Annualized Modified Duration

CFA Level I Fixed Income
#1

Question:

A zero-coupon bond that matures in 12 years has a YTM of 8.2% on a semiannual bond basis. The annualized modified duration of this bond is closet to:

a. 11.073

b. 11.091

c. 11.527

I’m lost on this question. Initially, I started to calc the Macaluay duration and then divide it by 1+YTM but that didn’t work. Any ideas on how to tackle this one…?

Thanks!

#2

Well, the Macaulay duration is 12 years. If you divide that by (1 + 8.2%/2) you get 11.527 years

#3

Since the bond is a pure discount bond the Macaulay duration would be the time when the bond matures, 12 in this case.

As for the denominator, I forgot to divide the YTM by 2.

Thanks!

#4

You’re welcome!