# dollar duration/controlling position

do we always use the bond with the highest duration as the controlling position bond? no exceptions to this rule?

whats controlling position?

when you want to change the dollar duration of only 1 bond instead of all of them

yes, because the highest duration bond results in the lowest dollar duration contribution to restore the portfolio to its previous dollar duration. that’s the whole point of the controlling position. i’m sure you know that you may but are not required to use a controlling position.

it will result in LOWEST CAPITAL not lowest dollar duration. Dollar duration will be the same

right, that’s what i meant. i got tangled up in my underwear.

so do we just look at duration and not MV. Ex: Bond A: duration of 8 MV of 30,000 Bond B: duration of 7.8 MV of 3,000,000 i choose bond A as controlling position?

yes, just a duration, cause to adjust you need a specific dollar duration DD = dur * cap. So DD constant and you want to minimize cap so you need highest dur

yes, just think of the higher duration bond as the fulcrum around which you are increasing the total dollar duration of the portfolio. which bond is going to get you there faster (with less capital)? choose bond A.

ok, just wanted to make sure because in the breakeven spread analysis schweser also said to use bond with highest duration when in fact you dont.

you don’t? how do you use the breakeven spread analysis then? i thought you could use either bond provided that you get the direction of the change of the bond right so that they breakeven.

exactly, you could use either bond but do NOT HAVE TO pick the bond with highest duration. but in dollar duration. you have to pick bond with highest dollar duration.

only in dollar duration for your controlling position do you pick the bond with the higest duration… you can pick any bond in your portfolio to adjust the dollar duration back to its original state.

correct striker. you are going to dominate this test.

Hi, on page 341 V3 CFAI they say that you can rebalance the dollar duration by adjusting the position of bond 2 by reducing it by 87%. I can’t get this calculation to work. Any one know what the calculation would be?

haven’t see the question, however the method would be… current market value (old dollar duration/old dollar duration). Where new dollar durations is current dollar duration + additional dollar duration, to bring the dollar duration to the old level hope that’s correct and makes sense!

sell 87% of bond #2 and use the proceeds to buy bond #3, then recalculate all dolar durations and add (you would be slightly off since 87% is probably rounded)

The question will be stated in such a way that you will know which bond’s duration to use. For instance, they usually word it “In terms of Bond X, what would the yield spread have to change for breakeven” In that case you would use Bond X’s duration even if it has a lower duration.