duration problems 1 2 3 5 from chapter 20
1. In the spreadsheet below, create a Data Table in which the duration is computed as a function of the coupon rate (coupon = 0%, 1%, … , 11%). Comment on the relation between the coupon rate and the duration.
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A |
B |
C |
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|
1 |
CHANGING THE COUPON RATE Effect on Duration |
||
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2 |
Current date |
21-May-07 |
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|
3 |
Maturity, in years |
21 |
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|
4 |
Maturity date |
21-May-27 |
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5 |
YTM |
15% |
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|
6 |
Coupon |
4% |
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|
7 |
Face value |
1,000 |
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|
8 |
|||
|
9 |
Duration |
9.03982 |
<– =DURATION(B2,B4,B6,B5,1) |
- What is the effect on a bond’s duration of increasing the bond’s maturity? As in the previ- ous example, use a numerical example and plot the answer. Note that as N → ∞, the bond becomes a consol (a bond that has no repayment of principal but an infinite stream of coupon payments). The duration of a consol is given by (1 + YTM) / YTM. Show that your numerical answers converge to this formula.
- “Duration can be viewed as a proxy for the riskiness of a bond. All other things being equal, the riskier of two bonds should have lower duration.†Check this claim with an example. What is its economic logic?
- Replicate the two graphs in section 20.5.
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