Managing Bond Portfolios Answer Key 4

Chapter 16 - Managing Bond Portfolios 61. Which of the following two bonds is more price sensitive to changes in interest rates? 1) A par value bond, A, with a 12-year-to-maturity and a 12% coupon rate. 2) A zero-coupon bond, B, with a 12-year-to-maturity and a 12% yield-to-maturity. A. Bond A because of the higher yield to maturity. B. Bond A because of the longer time to maturity. C. Bond B because of the longer duration. D. Both have the same sensitivity because both have the same yield to maturity. E. None of these is correct. Duration is the best measure of bond price sensitivity; the longer the duration the higher the price sensitivity. 62. Which of the following two bonds is more price sensitive to changes in interest rates? 1) A par value bond, D, with a 2-year-to-maturity and a 8% coupon rate. 2) A zero-coupon bond, E, with a 2-year-to-maturity and a 8% yield-to-maturity. A. Bond D because of the higher yield to maturity. B. Bond E because of the longer duration. C. Bond D because of the longer time to maturity. D. Both have the same sensitivity because both have the same yield to maturity. E. None of these is correct. Duration is the best measure of bond price sensitivity; the longer the duration the higher the price sensitivity. Chapter 16 - Managing Bond Portfolios 63. Holding other factors constant, which one of the following bonds has the smallest price volatility? A. 7-year, 0% coupon bond B. 7-year, 12% coupon bond C. 7 year, 14% coupon bond D. 7-year, 10% coupon bond E. Cannot tell from the information given. Duration (and thus price volatility) is lower when the coupon rates are higher. 64. Holding other factors constant, which one of the following bonds has the smallest price volatility? A. 20-year, 0% coupon bond B. 20-year, 6% coupon bond C. 20 year, 7% coupon bond D. 20-year, 9% coupon bond E. Cannot tell from the information given. Duration (and thus price volatility) is lower when the coupon rates are higher. Chapter 16 - Managing Bond Portfolios 65. The duration of a 15-year zero-coupon bond is A. smaller than 15. B. larger than 15. C. equal to 15. D. equal to that of a 15-year 10% coupon bond. E. None of these is correct. Duration of a zero-coupon bond equals the bond's maturity. 66. The duration of a 20-year zero-coupon bond is A. equal to 20. B. larger than 20. C. smaller than 20. D. equal to that of a 20-year 10% coupon bond. E. None of these is correct. Duration of a zero-coupon bond equals the bond's maturity. 67. The duration of a perpetuity with a yield of 10% is A. 13.50 years. B. 11 years. C. 6.66 years. D. cannot be determined. E. None of these is correct. D = 1.10/0.10 = 11 years. Chapter 16 - Managing Bond Portfolios 68. The duration of a perpetuity with a yield of 6% is A. 13.50 years. B. 12.11 years. C. 17.67 years. D. cannot be determined. E. None of these is correct. D = 1.06/0.06 = 17.67 years. 69. Par value bond F has a modified duration of 9. Which one of the following statements regarding the bond is true? A. If the market yield increases by 1% the bond's price will decrease by $90. B. If the market yield increases by 1% the bond's price will increase by $90. C. If the market yield increases by 1% the bond's price will decrease by $60. D. If the market yield decreases by 1% the bond's price will increase by $60. E. None of these is true. P/P = −D*y; −$90 = −9(0.01) × $1,000 Chapter 16 - Managing Bond Portfolios 70. Par value bond GE has a modified duration of 11. Which one of the following statements regarding the bond is true? A. If the market yield increases by 1% the bond's price will decrease by $55. B. If the market yield increases by 1% the bond's price will increase by $55. C. If the market yield increases by 1% the bond's price will decrease by $110. D. If the market yield increases by 1% the bond's price will increase by $110. E. None of these is true. P/P = −D*y; −$110 = −11(0.01) × $1,000 71. Which of the following bonds has the longest duration? A. A 15-year maturity, 0% coupon bond. B. A 15-year maturity, 9% coupon bond. C. A 20-year maturity, 9% coupon bond. D. A 20-year maturity, 0% coupon bond. E. Cannot tell from the information given. The longer the maturity and the lower the coupon, the greater the duration. Chapter 16 - Managing Bond Portfolios 72. Which of the following bonds has the longest duration? A. A 12-year maturity, 0% coupon bond. B. A 12-year maturity, 8% coupon bond. C. A 4-year maturity, 8% coupon bond. D. A 4-year maturity, 0% coupon bond. E. Cannot tell from the information given. The longer the maturity and the lower the coupon, the greater the duration. 