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1、Chapter 16 - Managing Bond Portfolios16-1Copyright 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.CHAPTER 16: MANAGING BOND PORTFOLIOSPROBLEM SETS 1. While it is true that short-term rates are more volatile
2、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 holder
3、s 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 ha
4、ve little impact and, eventually, virtually no impact on the weighted average.3. The percentage change in the bonds price is:or a 3.27% decline7.1940.5.327.%,1Dy4. a. YTM = 6%(1) (2) (3) (4) (5)Time until Payment (Years) Cash FlowPV of CF (Discount Rate = 6%) WeightColumn (1) Column (4)1 $ 60.00 $ 5
5、6.60 0.0566 0.05662 60.00 53.40 0.0534 0.10683 1,060.00 890.00 0.8900 2.6700Column sums $1,000.00 1.0000 2.8334Duration = 2.833 yearsChapter 16 - Managing Bond Portfolios16-2Copyright 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent o
6、f McGraw-Hill Education.b. YTM = 10%(1) (2) (3) (4) (5)Time until Payment (Years) Cash FlowPV of CF (Discount Rate = 10%) WeightColumn (1) Column (4)1 $ 60.00 $ 54.55 0.0606 0.06062 60.00 49.59 0.0551 0.11023 1,060.00 796.39 0.8844 2.6532Column sums $900.53 1.0000 2.8240Duration = 2.824 years, which
7、 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 FlowPV of CF (Discount Rate = 3%) WeightColumn (1) Col
8、umn (4)1 $ 3.00 $ 2.913 0.02913 0.029132 3.00 2.828 0.02828 0.056563 3.00 2.745 0.02745 0.082364 3.00 2.665 0.02665 0.106625 3.00 2.588 0.02588 0.129396 103.00 86.261 0.86261 5.17565Column sums $100.000 1.00000 5.57971D = 5.5797 half-year periods = 2.7899 yearsIf the bonds yield is 10%, use a semian
9、nual yield of 5% and semiannual coupon of 3%:(1) (2) (3) (4) (5)Time until Payment (Years) Cash FlowPV of CF (Discount Rate = 5%) WeightColumn (1) Column (4)1 $ 3.00 $ 2.857 0.03180 0.031802 3.00 2.721 0.03029 0.060573 3.00 2.592 0.02884 0.086534 3.00 2.468 0.02747 0.109885 3.00 2.351 0.02616 0.1308
10、16 103.00 76.860 0.85544 5.13265Column sums $89.849 1.00000 5.55223D = 5.5522 half-year periods = 2.7761 yearsChapter 16 - Managing Bond Portfolios16-3Copyright 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education
11、.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 inte
12、rmarket spread swap.7. D. Investors tend to purchase longer term bonds when they expect yields to fall so they can capture significant capital gains, and the lack of a coupon payment ensures the capital gain will be even greater. 8. a. Bond B has a higher yield to maturity than bond A since its coup
13、on 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
14、 Bond B. Moreover, A cannot be called, so that its maturity is at least as long as that of B, which generally increases duration.9. a.(1) (2) (3) (4) (5)Time until Payment (Years) Cash FlowPV of CF (Discount Rate = 10%) WeightColumn (1) Column (4)1 $10 million $ 9.09 million 0.7857 0.78575 4 million
15、 2.48 million 0.2143 1.0715Column sums $11.57 million 1.0000 1.8572D = 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
16、million10 In each case, choose the longer-duration bond in order to benefit from a rate decrease.a. ii. The Aaa-rated bond has the lower yield to maturity and therefore the longer duration.b. i. The lower-coupon bond has the longer duration and greater de facto call protection.Chapter 16 - Managing Bond Portfolios16-4Copyright 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior wr
