Modified Duration of a Zero

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tulkuu

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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.
 
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.
 
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 ?
 
are you aware that you can do this calculation on your calculator using the bond functions?
 
cpk123 wrote:
are you aware that you can do this calculation on your calculator using the bond functions?
Click to expand...
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 ?
 
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