BKM_Sol_Ch_11 - Chapter 11 - Managing Bond Portfolios...

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Chapter 11 - Managing Bond Portfolios Chapter 11 Managing Bond Portfolios 1. The percentage bond price change is: – Duration × 0327 . 0 10 . 1 0050 . 0 194 . 7 y 1 y - = × - = + or a 3.27% decline 2. Computation of duration: a. YTM = 6% (1) (2) (3) (4) (5) Time until Payment (Years) Payment Payment Discounted at 6% Weight Column (1) × Column (4) 1 60 56.60 0.0566 0.0566 2 60 53.40 0.0534 0.1068 3 1060 890 .00 0 .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 (Years) Payment Payment Discounted at 10% Weight Column (1) × Column (4) 1 60 54.55 0.0606 0.0606 2 60 49.59 0.0551 0.1101 3 1060 796.39 0 .8844 2 .6531 Column Sum: 900.53 1.0000 2.8238 Duration = 2.824 years, which is less than the duration at the YTM of 6% 11-1
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Chapter 11 - Managing Bond Portfolios 3. Computation of duration, interest rate = 10%: (1) (2) (3) (4) (5) Time until Payment (Years) Payment (in millions of dollars) Payment Discounted At 10% Weight Column (1) × Column (4) 1 1 0 . 9091 . 0 2744 . 0 2744 2 2 1.6529 0.4989 0.9977 3 1 0 .7513 0.2267 0.6803 Column Sum: 3.3133 1.0000 1.9524 Duration = 1.9524 years 4. The duration of the perpetuity is: (1 + y)/y = 1.10/0.10 = 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 w = 9.048/10 = 0.9048 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 × 00463 . 0 08 . 1 0010 . 0 0 . 5 y 1 y = - × - = + or a 0.463% 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, the duration of Bond B 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 that of Bond B. Moreover, Bond A cannot be called. Therefore, the maturity of Bond A is at least as long as that of Bond B, which implies that the duration of Bond A is at least as long as that of Bond B. 7. C: Highest maturity, zero 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
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Chapter 11 - Managing Bond Portfolios 8. a. Modified duration = YTM 1 duration Macaulay + If the Macaulay duration is 10 years and the yield to maturity is 8%, then the modified duration is: 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
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BKM_Sol_Ch_11 - Chapter 11 - Managing Bond Portfolios...

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