Chapter Nine 
Interest Rate Risk II

True/False Questions

T  F  1.  Duration measures the average life of a financial asset. 
Answer: True   

T  F  2.  The economic meaning of duration is the interest elasticity of a financial assets price. 
Answer: True   

T  F  3.  Duration considers the timing of all of the cash flows of an asset by summing the product of the cash flows multiplied by the time of occurrence. 
Answer: False   

T  F  4.  In evaluating the cash flows in the duration calculation, it is important to compare their relative sizes even though the cash flows do not occur at the same time. 
Answer: False   

T  F  5.  Duration is the weighted-average present value of the cash flows using the timing of the cash flows as weights. 
Answer: False   

T  F  6.  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. 
Answer: True   

T  F  7.  Duration normally is less than the maturity of a fixed-rate coupon asset. 
Answer: True   

T  F  8.  Duration is equal to maturity when at least some of the cash flows are received at the maturity of the asset. 
Answer: False   

T  F  9.  Duration of a fixed-rate coupon bond will always be greater than one half of the maturity. 
Answer: False   

T  F  10.  Duration is related to maturity in a linear manner through the interest rate of the asset. 
Answer: False   

T  F  11.  Duration is related to maturity in a nonlinear manner through the current yield to maturity of  the asset. 
Answer: True   

T  F  12.  Duration of a zero coupon bond is equal to the bonds maturity. 
Answer: True   

T  F  13.  The duration of a consol bond is infinity. 
Answer: False   

T  F  14.  As interest rates rise, the duration of a consol bond decreases. 
Answer: True   

T  F  15.  Duration increases with the maturity of a fixed-income asset at a decreasing rate. 
Answer: True   

T  F  16.  For a given maturity fixed-income asset, duration decreases as the market yield increases. 
Answer: True   

T  F  17.  For a given maturity fixed-income asset, duration increases as the promised interest payment is lower. 
Answer: False   

T  F  18.  Larger coupon payments of a fixed-income asset cause the present value weights of the cash flows to be lower in the duration calculation. 
Answer: False   

T  F  19.  A higher numerical value for duration implies more interest rate sensitivity of an asset to interest rate shocks. 
Answer: True   

T  F  20.  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. 
Answer: False   

T  F  21.  For any change in interest rates, market prices of bonds move in an inversely proportional manner according to the size of the duration value. 
Answer: False   

T  F  22.  For a given change in yields, short-duration securities suffer a smaller capital loss or receive a smaller capital gain than do long-duration securities. 
Answer: True   

T  F  23.  Immunization of a portfolio implies that changes in interest rates will not affect the value of the portfolio. 
Answer: True   

T  F  24.  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. 
Answer: True   

T  F  25.  Investing in a zero-coupon asset with a maturity equal to the desired investment horizon removes investment risk from the investment management process. 
Answer: True   

T  F  26.  Buying a fixed-rate asset whose duration is exactly equal to the desired investment horizon immunizes against interest rate risk. 
Answer: True   

T  F  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. 
Answer: False   

T  F  28.  Using a fixed-rate bond to immunize a desired investment horizon means that the changes in market value at the horizon time period are offset by changes in the reinvestment income from the coupon payments. 
Answer: True   

T  F  29.  The duration of a portfolio of assets can be found by calculating a book value weighted average of the durations of the individual assets. 
Answer: False   

T  F  30.  For given changes in interest rates, the change in the market value of net worth is equal to the difference in the changes of the market value of the assets and liabilities. 
Answer: True   

T  F  31.  The leverage adjusted duration gap for an FI is equal to the duration of the assets minus the duration of the liabilities. 
Answer: False   

T  F  32.  Immunizing the balance sheet of an FI against interest rate risk requires that the leverage adjusted duration gap (DA-k*DL) should be set to zero. 
Answer: True   

T  F  33.  The smaller is the leverage adjusted duration gap, the more exposed is the FI to interest rate shocks. 
Answer: False   

T  F  34.  The larger is the size of an FI, the smaller is the net worth exposure from any given interest rate shock. 
Answer: False   

T  F  35.  The larger is the interest rate shock, the smaller is the interest rate risk exposure of an FI. 
Answer: False   

