Ch16 Managing Bond Portfolios.docx

Chapter 16 Managing Bond Portfolios     Multiple Choice Questions   1. The duration of a bond is a function of the bond's  A. coupon rate. B. yield to maturity. C. time to maturity. D. All of these are correct. E. None of these is correct. Duration is calculated by discounting the bond's cash flows at the bond's yield to maturity and, except for zero-coupon bonds, is always less than time to maturity.  2. Ceteris paribus, the duration of a bond is positively correlated with the bond's  A. time to maturity. B. coupon rate. C. yield to maturity. D. All of these are correct. E. None of these is correct. Duration is negatively correlated with coupon rate and yield to maturity.  3. Ceteris paribus, the duration of a bond is negatively correlated with the bond's  A. time to maturity. B. coupon rate. C. yield to maturity. D. coupon rate and yield to maturity. E. None of these is correct. Duration is negatively correlated with coupon rate and yield to maturity.   4. Holding other factors constant, the interest-rate risk of a coupon bond is higher when the bond's:  A. term-to-maturity is lower. B. coupon rate is higher. C. yield to maturity is lower. D. current yield is higher. E. None of these is correct. The longer the maturity, the greater the interest-rate risk. The lower the coupon rate, the greater the interest-rate risk. The lower the yield to maturity, the greater the interest-rate risk. These concepts are reflected in the duration rules; duration is a measure of bond price sensitivity to interest rate changes (interest-rate risk).  5. Holding other factors constant, the interest-rate risk of a coupon bond is higher when the bond's:  A. term-to-maturity is higher. B. coupon rate is higher. C. yield to maturity is higher. D. All of these are correct. E. None of these is correct. The longer the maturity, the greater the interest-rate risk. The lower the coupon rate, the greater the interest-rate risk. The lower the yield to maturity, the greater the interest-rate risk. These concepts are reflected in the duration rules; duration is a measure of bond price sensitivity to interest rate changes (interest-rate risk).  6. Holding other factors constant, the interest-rate risk of a coupon bond is higher when the bond's:  A. term-to-maturity is lower. B. coupon rate is lower. C. yield to maturity is higher. D. term-to-maturity is lower and yield to maturity is higher. E. None of these is correct. The longer the maturity, the greater the interest-rate risk. The lower the coupon rate, the greater the interest-rate risk. The lower the yield to maturity, the greater the interest-rate risk. These concepts are reflected in the duration rules; duration is a measure of bond price sensitivity to interest rate changes (interest-rate risk).  7. Holding other factors constant, the interest-rate risk of a coupon bond is lower when the bond's:  A. term-to-maturity is lower. B. coupon rate is higher. C. yield to maturity is lower. D. term-to-maturity is lower and coupon rate is higher. E. All of these are correct. The longer the maturity, the greater the interest-rate risk. The lower the coupon rate, the greater the interest-rate risk. The lower the yield to maturity, the greater the interest-rate risk. These concepts are reflected in the duration rules; duration is a measure of bond price sensitivity to interest rate changes (interest-rate risk).   8. Holding other factors constant, the interest-rate risk of a coupon bond is lower when the bond's:  A. term-to-maturity is lower. B. coupon rate is higher. C. yield to maturity is higher. D. term-to-maturity is lower and coupon rate is higher. E. All of these are correct. The longer the maturity, the greater the interest-rate risk. The lower the coupon rate, the greater the interest-rate risk. The lower the yield to maturity, the greater the interest-rate risk. These concepts are reflected in the duration rules; duration is a measure of bond price sensitivity to interest rate changes (interest-rate risk).  9. Holding other factors constant, the interest-rate risk of a coupon bond is lower when the bond's:  A. term-to-maturity is higher. B. coupon rate is lower. C. yield to maturity is higher. D. term-to-maturity is higher and coupon rate is lower. E. All of these are correct. The longer the maturity, the greater the interest-rate risk. The lower the coupon rate, the greater the interest-rate risk. The lower the yield to maturity, the greater the interest-rate risk. These concepts are reflected in the duration rules; duration is a measure of bond price sensitivity to interest rate changes (interest-rate risk).  10. The "modified duration" used by practitioners is equal to the Macaulay duration  A. times the change in interest rate. B. times (one plus the bond's yield to maturity). C. divided by (one minus the bond's yield to maturity). D. divided by (one plus the bond's yield to maturity). E. None of these is correct. D* = D/(1 + y)  11. The "modified duration" used by practitioners is equal to ______ divided by (one plus the bond's yield to maturity).  