CFAI 2012 AM Question 8

A

agulani

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Can someone explain 2012 AM exam Q8A?
The question asks to increase bond exposure and decrease duration
Current portfolio has 98M in bonds with a duration of 7.2 and wants to increase allocation to 126M with a duration of 6
So to increase bond allocation you’d want the allocation to have a duration of 6 since that is your target. So I did this
(126M-98M)/103,000 * (6-0)/7.7
but the answer suggests that you do it this way
(126M-98M)/103,000 * (7.2-0)/7.7
Why would you use 7.2 as your target duration when you want the bond portfolio to have a target duration of 6? Wouldn’t using 7.2 as a target duration make the synthetic portion of the portfolio have a duration of 7.2 and not 6?
 
I don’t remember exactly this question but isn’t the answer in three parts ?
- First you increase the allocation to 126m by bringing an additional (126m-98m) to a duration of 7.2 so that you have one portfolio of 126m with a 7.2 duration => you buy ((7.2-0)/7.7)*(126-98)/0.103)=x contracts
- Then you decrease the duration by selling ((6-7.2)/7.7)*(126m/0.103m) to get the portfolio to 6 of duration => you sell y contracts
- Finally you net the number of contracts you had to buy and sell (x-y) to get the number of contracts you need in the end.
 
Yea, I guess that is the proper way of doing it.
Thanks Grrreg
 
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