Managing Bond Portfolios Answer Key 2

Chapter 16 - Managing Bond Portfolios 21. The duration of a perpetuity with a yield of 8% is A. 13.50 years. B. 12.11 years. C. 6.66 years. D. cannot be determined. E. None of these is correct. D = 1.08/0.08 = 13.50 years. 22. A seven-year par value bond has a coupon rate of 9% and a modified duration of A. 7 years. B. 5.49 years. C. 5.03 years. D. 4.87 years. E. None of these is correct. Calculations are shown below. Chapter 16 - Managing Bond Portfolios 23. Par value bond XYZ has a modified duration of 6. 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 $60. B. If the market yield increases by 1% the bond's price will increase by $50. C. If the market yield increases by 1% the bond's price will decrease by $50. D. If the market yield increases by 1% the bond's price will increase by $60. E. None of these is correct. P/P = -D*y; −$60 = −6(0.01) × $1,000. 24. Which of the following bonds has the longest duration? A. An 8-year maturity, 0% coupon bond. B. An 8-year maturity, 5% coupon bond. C. A 10-year maturity, 5% coupon bond. D. A 10-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 25. Which one of the following par value 12% coupon bonds experiences a price change of $23 when the market yield changes by 50 basis points? A. The bond with a duration of 6 years. B. The bond with a duration of 5 years. C. The bond with a duration of 2.7 years. D. The bond with a duration of 5.15 years. E. None of these is correct. DP/P = −D X [D(1 + y)/(1 + y)]; −.023 = −D X [.005/1.12]; D = 5.15. 26. Which one of the following statements is true concerning the duration of a perpetuity? A. The duration of 15% yield perpetuity that pays $100 annually is longer than that of a 15% yield perpetuity that pays $200 annually. B. The duration of a 15% yield perpetuity that pays $100 annually is shorter than that of a 15% yield perpetuity that pays $200 annually. C. The duration of a 15% yield perpetuity that pays $100 annually is equal to that of 15% yield perpetuity that pays $200 annually. D. The duration of a perpetuity cannot be calculated. E. None of these is true. Duration of a perpetuity = (1 + y)/y; thus, the duration of a perpetuity is determined by the yield and is independent of the cash flow. Chapter 16 - Managing Bond Portfolios 27. Which one of the following statements is false concerning the duration of a perpetuity? A. The duration of 15% yield perpetuity that pays $100 annually is longer than that of a 15% yield perpetuity that pays $200 annually. B. The duration of a 15% yield perpetuity that pays $100 annually is shorter than that of a 15% yield perpetuity that pays $200 annually. C. The duration of a 15% yield perpetuity that pays $100 annually is equal to that of 15% yield perpetuity that pays $200 annually. D. The duration of 15% yield perpetuity that pays $100 annually is longer than that of a 15% yield perpetuity that pays $200 annually, and the duration of a 15% yield perpetuity that pays $100 annually is shorter than that of a 15% yield perpetuity that pays $200 annually. E. All of these are false. Duration of a perpetuity = (1 + y)/y; thus, the duration of a perpetuity is determined by the yield and is independent of the cash flow. 28. The two components of interest-rate risk are A. price risk and default risk. B. reinvestment risk and systematic risk. C. call risk and price risk. D. price risk and reinvestment risk. E. None of these is correct. Default, systematic, and call risks are not part of interest-rate risk. Only price and reinvestment risks are part of interest-rate risk. Chapter 16 - Managing Bond Portfolios 29. The duration of a coupon bond A. does not change after the bond is issued. B. can accurately predict the price change of the bond for any interest rate change. C. will decrease as the yield to maturity decreases. D. All of these are correct. E. None of these is correct. Duration changes as interest rates and time to maturity change, can only predict price changes accurately for small interest rate changes, and increases as the yield to maturity decreases. 30. Indexing of bond portfolios is difficult because A. the number of bonds included in the major indexes is so large that it would be difficult to purchase them in the proper proportions. B. many bonds are thinly traded so it is difficult to purchase them at a fair market price. C. the composition of bond indexes is constantly changing. D. All of these are correct. E. None of these is correct. All listed answers are correct. Chapter 16 - Managing Bond Portfolios 31. You have an obligation to pay $1,488 in four years and 2 months. In which bond would you invest your $1,000 to accumulate this amount, with relative certainty, even if the yield on the bond declines to 9.5% immediately after you purchase the bond? A. a 6-year; 10% coupon par value bond B. a 5-year; 10% coupon par value bond C. a 5-year; zero-coupon bond D. a 4-year; 10% coupon par value bond E. None of these is correct. When duration = horizon date, one is immunized, or protected, against one interest rate change. The zero has D = 5. Since the other bonds have the same coupon and yield, solve for the closest value of T that gives D = 4.2 years. 