bkmsol-ch16-9e corrected 7.29.2010

bkmsol-ch16-9e corrected 7.29.2010 - CHAPTER 16 MANAGING...

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CHAPTER 16: MANAGING BOND PORTFOLIOS PROBLEM SETS 1. While it is true that short-term rates are more volatile than long-term rates, the longer duration of the longer-term bonds makes their prices and their rates of return more volatile. The higher duration magnifies the sensitivity to interest- rate changes. 2. Duration can be thought of as a weighted average of the ‘maturities’ of the cash flows paid to holders of the perpetuity, where the weight for each cash flow is equal to the present value of that cash flow divided by the total present value of all cash flows. For cash flows in the distant future, present value approaches zero (i.e., the weight becomes very small) so that these distant cash flows have little impact, and eventually, virtually no impact on the weighted average. 3. The percentage change in the bond’s price is: % 27 . 3 0327 . 0 005 . 0 10 . 1 194 . 7 y y 1 Duration - = - = × - = × + - or a 3.27% decline 4. a.YTM = 6% (1) (2) (3) (4) (5) Time until Payment (years) Cash Flow PV of CF (Discount rate = 6%) Weight Column (1) × Column (4) 1 \$60.00 \$56.60 0.0566 0.0566 2 \$60.00 \$53.40 0.0534 0.1068 3 \$1,060.00 \$890.00 0.8900 2.6700 Column Sums \$1,000.00 1.0000 2.8334 Duration = 2.833 years 16-1

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b. YTM = 10% (1) (2) (3) (4) (5) Time until Payment (years) Cash Flow PV of CF (Discount rate = 10%) Weight Column (1) × Column (4) 1 \$60.00 \$54.55 0.0606 0.0606 2 \$60.00 \$49.59 0.0551 0.1102 3 \$1,060.00 \$796.39 0.8844 2.6532 Column Sums \$900.53 1.0000 2.8240 Duration = 2.824 years, which is less than the duration at the YTM of 6%. 5. For a semiannual 6% coupon bond selling at par, we use the following parameters: coupon = 3% per half-year period, y = 3%, T = 6 semiannual periods. (1) (2) (3) (4) (5) Time until Payment (years) Cash Flow PV of CF (Discount rate = 3%) Weight Column (1) × Column (4) 1 \$3.00 \$2.913 0.02913 0.02913 2 \$3.00 \$2.828 0.02828 0.05656 3 \$3.00 \$2.745 0.02745 0.08236 4 \$3.00 \$2.665 0.02665 0.10662 5 \$3.00 \$2.588 0.02588 0.12939 6 \$103.00 \$86.261 0.86261 5.17565 Column Sums \$100.000 1.00000 5.57971 D = 5.5797 half-year periods = 2.7899 years If the bond’s yield is 10%, use a semiannual yield of 5%, and semiannual coupon of 3%: (1) (2) (3) (4) (5) Time until Payment (years) Cash Flow PV of CF (Discount rate = 5%) Weight Column (1) × Column (4) 1 \$3.00 \$2.857 0.03180 0.03180 2 \$3.00 \$2.721 0.03029 0.06057 3 \$3.00 \$2.592 0.02884 0.08653 4 \$3.00 \$2.468 0.02747 0.10988 5 \$3.00 \$2.351 0.02616 0.13081 6 \$103.00 \$76.860 0.85544 5.13265 Column Sums \$89.849 1.00000 5.55223 D = 5.5522 half-year periods = 2.7761 years 16-2
6. If the current yield spread between AAA bonds and Treasury bonds is too wide compared to historical yield spreads and is expected to narrow, you should shift from Treasury bonds into AAA bonds. As the spread narrows, the AAA bonds will outperform the Treasury bonds. This is an example of an intermarket spread swap. 7. D 8. 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 Bond A to have a longer duration than Bond B. Moreover, A cannot be called, so that its maturity is at least as long as that of B, which generally increases duration.

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