73. A 10%, 30-year corporate bond was recently being priced to yield 12%. The Macaulay duration for the bond is 11.3 years. Given this information, the bond's modified duration would be A. 8.05 B. 10.09 C. 9.27 D. 11.22 E. None of these is correct. D* = D/(1 + y); D* = 11.3/(1.12) = 10.09 Chapter 16 - Managing Bond Portfolios 74. A 6%, 30-year corporate bond was recently being priced to yield 8%. The Macaulay duration for the bond is 8.4 years. Given this information, the bond's modified duration would be A. 8.05 B. 9.44 C. 9.27 D. 7.78 E. None of these is correct. D* = D/(1 + y); D* = 8.4/(1.08) = 7.78 75. A 9%, 16-year bond has a yield to maturity of 11% and duration of 9.25 years. If the market yield changes by 32 basis points, how much change will there be in the bond's price? A. 1.85% B. 2.01% C. 2.67% D. 6.44% E. None of these is correct. P/P = (−9.25 × 0.0032)/1.11 = 2.67% Chapter 16 - Managing Bond Portfolios 76. A 7%, 14-year bond has a yield to maturity of 6% and duration of 7 years. If the market yield changes by 44 basis points, how much change will there be in the bond's price? A. 1.85% B. 2.91% C. 3.27% D. 6.44% E. None of these is correct. P/P = (−7 × 0.0044)/1.06 = 2.91% 77. Consider a bond selling at par with modified duration of 12 years and convexity of 265. A 1 percent decrease in yield would cause the price to increase by 12%, according to the duration rule. What would be the percentage price change according to the duration-withconvexity rule? A. 21.2% B. 25.4% C. 17.0% D. 13.3% E. None of these is correct. P/P = −D*y + (1/2) * Convexity * (y)2; = −12 * −.01 + (1/2) * 265 * (.01)2 = .12 + .01325 = .13325 or (13.3%) Chapter 16 - Managing Bond Portfolios 78. Consider a bond selling at par with modified duration of 22-years and convexity of 415. A 2 percent decrease in yield would cause the price to increase by 44%, according to the duration rule. What would be the percentage price change according to the duration-withconvexity rule? A. 21.2% B. 25.4% C. 17.0% D. 52.3% E. None of these is correct. P/P = −D*y + (1/2) * Convexity * (y)2; = −22 * −.02 + (1/2) * 415* (.02)2 = .44 + .083 = .523 or (52.3%) 79. The duration of a par value bond with a coupon rate of 6.5% and a remaining time to maturity of 4 years is A. 3.65 years. B. 3.45 years. C. 3.85 years. D. 4.00 years. E. None of these is correct. Calculations are shown below. Chapter 16 - Managing Bond Portfolios 80. The duration of a par value bond with a coupon rate of 7% and a remaining time to maturity of 3 years is A. 3 years. B. 2.71years. C. 2.81 years. D. 2.91 years. E. None of these is correct. Calculations are shown below. 81. The duration of a par value bond with a coupon rate of 8.7% and a remaining time to maturity of 6 years is A. 6.0 years. B. 5.1 years. C. 4.27 years. D. 3.95 years. E. None of these is correct. Calculations are shown below. Short Answer Questions Chapter 16 - Managing Bond Portfolios 82. Discuss duration. Include in your discussion what duration measures, how duration relates to maturity, what variables affect duration, and how duration is used as a portfolio management tool (include some of the problems associated with the use of duration as a portfolio management tool). Duration is a measure of the time it takes to recoup one's investment in a bond, assuming that one purchased the bond for $1,000. Duration is shorter than term to maturity on coupon bonds as cash flows are received prior to maturity. Duration equals term to maturity for zero-coupon bonds, as no cash flows are received prior to maturity. Duration measures the price sensitivity of a bond with respect to interest rate changes. The longer the maturity of the bond, the lower the coupon rate of the bond, and the lower the yield to maturity of the