A. current yield B. the Macaulay duration C. yield to call D. yield to maturity E. None of these is correct. D* = D/(1 + y)   12. Given the time to maturity, the duration of a zero-coupon bond is higher when the discount rate is  A. higher. B. lower. C. equal to the risk free rate. D. The bond's duration is independent of the discount rate. E. None of these is correct. The duration of a zero-coupon bond is equal to the maturity of the bond.  13. The interest-rate risk of a bond is  A. the risk related to the possibility of bankruptcy of the bond's issuer. B. the risk that arises from the uncertainty of the bond's return caused by changes in interest rates. C. the unsystematic risk caused by factors unique in the bond. D. the risk related to the possibility of bankruptcy of the bond's issuer and the risk that arises from the uncertainty of the bond's return caused by changes in interest rates. E. All of these are correct. Changing interest rates change the bond's return, both in terms of the price of the bond and the reinvestment of coupon payments.  14. Which of the following two bonds is more price sensitive to changes in interest rates? 1) A par value bond, X, with a 5-year-to-maturity and a 10% coupon rate. 2) A zero-coupon bond, Y, with a 5-year-to-maturity and a 10% yield-to-maturity.  A. Bond X because of the higher yield to maturity. B. Bond X because of the longer time to maturity. C. Bond Y 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. Bond Y has a longer duration.  15. Holding other factors constant, which one of the following bonds has the smallest price volatility?  A. 5-year, 0% coupon bond B. 5-year, 12% coupon bond C. 5 year, 14% coupon bond D. 5-year, 10% coupon bond E. Cannot tell from the information given. Duration (and thus price volatility) is lower when the coupon rates are higher.  16. Which of the following is not true?  A. Holding other things constant, the duration of a bond increases with time to maturity. B. Given time to maturity, the duration of a zero-coupon decreases with yield to maturity. C. Given time to maturity and yield to maturity, the duration of a bond is higher when the coupon rate is lower. D. Duration is a better measure of price sensitivity to interest rate changes than is time to maturity. E. All of these are correct. The duration of a zero-coupon bond is equal to time to maturity, and is independent of yield to maturity.  17. Which of the following is true?  A. Holding other things constant, the duration of a bond decreases with time to maturity. B. Given time to maturity, the duration of a zero-coupon increases with yield to maturity. C. Given time to maturity and yield to maturity, the duration of a bond is higher when the coupon rate is lower. D. Duration is a better measure of price sensitivity to interest rate changes than is time to maturity. E. Given time to maturity and yield to maturity, the duration of a bond is higher when the coupon rate is lower, and duration is a better measure of price sensitivity to interest rate changes than is time to maturity. The duration of a zero-coupon bond is equal to time to maturity, and is independent of yield to maturity. 18. The duration of a 5-year zero-coupon bond is  A. smaller than 5. B. larger than 5. C. equal to 5. D. equal to that of a 5-year 10% coupon bond. E. None of these is correct. Duration of a zero-coupon bond equals the bond's maturity.  19. The basic purpose of immunization is to  A. eliminate default risk. B. produce a zero net interest-rate risk. C. offset price and reinvestment risk. D. eliminate default risk and produce a zero net interest-rate risk. E. produce a zero net interest-rate risk and offset price and reinvestment risk. When a portfolio is immunized, price risk and reinvestment risk exactly offset each other resulting in zero net interest-rate risk.  20. The duration of a par value bond with a coupon rate of 8% and a remaining time to maturity of 5 years is  A. 5 years. B. 5.4 years. C. 4.17 years. D. 4.31 years. E. None of these is correct. Calculations are shown below.   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.  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.  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.  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, 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.  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.  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).   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.  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   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.  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.   41. Which one of the following is a correct 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 can be large 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. The higher the coupon, the shorter the duration; the difference in duration can be large between two bonds with different coupons each maturing in more than 15 years; and the duration is the same as term to maturity only in the case of zero-coupon bonds 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.   42. Immunization is not a strictly passive strategy because  A. it requires choosing an asset portfolio that matches an index. B. there is likely to be a gap between the values of assets and liabilities in most portfolios. C. it requires frequent rebalancing as maturities and interest rates change. D. durations of assets and liabilities fall at the same rate. E. None of these is correct. As time passes the durations of assets and liabilities fall at different rates, requiring portfolio rebalancing. Further, every change in interest rates creates changes in the durations of portfolio assets and liabilities.  