Chap011_New - Chapter 11 - Managing Bond Portfolios CHAPTER...

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Chapter 11 - Managing Bond Portfolios CHAPTER 11 MANAGING BOND PORTFOLIOS 1. 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. 2. A low coupon, long maturity bond will have the highest duration and will, therefore, produce the largest price change when interest rates change. 3. A rate anticipation swap should work. The trade would be to long the corporate bonds and short the treasuries. A relative gain will be realized when rate spreads return to normal. 4. -25 = -(D/1.06)x.0025x1050…solving for D = 10.09 5. d. 6. The increase will be larger than the decrease in price. 7. 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 rates of return more volatile. The higher duration magnifies the sensitivity to interest-rate savings. Thus, it can be true that rates of short-term bonds are more volatile, but the prices of long-term bonds are more volatile. 8. Computation of duration: a. YTM = 6% (1) (2) (3) (4) (5) Time until Payment (Years) Payment Payment Discounted at 6% Weight Column (1) × 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 11-1
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b. YTM = 10% (1) (2) (3) (4) (5) Time until Payment (Years) Payment Payment Discounted at 10% Weight Column (1) × Column (4) 1 60 54.55 0.0606 0.0606 2 60 49.59 0.0551 0.1101 3 1060 796.39 0 .8844 2 .6531 Column Sum: 900.53 1.0000 2.8238 Duration = 2.824 years, which is less than the duration at the YTM of 6% 9. The percentage bond price change is: – Duration × 0327 . 0 10 . 1 0050 . 0 194 . 7 y 1 y - = × - = + or a 3.27% decline 10. Computation of duration, interest rate = 10%: (1) (2) (3) (4) (5) Time until Payment (Years) Payment (in millions of dollars) Payment Discounted At 10% Weight Column (1) × Column (4) 1 1 0.9091 0.2744 0.2744 2 2 1.6529 0.4989 0.9977 3 1 0 .7513 0.2267 0.6803 Column Sum: 3.3133 1.0000 1.9524 Duration = 1.9524 years 11. The duration of the perpetuity is: (1 + y)/y = 1.10/0.10 = 11 years Let w be the weight of the zero-coupon bond. Then we find w by solving: (w × 1) + [(1 – w) × 11] = 1.9523 w = 9.048/10 = 0.9048 Therefore, your portfolio should be 90.48% invested in the zero and 9.52% in the perpetuity. 12. The percentage bond price change will be:
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Chap011_New - Chapter 11 - Managing Bond Portfolios CHAPTER...

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