic reality of a FIs balance sheet.
3. Marking-to-market accounting is a market value accounting method that reflects the purchase prices of assets and liabilities.
4. The difference between the changes in the market value of assets and market value of liabilities for a given change in interest rates is, by definition, the change in the FI's net worth.
5. Duration measures the average life of a financial asset or financial liability.
6. The economic meaning of duration is the interest elasticity of a financial asset’s price.
7. Interest elasticity is the percentage change in the price of a bond for any given change in interest rates.
8. 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.
9. 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.
10. Duration is the weighted-average present value of the cash flows using the timing of the cash flows as weights.
11. 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.
12. Normally, duration is less than the maturity for a fixed income asset.
13. Duration is equal to maturity when at least some of the cash flows are received upon maturity of the asset.
14. Duration of a fixed-rate coupon bond will always be greater than one-half of the maturity.
15. Duration is related to maturity in a linear manner through the interest rate of the asset.
16. Duration is related to maturity in a nonlinear manner through the current yield to maturity of the asset.
17. Duration of a zero coupon bond is equal to the bond's maturity.
18. As interest rates rise, the duration of a consol bond decreases.
19. Duration increases with the maturity of a fixed-income asset at a decreasing rate.
20. For a given maturity fixed-income asset, duration decreases as the market yield increases.
21. For a given maturity fixed-income asset, duration increases as the promised interest payment declines.
22. Larger coupon payments on a fixed-income asset cause the present value weights of the cash flows to be lower in the duration calculation.
23. The value for duration describes the percentage increase in the price of a fixed-income asset for a given increase in the required yield or interest rate.
24. 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.
25. 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.
26. Investing in a zero-coupon asset with a maturity equal to the desired investment horizon removes interest rate risk from the investment management process.
27. Buying a fixed-rate asset whose duration is exactly equal to the desired investment horizon immunizes against interest rate risk.
28. Deep discount bonds are semi-annual fixed-rate coupon bonds that sell at a market price that is less than par value.
29. 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.
30. An FI can immunize its portfolio by matching the maturity of its asset with its liabilities.
31. The immunization of a portfolio against interest rate risk means that the portfolio will neither gain nor lose value when interest rates change.
32. 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.
33. 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.
34. The duration of a portfolio of assets can be found by calculating the book value weighted average of the durations of the individual assets.
35. 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.
36. 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.
37. The smaller the leverage-adjusted duration gap, the more exposed the FI is to interest rate shocks.
38. The larger the interest rate shock, the smaller the interest rate risk exposure of an FI.
39. 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.
40. Immunization of a FIs net worth requires the duration of the liabilities to be adjusted for the amount of leverage on the balance sheet.
41. The leverage adjusted duration of a typical depository institution is positive.
42. To measure duration gap one should first determine the duration of an FI’s asset portfolio and the duration of its liability portfolio.
43. 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.
44. 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.
45. Immunizing the net worth ratio requires that the duration of the assets be set equal to the duration of the liabilities.
46. The cost in terms of both time and money to restructure the balance sheet of large and complex FIs has decreased over time.
47. Immunizing net worth from interest rate risk using duration matching requires that the duration match must be realigned periodically as the maturity horizon approaches.
48. The rate of change in duration values is less than the rate of change in maturity.
49. 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.
50. 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.
51. 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.
52. Convexity is a desirable effect to a portfolio manager because it is easy to measure and price.
53. All fixed-income assets exhibit convexity in their price-yield relationships.
54. The greater is convexity, the more insurance a portfolio manager has against interest rate increases and the greater potential gain from rate decreases.
55. The error from using duration to estimate the new price of a fixed-income security will be less as the amount of convexity increases.
56. Dollar duration is the dollar value change in a security’s price to a 1 percent change in the return on the security.
57. Modified duration is defined as duration multiplied by 1 plus the interest rate.
58. Which of the following statements is true regarding duration?
A. increases with the maturity of a fixed-income security but at a decreasing rate.
B. decreases as the yield on a security increases.
C. decreases as the coupon or interest payment increases.
D. is equal to the maturity of an immunized security.
E. all of the above are true.
59. Which of the following statements is true regarding effects of interest rate changes on the market value of an FI’s equity or net worth?
A. the leverage adjusted duration gap reflects the degree of duration mismatch in an FI’s balance sheet.
B. the size of the FI reflects the scale of the FI and its potential net worth exposure from any given interest rate shock.
C. the size of the interest rate shock; the larger the size the greater the FI’s exposure.
D. A, B, and C are true.
E. none of the above are true.
60. The economic interpretation of duration is
A. the percentage of the current market price of a security that is accounted for by the book value of the security.
B. the interest elasticity of a security to a small change in interest rates.
C. the maturity elasticity of a security to a small change in cash flows of the security.
D. the price elasticity of a security to a small change in interest rates.
E. The average time it will take to equate the present value of future cash flows from the security to the cost of the security.
