# 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.

 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)
1. What is the effect on a bondâ€™s duration of increasing the bondâ€™s maturity? As in the previ- ous example, use a numerical example and plot the answer. Note that as N â†’ âˆž, 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.
2. â€œDuration 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.â€ Check this claim with an example. What is its economic logic?
3. Replicate the two graphs in section 20.5.