bond, the greater the duration. Interest-rate risk consists of two components: price risk and reinvestment risk. These two risk components move in opposite direction; if duration equals horizon date, the two types of risk exactly offset each other, resulting in zero net interest-rate risk. This portfolio management strategy is immunization. Some of the problems associated with this strategy are: the portfolio is protected against one interest rate change only; thus, once interest rates change, the portfolio must be rebalanced to maintain immunization; duration assumes a horizontal yield curve (not the shape most commonly observed); duration also assumes that any shifts in the yield curve are parallel (resulting in a continued horizontal yield curve); in addition, the portfolio manager may have trouble locating acceptable bonds that produce immunized portfolios; finally, both duration and horizon dates change with the mere passage of time, but not in a lockstep fashion, thus rebalancing is required. Although immunization is considered a passive bond portfolio management strategy, considerable rebalancing must occur, as indicated above. The portfolio manager must consider the tradeoffs between the transaction costs and not being perfectly immunized at all times. Feedback: The rationale for the question is to be certain that the student thoroughly understands duration, how duration is used as a portfolio management tool, and the deficiencies of duration as a portfolio management tool. Chapter 16 - Managing Bond Portfolios 83. Discuss rate anticipation swaps as a bond portfolio management strategy. A rate anticipation swap is an active bond portfolio management strategy, based on predicting future interest rates. If a portfolio manager believes that interest rates will decline, the manager will swap into bonds of greater duration. Conversely, if the portfolio manager believes that interest rates will increase, the portfolio manager will swap into bonds of shorter duration. This strategy is an active one, resulting in high transactions costs, and the success of this strategy is predicated on the bond portfolio manager's ability to predict correctly interest rate changes consistently over time (a difficult task, indeed). Feedback: The rationale behind this question is to ascertain if the student understands the risk of one of the most common types of active bond portfolio management strategies and the relationship of this strategy to duration. Chapter 16 - Managing Bond Portfolios 84. You have purchased a bond for $973.02. The bond has a coupon rate of 6.4%, pays interest annually, has a face value of $1,000, 4 years to maturity, and a yield to maturity of 7.2%. The bond's duration is 3.6481 years. You expect that interest rates will fall by .3% later today. Use the modified duration to find the approximate percentage change in the bond's price. Find the new price of the bond from this calculation. Use your calculator to do the regular present value calculations to find the bond's new price at its new yield to maturity. What is the amount of the difference between the two answers? Why are your answers different? Explain the reason in words and illustrate it graphically. Calculations are shown below. Find new price using modified duration: Modified duration = 3.6481/1.072 = 3.403 years. Approximate percentage price change using modified duration = −3.403*(−.003) = 1.02%. New Price = $973.02 * 1.0102 = $982.94 ($982.96 if duration isn't rounded) Find new price by taking present value at the new yield to maturity: N=4, I=6.9%, PMT=64, FV=1000, CPT PV=983.03. The answers are different by $0.09. The reason is that using modified duration gives an approximation of the percentage change in price. It should only be used for small changes in yields because of bond price convexity. As you move farther away from the original yield, the slope of the straight line that shows the duration approximation no longer matches the slope of the curved line that shows the actual price changes. Feedback: This question investigates the depth of the student's understanding of duration, its use in approximating interest rate sensitivity, and the potential shortcomings of using it.