Rebalancing quiz

CFA Level III Fixed Income
#1

Initial market value and dollar duration of the three bond portfolio:

MV Duration

Bond A: 1,753,193 5.951

Bond B: 953,456 2.495

Bond C: 1,032,375 5.308

As part of the rebalancing process, bond A is used as a controlling position and 997,394 is invested in the market value of the bond. After the yield curve changes, the duration of the bond had decreased to 4.903. The market value of the bond, before the additional investment, and after the change, was 1,235,940.

What is the new dollar duration of the bond portfolio, after the interest rates change, but before the rebalancing transaction?

#2

where is it from…

DD new = 231845?

#3

I don’t know but I got something like $133299.67

#4

my logic (according to schweser) is this:

First:

Find the old DD for portfolio which is 182943

Then:

since bond A is the control position, based on 997394 is newly invested in A to rebalance, we can find the change in DD of A, which is 997394x0.01x4.903=48902

48902+182943 will give you the new DD

#5

shouldn’t it be 182,919 - 48902 = 134017?

#6

The original dollar duration = $182,920

DD of increase = $48,902

$182,920 - $48,902 = $134,018

#7

Yeah I solved by CPK’s method but made a calculation mistake :frowning:

#8

these kinds of questions test algebra more than concept. Annoying.

#9

Why do you deduct from original DD?

#10

Controlling position (biggest duration bond’s) duration after the change has dropped (5.951 -> 4.903) - so that means the remaining bonds should also drop in duration at the end. since you are increasing the controlling position’s holding - duration is dropping and you are compensating by increasing the position of the holding.

#11

Can someone post the calc algebraicaly? Should this at all tie to the rebalance ratio?

#12

algebraically…

Orig DD = 182919

DD of New Position bought = 997394*0.01*4.903 = 60598

DD of Controlling position at the end = 2,233,334*4.903*0.01 = 109,500

Change in DD of Controlling position = 109,500 - 60,598 = 48,902

Since the position increased in value - and looking at the rebalancing ratio approach (which incidentally is not applicable here since you do not know the final market value of the portfolio ) - the position must have decreased in $ Duration (your new purchase = (Old DD / New DD -1 ) * Market Value.

Since you bought something - the DD must have reduced. So new DD = 182.919 - 48,902 = 134,017.

#13

right…

should deduct, not add.

#14

This is a great question, i never saw the rebalancing question asked in reverse this way. So can we confirm that the new value of the controlling position before the rebalancing is irrelevant and just there to throw us off?

#15

Initial DD 182,920

Change in DD of bond 997,394*4.903*0.01 = 48,902

New DD 182,920-48,902 = 134,017

DD of bond A before rebalancing 1,235,940*4.903*0.01 = 60,598

DD of bond A after rebalancing 2,233,334*4.903*0.01 = 109,500

Change in DD of bond A 109,500-60,598 = 48,902

New DD 182,920-48902 = 134,017

#16

although I know thats the right answer, I dont see how the new DD for new portfolio is just old DD less the increase in one of the bonds. Doesnt seem intuitive.

So DD for all 3 new bonds is 134017? So the old DD / new DD ratio (36%) should apply but it doesn’t. I think that’s where the intuition falls apart for me.

#17

it doesn’t apply because they did not give you the market value of all the bonds post the interest rate shift.

That is what I mentioned above as well.