Modified Duration of a Zero

CFA Level III
#1

What is the modified duration of a 7-year zero-coupon bond with BEY=4.348%?

This isn’t a L3 question, but some samples touched on this. The data is from an article on portfolio VAR.

#2

3.357? I could be way off…

#3

7/(1+0.043438) = 6.7 ?

#4

7/(1+0.04348/2)=6.85

#5

Are you sure ?

#6

pretty sure about that …

#7

Thank you !

#8

Tuulku, could you provide some explanation on this please?

#9

Macaulay Duration(weighted avg time to receive C/F) = 7. Modified Duration(price change over a 1% yield change) = Macaulay Duration/ (1+YTM/m) = 7/(1+0.04348/2) There must be a math proof of the conversion formluma, but I can’t derive it off the top of my head.

#10

Sorry, I come back here to ask some questions :

Why the yield shall be devided by 2 ? Is it because the coupons are paid semi-annually for coupon bonds ? If so, how to calulate the modified duration if the the coupons are paid annually (as in some countries) or quarterly ?

#11

are you aware that you can do this calculation on your calculator using the bond functions?

#12

I guess that the yield is devided by 2 (as the way tulkuu did) if the calculation is done using calculator. But my questiones are not answered. Moreover, do you think a zero coupon bond will have different modified duration in some countries which pay coupon annually for coupon bonds ?

#13

Can anyone answer to my questions raised above ?