T  F  36.  Setting the duration of the assets to the duration of the liabilities will exactly immunize the net worth of an FI from interest rate shocks. 
Answer: False   

T  F  37.  Immunization of net worth for an FI requires the duration of the liabilities to be adjusted for the amount of leverage. 
Answer: True   

T  F  38.  The leverage adjusted duration of a typical depository institution is positive. 
Answer: True   

T  F  39.  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. 
Answer: False   

T  F  40.  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. 
Answer: False   

T  F  41.  Immunizing the net worth ratio requires that the duration of the assets be set equal to the duration of the liabilities. 
Answer: True   

T  F  42.  The duration of all floating rate debt instruments is equal to the time to maturity. 
Answer: False   

Multiple Choice Questions

Use the following to answer questions 43-45:

43.  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 
Answer: D   

44.  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 
Answer: B   

45.  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 
Answer: A   

Use the following to answer questions 46-50:

Current spot rates for an FI's assets (loans) and liabilities (CDs).  All interest rates are fixed and paid annually.

46.  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. 
Answer: D   

47.  What is the interest rate risk exposure of the optimal transaction in question 46 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. 
Answer: B   

48.  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 
Answer: B   

49.  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 question 47. 
A)  +1.25 years 
B)  +1.12 years 
C)  -1.12 years 
D)  +0.92 years 
E)  -1.25 years 
Answer: B   

50.  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 
Answer: B   

Use the following to answer questions 51-52:

Questions are based on an 18-month, 8 percent (semiannual) coupon Treasury note selling at par. 

51.  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 
Answer: C   

52.  If interest rates increase by 20 basis points (i.e., DR = 20 basis points), use the duration 
approximation to determine the approximate price change. 
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. 
Answer: B   

Use the following to answer questions 53-55:

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.

53.  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 
Answer: D   

54.  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 
Answer: B   

55.  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 
Answer: A   

56.  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. 
Answer: C   

57.  A major shortcoming of the maturity model is its 
A)  focus on market values. 
B)  neglect of reinvestment income on interim cash flows. 
C)  computational simplicity. 
D)  concern with mismatches on the balance sheet. 
E)  oversimplified assumptions. 
Answer: B   

Use the following to answer questions 58-59:

An FI has a leveraged-adjusted duration gap of 1.21 years, $60 million in assets, 7 percent equity to assets ratio, and market rates are 8 percent. 

58.  What is the impact on the dealer's market value of equity per $100 of assets if the relative 
change in all interest rates is an increase of 0.5 percent [i.e., DR/(1+R) = 0.5 percent]? 
A)  +$336,111 
B)  -$0.605 
C)  -$336,111 
D)  +$0.605 
E)  -$363,000 
Answer: B   

59.  What conclusions can you draw from the duration gap in your answer to question 58? 
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. 
Answer: C   

60.  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. 
Answer: C   

61.  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. 
A)  2 years. 
B)  1.89 years. 
C)  1.94 years. 
D)  1.49 years. 
E)  1.73 years. 
Answer: D   

62.  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. 
Answer: E   

63.  Which of the following statements is true? 
A)  The optimal duration gap is zero. 
B)  Duration gap measures the impact of unanticipated 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. 
Answer: B   

Use the following to answer questions 64-66:

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

64.  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 
Answer: B   

65.  If interest rates increase by 20 basis points, what is the approximate change in the market price using the duration approximation? 
A)  -$7.98 
B)  -$7.94 
C)  -$3.99 
D)  +$3.99 
E)  -$7.94 
Answer: A   

66.  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)  $1003.99 
Answer: C   

Use the following to answer questions 67-69:

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 .003 years. 

67.  What is the duration of the bank's Treasury note portfolio? 
A)  1.07 years 
B)  1.00 year 
C)  0.98 years 
D)  0.92 years 
E)  insufficient information. 
Answer: C   

68.  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 
Answer: D   

69.  If all interest rates fall by 1 percent, calculate the impact on the bank's market value of 
quity using the duration approximation.    (That is, DR/(1+R) = -1 percent) 
A)  The bank's market value of equity increases by $325,450. 
B)  The bank's market value of equity decreases by $325,450. 
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. 
Answer: A   

Use the following to answer questions 70-73:

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. 

