# ch_11_sol - CHAPTER 11 MANAGING FIXED-INCOME INVESTMENTS 1...

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CHAPTER 11: MANAGING FIXED-INCOME INVESTMENTS 1. The percentage bond price change will be – Duration × = –7.194 × = –.0327 or a 3.27% decline. 2. Computation of duration: a. YTM = 6% (1) (2) (3) (4) (5) Time Until Payment (in years) Payment PV of Payment Disc. at 6% Weight of each Payment Column (1) × Column (4) 1 60 56.60 .0566 .0566 2 60 53.40 .0534 .1068 3 1060 890.00 .8900 2.6700 Column Sum 1000.00 1.0000 2.8334 Duration = 2.833 years b. YTM = 10% (1) (2) (3) (4) (5) Time Until Payment (in years) Payment PV of Payment Disc. at 10% Weight of each Payment Column (1) × Column (4) 1 60 54.55 .0606 .0606 2 60 49.59 .0551 .1102 3 1060 796.39 .8844 2.6532 Column Sum 900.53 1.0000 2.8240 Duration = 2.824 years, which is less than the duration at the YTM of 6%. 11-1

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3. Computation of duration, interest rate = 10% (1) (2) (3) (4) (5) Time Until Payment (in years) Payment (in millions of dollars) PV of Payment Disc. at 10% (in \$ millions) Weight of each Payment Column (1) × Column (4) 1 1 .9091 .2744 .2744 2 2 1.6529 .4989 .9978 3 1 .7513 .2267 .6801 Column Sum 3.3133 1.0000 1.9523 Duration = 1.9523 years 4. The duration of the perpetuity is 1.1/.10 = 11 years. Let w be the weight of the zero- coupon bond. Then we find w by solving: w × 1 + (1 – w) × 11 = 1.9523 11 – 10w = 1.9523 w = 9.048/10 = .9048 Therefore, your portfolio should be 90.48% invested in the zero and 9.52% in the perpetuity. 5. The percentage bond price change will be – Duration × = –5.0 × = .00463 or a .463% increase. 6. a. Bond B has a higher yield to maturity than bond A since its coupon payments and maturity are equal to those of A, while its price is lower. (Perhaps the yield is higher because of differences in credit risk.) Therefore, its duration must be shorter. b. Bond A has a lower yield and a lower coupon, both of which cause it to have a longer duration than B. Moreover, A cannot be called, which makes its maturity at least as long as that of B, which generally increases duration. 7. C: Highest maturity, lowest coupon D: Highest maturity, next-lowest coupon A: Highest maturity, same coupon as remaining bonds B: Lower yield to maturity than bond E E: Highest coupon, shortest maturity, highest yield of all bonds. 11-2
8. a. Modified duration = If the Macaulay duration is 10 years and the yield to maturity is 8%, then the modified duration equals 10/1.08 = 9.26 years. b. For option-free coupon bonds, modified duration is better than maturity as a measure of the bond’s sensitivity to changes in interest rates. Maturity considers only the final cash flow, while modified duration includes other factors such as the size and timing of coupon payments and the level of interest rates (yield to maturity). Modified duration, unlike maturity, tells us the approximate proportional change in the bond price for a given change in yield to maturity. c. i. Modified duration increases as the coupon decreases. ii. Modified duration decreases as maturity decreases. 9. a. PV of the obligation = \$10,000 × PA (8%, 2) = \$17,832.65 Duration = 1.4808 years, which can be verified from a table such as Table 11.3. b. To immunize my obligation I need a zero-coupon bond maturing in 1.4808 years.

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