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Q.21I

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Essentials Of Investments
Found in: Page 362
Essentials Of Investments

Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

Short Answer

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.

Answer

Macaulay Duration

6.884422932

Modified Duration

6.374465678

See the step by step solution

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

Step 2: 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 15th May 2021 and the other on 15th Nov. 2021. Since the weighted average of the maturity would be shorter than the other ones, the decrease is noted.

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