4.2 = (1.10))/.10 − [(1.10) + T(.10 − .10)]/= 1.1; .68 (1.10) T − .68 + .68 = 1.1; .68 (1.10) T = 1.1; (1.10) T = 1.6176; T [ln (1.10)] = ln (1.6176); T = 5.05 years, so choose the 5-year 10% coupon bond. 32. Duration measures A. weighted average time until a bond's half-life. B. weighted average time until cash flow payment. C. the time required to make excessive profit from the investment. D. weighted average time until a bond's half-life and the time required to make excessive profit from the investment. E. weighted average time until cash flow payment and the time required to make excessive profit from the investment. Duration measures weighted average time until cash flow payment because one receives coupon payments throughout the life of the bond (for coupon bonds); thus, duration is less than time to maturity (except for zeros). Chapter 16 - Managing Bond Portfolios 33. Duration A. assesses the time element of bonds in terms of both coupon and term to maturity. B. allows structuring a portfolio to avoid interest-rate risk. C. is a direct comparison between bond issues with different levels of risk. D. assesses the time element of bonds in terms of both coupon and term to maturity and allows structuring a portfolio to avoid interest-rate risk. E. assesses the time element of bonds in terms of both coupon and term to maturity and is a direct comparison between bond issues with different levels of risk. Duration is a weighted average of when the cash flows of a bond are received; thus both coupon and time to maturity are considered. If the duration of the portfolio equals the investor's horizon date, the investor is protected against interest rate changes. 34. Identify the bond that has the longest duration (no calculations necessary). A. 20-year maturity with an 8% coupon. B. 20-year maturity with a 12% coupon. C. 20-year maturity with a 0% coupon. D. 10-year maturity with a 15% coupon. E. 12-year maturity with a 12% coupon. The lower the coupon, the longer the duration. The zero-coupon bond is the ultimate low coupon bond, and thus would have the longest duration. Chapter 16 - Managing Bond Portfolios 35. When interest rates decline, the duration of a 10-year bond selling at a premium A. increases. B. decreases. C. remains the same. D. increases at first, then declines. E. decreases at first, then increases. The relationship between interest rates and duration is an inverse one. 36. An 8%, 30-year corporate bond was recently being priced to yield 10%. The Macaulay duration for the bond is 10.20 years. Given this information, the bond's modified duration would be ________. A. 8.05 B. 9.44 C. 9.27 D. 11.22 E. None of these is correct. D* = D/(1 + y); D* = 10.2/(1.1) = 9.27 Chapter 16 - Managing Bond Portfolios 37. An 8%, 15-year bond has a yield to maturity of 10% and duration of 8.05 years. If the market yield changes by 25 basis points, how much change will there be in the bond's price? A. 1.85% B. 2.01% C. 3.27% D. 6.44% E. None of these is correct. P/P = (−8.05 X 0.0025)/1.1 = 1.85% 38. One way that banks can reduce the duration of their asset portfolios is through the use of A. fixed rate mortgages. B. adjustable rate mortgages. C. certificates of deposit. D. short-term borrowing. E. None of these is correct. One of the gap management strategies practiced by banks is the issuance of adjustable rate mortgages, which reduce the interest rate sensitivity of their asset portfolios. Chapter 16 - Managing Bond Portfolios 39. The duration of a bond normally increases with an increase in A. term to maturity. B. yield to maturity. C. coupon rate. D. All of these are correct. E. None of these is correct. The relationship between duration and term to maturity is a direct one; the relationship between duration and yield to maturity and to coupon rate is negative. 40. Which one of the following is an incorrect statement concerning duration? A. The higher the yield to maturity, the greater the duration. B. The higher the coupon, the shorter the duration. C. The difference in duration is small between two bonds with different coupons each maturing in more than 15 years. D. The duration is the same as term to maturity only in the case of zero-coupon bonds. E. All of the statements are correct. The relationship between duration and yield to maturity is an inverse one; as is the relationship between duration and coupon rate. The difference in the durations of longer-term bonds of varying coupons (high coupon vs. zero) is considerable. Duration equals term to maturity only with zeros.