CFAI 2012 AM Question 8

CFA Level III
#1

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?

#2

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.

#3

Yea, I guess that is the proper way of doing it.

Thanks Grrreg

#4

I wrote an article that may be helpful here:http://financialexamhelp123.com/adjusting-the-valueduration-of-a-fixed-income-portfolio-using-bond-futures/