70.  What is the bond's price? 
A)  $962.09 
B)  $961.39 
C)  $1,000 
D)  $1,038.90 
E)  $995.05 
Answer: A   

71.  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 
Answer: E   

72.  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 
Answer: E   

73.  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 
Answer: E   

74.  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 
Answer: D   

75.  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 
Answer: B   

Use the following to answer questions 76-79:

76.  Calculate the duration of the assets. 
A)  2.54 years. 
B)  4.375 years. 
C)  1.75 years. 
D)  3.08 years. 
E)  2.50 years. 
Answer: A   

77.  Calculate the duration of the liabilities. 
A)  2.05 years. 
B)  1.75 years. 
C)  2.22 years. 
D)  2.125 years. 
E)  2.50 years. 
Answer: C   

78.  Calculate the leveraged-adjusted duration gap and state the FI's interest rate risk exposure. 
A)  +1.03 years; exposed to interest rate increases. 
B)  +0.32 years; exposed to interest rate increases. 
C)  +0.86 years; exposed to interest rate increases. 
D)  +0.49 years; exposed to interest rate increases. 
E)  -1.32 years; exposed to interest rate decreases. 
Answer: D   

79.  If all interest rates decline 90 basis points (DR/(1+R) = -90 basis points), what is the change in the market value of equity? 
A)  -$4.430 million 
B)  +$3.925 million 
C)  +$4.380 million 
D)  +$2.550 million 
E)  +$0.022 million 
Answer: C   

80.  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)  +$28,571.43 
B)  -$20,864.46 
C)  -$15,000.00 
D)  +$20,864.46 
E)  -$28,571.43 
Answer: E   

81.  What is the duration of a two-year note selling at par and receiving 8 percent interest annually? 
A)  2 years. 
B)  1.75 years. 
C)  1.93 years. 
D)  1.5 years. 
E)  1.97 years. 
Answer: C   

82.  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 
Answer: D   

Use the following to answer questions 83-84:

Use the following Treasury quotes from the WSJ on Oct. 15,1993.

83.  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)  1.80 years 
D)  1.90 years 
E)  3.40 years 
Answer: B   

84.  .  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)  -$160.51 
B)  +$16.05 
C)  -$1,605.05 
D)  -$16.05 
E)  +$160.51 
Answer: A   

Use the following to answer questions 85-91:

Use the following balance sheet of an FI to answers questions. The numbers provided are in millions of dollars and reflect market values:

85.  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 
Answer: C   

86.  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 
Answer: C   

87.  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. 
Answer: B   

88.  What is the leveraged adjusted duration gap of the FI? 
A)  3.61years 
B)  3.74 years 
C)  4.01 years 
D)  4.26 years 
E)  4.51 years 
Answer: B   

89.  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)  decreasing the average duration of its liabilities to 6.78 years 
D)  increasing the average duration of its liabilities to 9.782 years 
E)  Increase the leverage ratio, k, to 1. 
Answer: D   

90.  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. 
Answer: E   

91.  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 
Answer: C   

Use the following to answer questions 92-94:

Use the following balance sheet ($millions) information

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. 

92.  What is the duration of the municipal notes (the value of x)? 
A)  1.94 years 
B)  2.00 years 
C)  1.00 year 
D)  1.81 years 
E)  0.97 years 
Answer: A   

93.  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. 
Answer: C   

94.  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., DR/(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. 
Answer: C   

True/False Questions

T  F  95.  The cost in terms of both time and money to restructure the balance sheet of large and complex FIs has decreased over time. 
Answer: True   

T  F  96.  Managers can achieve the results of duration matching by using derivatives to hedge interest rate risk. 
Answer: True   

T  F  97.  Immunizing net worth from interest rate risk using duration matching requires that the duration match must be realigned periodically as the maturity horizon approaches. 
Answer: True   

T  F  98.  The rate of change in duration values is less than the rate of change in maturity. 
Answer: True   

T  F  99.  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. 
Answer: False   

T  F  100.  As interest rate shocks increase in size, duration becomes a less accurate predictor of how much the prices of securities will change. 
Answer: True   

T  F  101.  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. 
Answer: False   

