ch11ans - of the zero-coupon bond, so that we find w by...

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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 Note: Modified duration = Duration / (1+y) 2. Computation of duration: a. YTM = 6% (1) (2) (3) (4) (5) Time until Payment (Years) Payment Payment Discounted at 6% Weight Column (1) x 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) x Column (4) 1 60 54.55 0.0606 0.0606 2 60 49.59 0.0551 0.1102 3 1060 796.39 0.8844 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. a. The duration of the perpetuity is: (1.05/0.05) = 21 years. Let w be the weight
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Unformatted text preview: of the zero-coupon bond, so that we find w by solving: (w 5) + [(1 w) 21] = 10 w = 11/16 = 0.6875 Therefore, the portfolio will be 11/16 invested in the zero and 5/16 in the perpetuity. b. The zero-coupon bond will then have a duration of 4 years while the perpetuity will still have a 21-year duration. To have a portfolio with duration equal to nine years, which is now the duration of the obligation, we again solve for w: (w 4) + [(1 w) 21] = 9 w = 12/17 = 0.7059 So the proportion invested in the zero increases to 12/17 and the proportion in the perpetuity falls to 5/17....
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This note was uploaded on 04/09/2012 for the course FIN 431 taught by Professor Sun during the Spring '12 term at Old Dominion.

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ch11ans - of the zero-coupon bond, so that we find w by...

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