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# bkmsol_ch16 - CHAPTER 16 MANAGING BOND PORTFOLIOS 1 The...

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CHAPTER 16: MANAGING BOND PORTFOLIOS 1. 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. 2. 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 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 \$49.40 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%. 3. 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. Using Rule 8, we find: D = (1.03/0.03) × [1 – (1/1.03) 6 ] = 5.58 half-year periods = 2.79 years If the bond’s yield is 10%, use Rule 7, setting the semiannual yield to 5%, and semiannual coupon to 3%: 4478 . 15 21 05 . 0 ] 1 ) 05 . 1 [( 03 . 0 )] 05 . 0 03 . 0 ( 6 [ ) 05 . 1 ( 05 . 0 05 . 1 D 6 - = + × - × + - = - = 5.5522 half-year periods = 2.7761 years 16-1

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4. 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. 5. a. (1) (2) (3) (4) (5) Time until Payment (years) Cash Flow PV of CF (Discount rate = 10%) Weight Column (1) × Column (4) 1 \$10 million \$9.09 million 0.7857 0.7857 5 \$4 million \$2.48 million 0.2143 1.0715 Column Sums \$11.57 million 1.0000 1.8572 D = 1.8572 years = required maturity of zero coupon bond. b. The market value of the zero must be \$11.57 million, the same as the market value of the obligations. Therefore, the face value must be: \$11.57 million × (1.10) 1.8572 = \$13.81 million 6. a.The call feature provides a valuable option to the issuer, since it can buy back the bond at a specified call price even if the present value of the scheduled remaining payments is greater than the call price. The investor will demand, and the issuer will be willing to pay, a higher yield on the issue as compensation for this feature. b. The call feature reduces both the duration (interest rate sensitivity) and the convexity of the bond. If interest rates fall, the increase in the price of the callable bond will not be as large as it would be if the bond were noncallable. Moreover, the usual curvature that characterizes price changes for a straight bond is reduced by a call feature. The price-yield curve (see Figure 16.6) flattens out as the interest rate falls and the option to call the bond becomes more attractive. In fact, at very low interest rates, the bond exhibits negative convexity. 16-2
7. In each case, choose the longer-duration bond in order to benefit from a rate decrease.

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bkmsol_ch16 - CHAPTER 16 MANAGING BOND PORTFOLIOS 1 The...

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