T  F  102.  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. 
Answer: True   

T  F  103.  Convexity is a desirable effect to a portfolio manager because it is easy to measure and price. 
Answer: False   

T  F  104.  All fixed-income assets exhibit convexity in their price-yield relationships. 
Answer: True   

T  F  105.  The greater is convexity, the more insurance a portfolio manager has against interest rate increases and the greater potential gain from rate decreases. 
Answer: True   

T  F  106.  The error from using duration to estimate the new price of a fixed-income security will be less as the amount of convexity increases. 
Answer: False   

T  F  107.  Calculating modified duration involves dividing the value of duration by the change in the market interest rate. 
Answer: False   

T  F  108.  The degree of curvature in the price-yield relationship is reflected by the CX parameter which measures the degree to which the capital loss effect exceeds the capital gain effect. 
Answer: False   

T  F  109.  Convexity decreases as the maturity decreases. 
Answer: True   

T  F  110.  Given the same maturity, zero coupon bonds have more convexity than do coupon bonds. 
Answer: True   

T  F  111.  Given the same duration, zero coupon bonds have more convexity than do coupon bonds. 
Answer: False   

T  F  112.  A key assumption of the duration model is that the term structure of interest rates must not be flat. 
Answer: False   

T  F  113.  In the purest sense, the appropriate duration measure of a bond should be found by discounting the cash flows of the bond by the discount rates on similar maturity zero coupon bonds. 
Answer: True   

T  F  114.  The purest duration measure, D*, is robust in the sense that changes in the yield curve from which it was calculated will not change its value. 
Answer: False   

T  F  115.  The effect of rescheduling an interest payment on a defaulted bond will cause the measure of duration to increase. 
Answer: True   

T  F  116.  The duration value for floating-rate assets is calculated in the same manner as for fixed-rate assets. 
Answer: False   

T  F  117.  One method of calculating the duration of demand deposits is to consider duration to be the average turnover of the deposit accounts in days. 
Answer: True   

T  F  118.  Duration is difficult to calculate for mortgages and mortgage-backed securities because of prepayment risk. 
Answer: True   

Multiple Choice Questions

Use the following to answer questions 119-122:

Consider a six-year, $1,000 par value, zero-coupon bond yielding 8 percent. 

119.  What is the duration of this bond? 
A)  4 years 
B)  5 years 
C)  6 years 
D)  4.5 years 
E)  5.25 years 
Answer: C   

120.  If interest rates increase to 9 percent, what is the amount of error (Pduration - Pmarket) in the price estimate using the duration relationship versus the true bond price determined in the market? 
A)  -$1.11 
B)  +$2.47 
C)  +$1.16 
D)  -$2.47 
E)  -$1.16 
Answer: A   

121.  What is the convexity factor (CX) for this bond? 
A)  36 
B)  28 
C)  130 
D)  25.72 
E)  312 
Answer: A   

122.  What is the change in price caused by convexity in the duration-convexity model for an interest rate increase to 9 percent? 
A)  $0.882 
B)  $1.134 
C)  $4.096 
D)  $0.810 
E)  $9.831 
Answer: B   

123.  The convexity adjustment 
A)  overestimates price decreases. 
B)  underestimates price increases. 
C)  approximates the curvature of the nonlinear price valuation function. 
D)  is less accurate for large interest rate changes because of its nonlinearity. 
E)  is more accurate for large interest rate changes because of its linearity. 
Answer: C   

124.  All of the following statements are true for fixed-rate bonds except? 
A)  Given the market interest rate and coupon rates, convexity increases as maturity increases. 
B)  Given the same maturity and market interest rate, convexity is lower for coupon bonds than for zeros. 
C)  Given the same duration and market interest rates, zero-coupon bonds are less convex than coupon bonds. 
D)  For incremental changes in the various properties of convexity, duration and convexity always change in the same direction. 
E)  Given the same maturity and coupon rates, convexity changes with changes in the market interest rates. 
Answer: D   

Use the following to answer questions 125-128:

Consider a 4-year, $1,000 par value, 7 percent annual coupon bond that is trading to yield 7 percent. 

