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1、Chapter 16 Managing Bond Portfolios Multiple Choice Questions1.The duration of a bond is a function of the bonds A)coupon rate. B)yield to maturity. C)time to maturity. D)all of the above. E)none of the above. Answer: D Difficulty: Easy Rationale: Duration is calculated by discounting the bonds cash
2、 flows at the bonds 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 bonds A)time to maturity. B)coupon rate. C)yield to maturity. D)all of the above. E)none of the above. Answer: A D
3、ifficulty: Moderate Rationale: Duration is negatively correlated with coupon rate and yield to maturity.3.Holding other factors constant, the interest-rate risk of a coupon bond is higher when the bonds: A)term-to-maturity is lower. B)coupon rate is higher. C)yield to maturity is lower. D)current yi
4、eld is higher. E)none of the above. Answer: C Difficulty: Moderate Rationale: 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
5、in the duration rules; duration is a measure of bond price sensitivity to interest rate changes (interest-rate risk).4.The modified duration used by practitioners is equal to the Macaulay duration A)times the change in interest rate. B)times (one plus the bonds yield to maturity). C)divided by (one
6、minus the bonds yield to maturity). D)divided by (one plus the bonds yield to maturity). E)none of the above. Answer: D Difficulty: Moderate Rationale: D* = D/(1 + y)5.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
7、 risk free rate. D)The bonds duration is independent of the discount rate. E)none of the above. Answer: D Difficulty: Moderate Rationale: The duration of a zero-coupon bond is equal to the maturity of the bond.6.The interest-rate risk of a bond is A)the risk related to the possibility of bankruptcy
8、of the bonds issuer. B)the risk that arises from the uncertainty of the bonds return caused by changes in interest rates. C)the unsystematic risk caused by factors unique in the bond. D)A and B above. E)A, B, and C above. Answer: B Difficulty: Moderate Rationale: Changing interest rates change the b
9、onds return, both in terms of the price of the bond and the reinvestment of coupon payments.7.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-matur
10、ity 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 the above Answer: C Difficulty: Modera
11、te Rationale: Duration is the best measure of bond price sensitivity; the longer the duration the higher the price sensitivity.8.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
12、 bond D)5-year, 10% coupon bond E)Cannot tell from the information given. Answer: C Difficulty: Moderate Rationale: Duration (and thus price volatility) is lower when the coupon rates are higher.9.Which of the following is not true? A)Holding other things constant, the duration of a bond increases w
13、ith 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
14、 than is time to maturity. E)All of the above. Answer: B Difficulty: Moderate Rationale: The duration of a zero-coupon bond is equal to time to maturity, and is independent of yield to maturity.10.The duration of a 5-year zero-coupon bond is A)smaller than 5. B)larger than 5. C)equal to 5. D)equal t
15、o that of a 5-year 10% coupon bond. E)none of the above. Answer: C Difficulty: Easy Rationale: Duration of a zero-coupon bond equals the bonds maturity.11.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.
16、D)A and B. E)B and C. Answer: E Difficulty: Moderate Rationale: When a portfolio is immunized, price risk and reinvestment risk exactly offset each other resulting in zero net interest-rate risk.12.The duration of a par value bond with a coupon rate of 8% and a remaining time to maturity of 5 years
17、is A)5 years. B)5.4 years. C)4.17 years. D)4.31 years. E)none of the above. Answer: D Difficulty: Moderate Rationale: Calculations are shown below.Yr.CFPV of CF08%Weight * Yr.1$80$80/1.08 = $74.070.0741 * 1 = 0.07412$80$80/(1.08)2 = $68.590.0686 * 2 = 0.13723$80$80/(1.08)3 = $63.510.0635 * 3 = 0.190
18、54$80$80/(1.08)4 = $58.800.0588 * 4 = 0.23525$1,080$1,080/(1.08)5 = $735.030.7350 * 5 = 3.6750Sum$1000.004.3120 yrs. (duration)13.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 the above. Answer: A Difficulty: Easy Rat
19、ionale: D = 1.08/0.08 = 13.50 years.14.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 the above. Answer: C Difficulty: Difficult Rationale: Calculations are shown below.Yr.CFPV of CF9%Weight * Yr.1$90$82.5
20、70.0826 X 1 = 0.08262$90$75.750.0758 X 2 = 0.15163$90$69.500.0695 X 3 = 0.20854$90$63.760.0638 X 4 = 0.25525$90$58.490.0585 X 5 = 0.29256$90$53.660.0537 X 6 = 0.32227$1,090$596.260.5963 X 7 = 4.1741Sum$1000.005.4867 years (duration)modified duration = 5.4867 years/1.09 = 5.03 years.15.Par value bond