61. All else equal, as compared to an annual payment fixed income security, a semi-annual payment security has a
A. lower duration value and lower market value.
B. higher duration but lower price sensitivity.
C. lower duration and more cash flows.
D. higher duration and more cash flows.
E. none of the options.
62. A relatively high numerical value of the duration of an asset means which of the following t?
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.
63. For small change in interest rates, market prices of bonds are inversely proportional to their
A. equity.
B. asset value.
C. liability value.
D. duration value.
E. none of the options.
64. 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. infinity.
65. 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. Derivatives.
66. Immunizing the balance sheet to protect equity holders from the effects of interest rate risk occurs when
A. the maturity gap is zero, so that all assets have a matching-maturity liability.
B. the repricing gap is zero, so that all assets have a matching liability that reprices at the same time.
C. the modified duration gap of the balance sheet 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. When the modified duration is equal to the dollar duration.
67. Suppose a pension fund must have $10,000,000 five years from now to make required payments to retirees. If the pension wants to guarantee the funds are available regardless of future interest rate changes, it should
A. sell a 5-year duration bond so that it matures with a book value of $10,000,000.
B. sell $10,000,000 face value discount bonds with a duration of five years.
C. purchase 7-year, semi-annual coupon bonds that have a duration of five years.
D. purchase 8-year, annual payment bonds that have a dollar duration of $10,000,000.
E. none of the options since future interest rates are too unpredictable.
68. Why does immunization against interest rate shocks using duration for fixed-income securities work?
A. Because interest rate changes are relatively predictable.
B. Because the gains or losses on reinvested cash flows that result from an interest rate change are exactly offset by losses or gains from the security when it is sold.
C. Because the fixed-income security gravitates toward its maturity value as it approaches its maximum duration.
D. Because cash flows that result from the security are not reinvested so they are not affected by interest rate changes in the same way as the security’s gain or loss when it is sold.
E. It doesn’t work because perfect immunization is impossible to accomplish.
69. 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).
70. 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
71. The duration of a consol bond is
A. less than its maturity.
B. infinity.
C. 30 years.
D. more than its maturity.
E. given by the formula D = 1/(1-R).
72. 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.
73. Dollar duration of a fixed-income security is defined as
A. the dollar value change in the price of a security to a one-percent change in the return on the security.
B. the dollar value change in the price of a security to a change in the Macaulay’s duration of the security.
C. The market price of a security following a one-percent change in the return on the security.
D. Macaulay’s duration divided by one plus the interest rate times the market price of the security.
E. the modified duration of a security times the price of the security.
74. Immunization of a portfolio implies that changes in _____ will not affect the value of the portfolio.
A. book value of assets
B. maturity
C. market prices
D. interest rates
E. duration
75. 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.
76. 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.
77. 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
78. 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.
Feedback:
79. 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.
Feedback: Fully amortizing loan cash flows:
Macaulay's Duration
80. 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.
Feedback: Fully amortizing loan cash flows:
Fair Market Value
Macaulay's Duration
Modified Duration
81. 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.
Feedback: Fully amortizing loan cash flows:
Macaulay's Duration
82. 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. $23.10.
B. $976.90.
C. $977.23.
D. $1,023.10.
E. -$23.10.
Feedback: Modified Duration
Dollar Duration
Change in Price
New Price
83. 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. $28,572
B. $20,864
C. $15,000
D. $22,642
E. $71,428
Feedback: Modified Duration, semi-annual
Dollar Duration
Change in Price
New Price
84. 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.
Feedback: Macaulay's Duration
85. 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.
Feedback: Macaulay's Duration
The duration of a zero coupon bond is equal to its maturity.
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.
[Reference: 9-80]
86. 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.
[Refer to: 9-80]
Feedback: Change in the market value of equity, leverage-adjusted duration gap
∆E = −1.21 × $60,000,000 × (0.005 ÷ 1.08) = −$336,111
87. 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.
[Refer to: 9-80]
88. Consider a one-year maturity, $100,000 face value bond that pays a 6 percent fixed coupon annually. What is the price of the bond if market interest rates are 7 percent?
A. $99,050.15.
B. $99,457.94.
C. $99,249.62.
D. $100,000.00.
E. $99,065.42.
Feedback: $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
Consider a six-year maturity, $100,000 face value bond that pays a 5 percent fixed coupon annually.
[Reference: 9-89]
89. What is the price of the bond if market interest rates are 4 percent?
A. $105,816.44.
B. $105,287.67.
C. $105,242.14.
D. $100,000.00.
E. $106,290.56.
[Refer to: 9-89]
Feedback: $100,000 face value, 5% annual coupon, 6 year maturity, 4% rate
90. What is the price of the bond if market interest rates are 6 percent?
A. $95,082.68.
B. $95,769.55.
C. $95,023.00.
D. $100,000.00.
E. $96,557.87.
[Refer to: 9-89]
Feedback: $100,000 face value, 5% annual coupon, 6 year maturity, 6% rate
91. 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.