125.  What is the duration of this bond? 
A)  4.000 years 
B)  3.557 years 
C)  2.000 years 
D)  3.624 years 
E)  3.847 years 
Answer: D   

126.  If interest rates increase to 8 percent, what is the amount of error (Pduration - Pmarket) in the price estimate using the duration relationship versus the true bond price determined in the market? 
A)  +$0.12 
B)  -$0.75 
C)  -$4.26 
D)  +$0.75 
E)  -$0.12 
Answer: B   

127.  What is the convexity factor (CX) for this bond? 
A)  36 
B)  28 
C)  130 
D)  15.30 
E)  312 
Answer: A   

128.  What is the change in price caused by convexity in the duration-convexity model for an interest rate increase to 8 percent? 
A)  $0.765 
B)  $15.60 
C)  $1.80 
D)  $1.40 
E)  $6.50 
Answer: B   

Use the following to answer questions 129-139:

Assume all interest is paid annually. All coupon instruments are priced at par.

129.  If your bank wanted to maximize net interest income, what position would you put on? 
A)  Earn a spread of 15 basis points by selling 1-year T-bills to invest in 2-year T-notes. 
B)  Earn a spread of 25 basis points by selling 1-year T-bills to invest in AAA-debt. 
C)  Earn a spread of 20 basis points by issuing 1-year CDs to invest in AAA-debt. 
D)  Earn a spread of 25 basis points by selling 2-year T-note to invest in 2-year CDs. 
E)  Earn a spread of 5 basis points by issuing 2-year CDs to invest in AAA-debt. 
Answer: C   

130.  What would be the risk exposure of the position that maximizes net interest income? 
A)  credit risk only. 
B)  interest rate risk only. 
C)  currency risk only. 
D)  Answers a and b. 
E)  Answers a, b, and c. 
Answer: D   

131.  If your bank puts on the position to maximize net interest income, what will be the impact on the bank's end of year 2 net interest income if all interest rates immediately (at t=0) increase 25 basis points? 
A)  End of year 2 net interest income is -0.05 percent. 
B)  End of year 2 net interest income is +0.05 percent. 
C)  End of year 2 net interest income is +0.25 percent. 
D)  End of year 2 net interest income is +0.20 percent. 
E)  End of year 2 net interest income is -0.20 percent. 
Answer: A   

132.  What is the duration of the Treasury note? 
A)  2.00 years 
B)  1.95 years 
C)  1.93 years 
D)  3.00 years 
E)  1.00 year 
Answer: B   

133.  What is the duration of the Treasury bill? 
A)  2.00 years 
B)  1.95 years 
C)  1.93 years 
D)  3.00 years 
E)  1.00 year 
Answer: E   

134.  What is the duration of the 2-year CD? 
A)  2.00 years 
B)  1.95 years 
C)  1.93 years 
D)  3.00 years 
E)  1.00 year 
Answer: B   

135.  What is the duration of the AAA-corporate debt? 
A)  2.00 years 
B)  1.95 years 
C)  1.93 years 
D)  3.00 years 
E)  1.00 year 
Answer: B   

136.  If AAA-corporate debt rates increase 10 basis points, use duration to calculate the approximate price change for a $100,000 bond. 
A)  -$185.71 
B)  +$185.71 
C)  -$95.24 
D)  +$95.24 
E)  -$1,838.10 
Answer: A   

137.  Use convexity to find the approximate price change for the 2-year AAA-corporate debt if interest rates increase by 10 basis points. 
A)  -$185.41 
B)  +$184.41 
C)  -$94.94 
D)  $94.94 
E)  -$1,837.80 
Answer: A   

138.  If the position that maximizes net interest income is fully financed using liabilities (i.e., there is no capital contribution), what is the position's duration gap? 
A)  0 
B)  1 year 
C)  0.95 years 
D)  1.93 years 
E)  0.05 years 
Answer: C   

139.  Using the position's duration gap, what is the impact on the bank's capital if all interest 
rates increase by a percentage rate of 10 basis points?  (That is, DR/1+R = 0.10 percent) 
A)  No impact. 
B)  A decline in the market value of capital of 0.095 percent. 
C)  An increase in the market value of capital of 0.095 percent. 
D)  A decline in the market value of capital of 0.50 percent. 
E)  An increase in the market value of capital of 0.50 percent. 
Answer: B