21、 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 bonds price will decrease by $60. B)If the market yield increases by 1% the bonds price will increase by $50. C)If the market yield increases by 1% the bonds
22、 price will decrease by $50. D)If the market yield increases by 1% the bonds price will increase by $60. E)None of the above. Answer: A Difficulty: Moderate Rationale: = -D*-$60 = -6(0.01) X $1,00016.Which of the following bonds has the longest duration? A)An 8-year maturity, 0% coupon bond. B)An 8-
23、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. Answer: D Difficulty: Moderate Rationale: The longer the maturity and the lower the coupon, the greater the duration17.Which one of the following par v
24、alue 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 the above. Answer: D Di
25、fficulty: Difficult Rationale: DP/P = -D X D(1+y) / (1+y); -.023 = -D X .005 / 1.12; D = 5.15.18.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 pa
26、ys $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
27、 of a perpetuity cannot be calculated. E)None of the above. Answer: C Difficulty: Easy Rationale: 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.19.The two components of interest-rate risk are A)price risk and d
28、efault risk. B)reinvestment risk and systematic risk. C)call risk and price risk. D)price risk and reinvestment risk. E)none of the above. Answer: D Difficulty: Easy Rationale: Default, systematic, and call risks are not part of interest-rate risk. Only price and reinvestment risks are part of inter
29、est-rate risk.20.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 the above are true. E)none of the above is true. Answer: E Diffi
30、culty: Easy Rationale: 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.21.Indexing of bond portfolios is difficult because A)the number of bonds included in the
31、 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 the above are true. E)both A and B are true.
32、 Answer: D Difficulty: Moderate Rationale: All of the above are true statements about bond indexes.22.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
33、 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 the above Answer: B Difficulty: Difficult Rationale: When duration = horizon date, one is immuniz
34、ed, 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 = 1.61
35、76; T ln (1.10) = ln (1.6176); T = 5.05 years, so choose the 5-year 10% coupon bond.23.Duration measures A)weighted average time until a bonds half-life. B)weighted average time until cash flow payment. C)the time required to recoup ones investment, assuming the bond was purchased for $1,000. D)A an
36、d C. E)B and C. Answer: E Difficulty: Moderate Rationale: B and C are true, as one receives coupon payments throughout the life of the bond (for coupon bonds); thus, duration is less than time to maturity (except for zeros).24.Duration A)assesses the time element of bonds in terms of both coupon and
37、 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)A and B. E)A and C. Answer: D Difficulty: Moderate Rationale: Duration is a weighted average of when the cash flows of a bond are received; t
38、hus both coupon and time to maturity are considered. If the duration of the portfolio equals the investors horizon date, the investor is protected against interest rate changes.25.Identify the bond that has the longest duration (no calculations necessary). A)20-year maturity with an 8% coupon. B)20-
39、year maturity with a 12% coupon. C)15-year maturity with a 0% coupon. D)10-year maturity with a 15% coupon. E)12-year maturity with a 12% coupon. Answer: C Difficulty: Moderate Rationale: The lower the coupon, the longer the duration. The zero-coupon bond is the ultimate low coupon bond, and thus wo
40、uld have the longest duration.26.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. Answer: A Difficulty: Moderate Rationale: The relationship betwee
41、n interest rates and duration is an inverse one.27.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 bonds modified duration would be_. A)8.05 B)9.44 C)9.27 D)11.22 E)none of the above Answer: C Diffic
42、ulty: Easy Rationale: D* = D/(1 + y); D* = 10.2/(1.1) = 9.2728.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 bonds price? A)1.85% B)2.01% C)3.27% D)6.44% E)none of the above Answer:
43、A Difficulty: Moderate Rationale: P/P = (-8.05 X 0.0025)/1.1 = 1.85%29.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 the above. Answer: B Dif
44、ficulty: Easy Rationale: 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.30.The duration of a bond normally increases with an increase in A)term to maturity. B)yield to maturity
45、. C)coupon rate. D)all of the above. E)none of the above. Answer: A Difficulty: Moderate Rationale: 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.31.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