43. Some of the problems with immunization are  A. duration assumes that the yield curve is flat. B. duration assumes that if shifts in the yield curve occur, these shifts are parallel. C. immunization is valid for one interest rate change only. D. durations and horizon dates change by the same amounts with the passage of time. E. duration assumes that the yield curve is flat, duration assumes that if shifts in the yield curve occur, these shifts are parallel, and immunization is valid for one interest rate change only. Durations and horizon dates change with the passage of time, but not by the same amounts.  44. If a bond portfolio manager believes  A. in market efficiency, he or she is likely to be a passive portfolio manager. B. that he or she can accurately predict interest rate changes, he or she is likely to be an active portfolio manager. C. that he or she can identify bond market anomalies, he or she is likely to be a passive portfolio manager. D. in market efficiency, he or she is likely to be a passive portfolio manager; and that he or she can accurately predict interest rate changes, he or she is likely to be an active portfolio manager. E. in market efficiency, he or she is likely to be a passive portfolio manager; that he or she can accurately predict interest rate changes, he or she is likely to be an active portfolio manager; and that he or she can identify bond market anomalies, he or she is likely to be a passive portfolio manager. If one believes that one can predict bond market anomalies, one is likely to be an active portfolio manager.  45. Cash flow matching on a multiperiod basis is referred to as  A. immunization. B. contingent immunization. C. dedication. D. duration matching. E. rebalancing. Cash flow matching on a multiperiod basis is referred to as a dedication strategy.  46. Immunization through duration matching of assets and liabilities may be ineffective or inappropriate because  A. conventional duration strategies assume a flat yield curve. B. duration matching can only immunize portfolios from parallel shifts in the yield curve. C. immunization only protects the nominal value of terminal liabilities and does not allow for inflation adjustment. D. conventional duration strategies assume a flat yield curve; and immunization only protects the nominal value of terminal liabilities and does not allow for inflation adjustment. E. All of these are correct. All of these are correct statements about the limitations of immunization through duration matching.  47. The curvature of the price-yield curve for a given bond is referred to as the bond's  A. modified duration. B. immunization. C. sensitivity. D. convexity. E. tangency. Convexity measures the rate of change of the slope of the price-yield curve, expressed as a fraction of the bond's price.   48. Consider a bond selling at par with modified duration of 10.6 years and convexity of 210. A 2 percent decrease in yield would cause the price to increase by 21.2%, according to the duration rule. What would be the percentage price change according to the duration-with-convexity rule?  A. 21.2% B. 25.4% C. 17.0% D. 10.6% E. None of these is correct. P/P = ?D*y + (1/2) * Convexity * (y)2; = ?10.6 * ?.02 + (1/2) * 210 * (.02)2 = .212 + .042 = .254 (25.4%)  49. A substitution swap is an exchange of bonds undertaken to  A. change the credit risk of a portfolio. B. extend the duration of a portfolio. C. reduce the duration of a portfolio. D. profit from apparent mispricing between two bonds. E. adjust for differences in the yield spread. A substitution swap is an example of bond price arbitrage, undertaken when the portfolio manager attempts to profit from apparent mispricing.  50. A rate anticipation swap is an exchange of bonds undertaken to  A. shift portfolio duration in response to an anticipated change in interest rates. B. shift between corporate and government bonds when the yield spread is out of line with historical values. C. profit from apparent mispricing between two bonds. D. change the credit risk of the portfolio. E. increase return by shifting into higher yield bonds. A rate anticipation swap is pegged to interest rate forecasting, and involves increasing duration when rates are expected to fall and vice-versa.  51. An analyst who selects a particular holding period and predicts the yield curve at the end of that holding period is engaging in  A. a rate anticipation swap. B. immunization. C. horizon analysis. D. an intermarket spread swap. E. None of these is correct. Horizon analysis involves selecting a particular holding period and predicting the yield curve at the end of that holding period. The holding period return for the bond can then be predicted.   52. Interest-rate risk is important to  A. active bond portfolio managers. B. passive bond portfolio managers. C. both active and passive bond portfolio managers. D. neither active nor passive bond portfolio managers. E. obsessive bond portfolio managers. Active managers try to identify interest rate trends so they can move in the right direction before the changes. Passive managers try to minimize interest-rate risk by offsetting it with price changes in strategies such as immunization.  53. Which of the following are true about the interest-rate sensitivity of bonds? I) Bond prices and yields are inversely related. II) Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds. III) Interest-rate risk is directly related to the bond's coupon rate. IV) The sensitivity of a bond's price to a change in its yield to maturity is inversely related to the yield to maturity at which the bond is currently selling.  