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duration problems 1 2 3 5 from chapter 20

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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.

A

B

C

1

CHANGING THE COUPON RATE Effect on Duration

2

Current date

21-May-07

3

Maturity, in years

21

4

Maturity date

21-May-27

5

YTM

15%

6

Coupon

4%

7

Face value

1,000

8

9

Duration

9.03982

<– =DURATION(B2,B4,B6,B5,1)
  2. 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.
  3. “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?
  5. Replicate the two graphs in section 20.5.
 
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