[Refer to: 9-83]
Feedback: 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
[Reference: 92]
92. 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.
[Refer to: 9-92]
Feedback: Duration of commercial loans
93. 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.
[Refer to: 9-92]
Feedback: 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
94. 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.
[Refer to: 9-92]
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.
[Reference: 8-95]
95. If rates do not change, the balance sheet position that maximizes the FI's returns is
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.
[Refer to: 9-95]
96. 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.
[Refer to: 9-95]
97. 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
[Refer to: 9-95]
Feedback:
98. 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
[Refer to: 9-95]
Feedback:
99. 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. -$1.756
B. -$1.775
C. +$98.24
D. -$1.000
E. +$1.924
[Refer to: 9-95]
Feedback: Modified Duration
Dollar Duration
Change in Price
Based on an 18-month, 8 percent (semiannual) coupon Treasury note selling at par.
100. 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.
[Refer to: 9-95]
Feedback:
101. 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. $0.000.
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.
[Refer to: 9-95]
Feedback: 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.
[Reference: 9-102]
102. 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.
[Refer to: 9-102]
Feedback:
103. 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.
[Refer to: 9-102]
Feedback:
104. 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.
[Refer to: 9-102]
Feedback:
Consider a five-year, 8 percent annual coupon bond selling at par of $1,000.
105. 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.
[Refer to: 9-102]
Feedback:
106. If interest rates increase by 20 basis points, what is the approximate change in the market price using the duration approximation?
A. -$7.985
B. -$7.941
C. -$3.990
D. +$3.990
E. +$7.949
[Refer to: 9-102]
Feedback: Modified Duration
Dollar Duration
Change in Price
107. Using present value bond valuation techniques, calculate the exact price of the bond after the interest rate increase of 20 basis points.
A. $1,007.94.
B. $992.02.
C. $992.06.
D. $996.01.
E. $1,003.99.
[Refer to: 9-102]
Feedback:
∆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.
[Reference: 9-108]
108. 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.
[Refer to: 9-108]
Feedback: Duration of 1-year Treasury note ($55,000,000, semi-annual coupon)
109. 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.
[Refer to: 9-108]
Feedback:
a. Find weighted average duration for all assets and liabilities
b. Find weighted average duration of liabilities
c. Find leverage-adjusted duration gap
110. 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.
[Refer to: 9-108]
Feedback: 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.
111. 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. What is the bond's current market price?
A. $962.09.
B. $961.39.
C. $1,000.
D. $1,038.90.
E. $995.05.
Feedback: $1,000 face value, 9% annual coupon, 5 year maturity, 10% rate
112. 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. 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
Feedback:
113. 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. 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
Feedback:
114. 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. 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
Feedback:
[Reference: 9-115]
115. 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.
[Refer to: 9-115]
Feedback:
116. 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.
[Refer to: 9-115]
Feedback:
117. 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.
[Refer to: 9-115]
Feedback:
The institution is exposed to increasing interest rates because the market value of assets will decline faster than the market value of liabilities.
118. 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
[Refer to: 9-115]
Feedback: Change in the market value of equity, leverage-adjusted duration gap
∆E = −0.4875 × $1,000,000,000 × (−0.009) = +$4,378,500
U.S. Treasury quotes from the WSJ on Oct. 15, 2003:
[Reference: 9-119]
119. 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.
[Refer to: 9-119]
Feedback: In addition to paying interest semi-annually, also recall that Treasuries are quoted on 32nds, so 102:8 = 102 + (8/32) = 102.25
120. 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. -$1,605.05
D. -$16.05
E. +$160.51
[Refer to: 9-119]
Feedback: 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:
[Reference: 9-121]
121. 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.
[Refer to: 9-121]
Feedback: 
122. 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.
[Refer to: 9-121]
Feedback: 
123. 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.
[Refer to: 9-121]
Feedback: 
124. 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.
[Refer to: 9-121]
Feedback:
125. 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.
[Refer to: 9-121]
Feedback: 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.
126. 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.
[Refer to: 9-121]
127. 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.
[Refer to: 9-121]
Feedback: 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.
[Reference: 9-128]
128. 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.
[Refer to: 9-128]
Feedback:
129. What is this bank's interest rate risk exposure, if any?
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.
[Refer to: 9-128]
Feedback:
Weighted Average Duration of Assets
Weighted Average Duration of Liabilities
Leverage-Adjusted Duration Gap
130. 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)
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.
[Refer to: 9-128]
Feedback:
Change in the market value of equity, leverage-adjusted duration gap
∆E = −0.21 × $271,000,000 × (0.0075) = −$426,825