Finance 465 Chapter 9

95. If interest rates increase by 20 basis points (i.e., ∆R = 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.

D. $0.2672 per $100 face value.

111. 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.

D. +0.4875 years; exposed to interest rate increases.

96. 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

D. 0.955 years.

73. 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.

D. 1.49 years.

113. 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.

D. 1.90 years.

86. 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.

D. 1.91 years.

75. 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.

D. 2.85 years.

79. 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.

D. 5.00 years.

103. 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

D. 6.51 years

76. 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.

B. $976.90.

92. 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

B. +1.12 years

85. 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.

B. +2.579 percent.

93. 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

B. -$1.775

97. 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.

B. 0.354 years.

87. 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.

B. 0.83 years.

91. 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

B. 1.92 years

118. 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.

B. 3.74 years.

99. 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.

B. 4.31 years.

117. 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.

B. 5.35 years.

124. 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., ∆R/(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.

C. The market value of equity will decrease by $426,825.

Consider a six-year maturity, $100,000 face value bond that pays a 5 percent fixed coupon annually. 83. 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.

C. $105,242.14.

82. 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.

C. $99,249.62.

101. 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.

C. $992.06.

112. If all interest rates decline 90 basis points (∆R/(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

C. +$4.3875 million

80. 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., ∆R = 0.5 percent] A. +$336,111. B. -$0.605. C. -$336,111. D. +$0.605. E. -$363,000.

C. -$336,111.

121. 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.

C. -29.85 million.

71. 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.

C. 0.9756 years.

102. 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.

C. 0.98 years.

94. 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.

C. 1.443 years.

78. 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.

C. 1.93 years.

72. 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.

C. 1.94 years

110. 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.

C. 2.22 years.

116. 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.

C. 8.25 years.

56. A relatively high numerical value of the duration of an asset means which of the following? 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.

C. High sensitivity of an asset price to interest rate shocks.

123. 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.

C. The bank is exposed to increasing interest rates because it has a positive duration gap of +0.21 years.

84. 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.

A. $95,082.68.

105. 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.

A. $962.09.

114. 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

A. +$179.39

100. 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

A. -$7.985

98. 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.

A. 0.605 years.

122. 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.

A. 1.94 years.

109. 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.

A. 2.5375 years.

115. 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.

A. 3.28 years

70. 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.

A. As interest rate shocks increase in size.

88. 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.

A. Exposed to increasing rates.

104. 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, ∆R/(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.

A. The bank's market value of equity increases by $325,550.

65. 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).

A. less than its maturity.

67. 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.

A. the dollar value change in the price of a security to a one-percent change in the return on the security.

62. 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.

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.

69. 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.

B. Duration gap measures the impact of changes in interest rates on the market value of equity.

63. 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).

B. Larger the gap in absolute terms, the more exposed the FI is to interest rate shocks.

90. 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.

B. The risk that interest rates will rise since the FI must sell a 1-year CD in one year.

54. 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.

B. the interest elasticity of a security to a small change in interest rates.

81. 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.

C. The market value of the dealer's equity decreases slightly if interest rates rise.

64. 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

C. net worth exposure

61. 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.

C. purchase 7-year, semi-annual coupon bonds that have a duration of five years.

89. 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.

D. a positive spread of 165 basis points by selling 1-year CDs to finance 2-year loans.

57. 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.

D. duration value.

58. 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.

D. equal to time to repricing of the instrument.

55. 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.

D. higher duration and more cash flows.

119. 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.

D. increasing the average duration of its liabilities to 9.782 years.

68. 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

D. interest rates

60. 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. the modified duration is equal to the dollar duration.

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.

77. 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

E. $71,428

107. 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

E. +11.52 percent

108. 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

E. -3.84 percent

74. 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.

E. 1.36 years.

106. 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

E. 4.223 years.

59. 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. Console bonds. E. Derivatives.

E. Derivatives.

120. 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.

E. it does not assume a flat term structure, so its estimation is imprecise.