Question

What is the bond duration in the previous problem if coupons are paid annually? Please explain why the duration changes in the direction it does.

Find the bond's duration with a settlement date of May 27, 2012, and a maturity date of November 15, 2021. The bond's coupon rate is 7%, and the bond pays coupons semi-annually.

The bond is selling at a yield to maturity of 8%. You can use Spreadsheet 11.2, available at www.mhhe.com/bkm; link to Chapter 11 material.

Short answer

Answer

Macaulay Duration	6.884422932
Modified Duration	6.374465678

Step-by-step solution

Step by Step Solution Step 1: Given information

Settlement Date	27-05-2010
Maturity Date	15-11-2019
Coupon rate	0.07
Yield to maturity	0.08
Coupons per year	1

Calculation of duration of the bond

To calculate the bond’s duration in excel, we can use the formulae given in the screenshot.

Usually, with a decrease in payment frequency, the duration increases, as in the above case. However, in this specific case, the reduction is noted because of the timing of the settlement. This implies that in place of maturity of $70 on 15 Nov.2021, there are two maturities of $35, first on 15^th May 2021 and the other on 15^th Nov. 2021. Since the weighted average of the maturity would be shorter than the other ones, the decrease is noted.