SolCh16 - Chapter 16 Managing Bond Portfolios CHAPTER 16...

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Chapter 16 - Managing Bond Portfolios 16-1 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 = = × = Δ × + 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

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Chapter 16 - Managing Bond Portfolios 16-2 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
Chapter 16 - Managing Bond Portfolios 16-3 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.

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SolCh16 - Chapter 16 Managing Bond Portfolios CHAPTER 16...

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