A. I and II B. I and III C. I, II, and IV D. II, III, and IV E. I, II, III, and IV Number III is incorrect because interest-rate risk is inversely related to the bond's coupon rate.  54. Which of the following are false about the interest-rate sensitivity of bonds? I) Bond prices and yields are inversely related. II) Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds. III) Interest-rate risk is directly related to the bond's coupon rate. IV) The sensitivity of a bond's price to a change in its yield to maturity is inversely related to the yield to maturity at which the bond is currently selling.  A. I B. III C. I, II, and IV D. II, III, and IV E. I, II, III, and IV Number III is incorrect because interest-rate risk is inversely related to the bond's coupon rate.   55. Which of the following researchers have contributed significantly to bond portfolio management theory? I) Sidney Homer II) Harry Markowitz III) Burton Malkiel IV) Martin Liebowitz V) Frederick Macaulay  A. I and II B. III and V C. III, IV, and V D. I, III, IV, and V E. I, II, III, IV, and V Harry Markowitz developed the mean-variance criterion but not a theory of bond portfolio management.  56. According to the duration concept  A. only coupon payments matter. B. only maturity value matters. C. the coupon payments made prior to maturity make the effective maturity of the bond greater than its actual time to maturity. D. the coupon payments made prior to maturity make the effective maturity of the bond less than its actual time to maturity. E. coupon rates don't matter. Duration considers that some of the cash flows are received prior to maturity and this effectively makes the maturity less than the actual time to maturity.  57. Duration is important in bond portfolio management because I) it can be used in immunization strategies. II) it provides a gauge of the effective average maturity of the portfolio. III) it is related to the interest rate sensitivity of the portfolio. IV) it is a good predictor of interest rate changes.  A. I and II B. I and III C. III and IV D. I, II, and III E. I, II, III, and IV Duration can be used to calculate the approximate effect of interest rate changes on prices, but is not used to forecast interest rates.   58. Two bonds are selling at par value and each has 17 years to maturity. The first bond has a coupon rate of 6% and the second bond has a coupon rate of 13%. Which of the following is true about the durations of these bonds?  A. The duration of the higher-coupon bond will be higher. B. The duration of the lower-coupon bond will be higher. C. The duration of the higher-coupon bond will equal the duration of the lower-coupon bond. D. There is no consistent statement that can be made about the durations of the bonds. E. The bond's durations cannot be determined without knowing the prices of the bonds. In general, duration is negatively related to coupon rate. The greater the cash flows from coupon interest, the lower the duration will be. Since the bonds have the same time to maturity, that isn't a factor. The duration of the 6% coupon bond equals (1.06/.06)*(1 ? (1/1.0617)) = 11.10. The duration of the 13% coupon bond equals (1.13/.13)*(1 ? (1/1.1317)) = 7.60.  59. Two bonds are selling at par value and each has 17 years to maturity. The first bond has a coupon rate of 6% and the second bond has a coupon rate of 13%. Which of the following is most false about the durations of these bonds?  A. The duration of the higher-coupon bond will be higher. B. The duration of the lower-coupon bond will be higher. C. The duration of the higher-coupon bond will equal the duration of the lower-coupon bond. D. There is no consistent statement that can be made about the durations of the bonds. E. The duration of the higher-coupon bond will be higher and will equal the duration of the lower-coupon bond; and there is no consistent statement that can be made about the durations of the bonds In general, duration is negatively related to coupon rate. The greater the cash flows from coupon interest, the lower the duration will be. Since the bonds have the same time to maturity, that isn't a factor. The duration of the 6% coupon bond equals (1.06/.06)*(1 ? (1/1.0617)) = 11.10. The duration of the 13% coupon bond equals (1.13/.13)*(1 ? (1/1.1317)) = 7.60.  60. Which of the following offers a bond index?  A. Merrill Lynch B. Salomon C. Barclays Capital D. All of these are correct. E. All but Merrill Lynch All of these are mentioned in the text's discussion of bond indexes.   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.  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.   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.  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   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.  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   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%  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-with-convexity 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%)   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-with-convexity 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.  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   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.   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.   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.