# Rebalancing based on \$ duration

There is a problem illustrated in Page 340-341 in CFA book about how to rebalance the portfolio for a change in duration. Port has initial dur of 111,945 and it changes to 82,579 due to shift in yield curve and further they suggest that to rebalance it to make the duration equal to where it started we need to increase the positions and it requires cash. What does it mean in real terms. The client lost a million and we need to inject additonal 1mn \$ to make the dollar duration balance. where does this money come from??

from the client. into the account at their new portfolio manager…

actually, in all seriousness, i remember one of the cfai problems had a DD rebalancing where there was something like \$10MM in cash sitting in the portfolio and we needed \$8MM for rebalancing. i figured, well, we’d just take the \$8MM from the cash already in the account. but no, the right answer required an infusion of \$8MM from outside the account (no idea if those were the actual #'s but you get the point).

the other option would be to sell bond with lower duration (bond #2 in this example) and use the proceeds to buy appropriate portions of bonds #1 and #3 to make dollar duration equal to the original dollar duration

That makes alot of sense Volkovv. Now I don’t remember seeing that option presented in any of the material. Do you know if it was??

In addition , at the very end of the page, it states “controllign position may also consist of derivatives”. they could use the three choices in multipls exam to aks which one is not the correct.

by the way, check errata… they did this example assuming DD = weighted average instead of sum…

Big Babbu Wrote: ------------------------------------------------------- > That makes alot of sense Volkovv. > Now I don’t remember seeing that option presented > in any of the material. > Do you know if it was?? Yeah…even though this is what most individuals and institutions would do.

I asked last night but I guess noone answered on a nother post. When using the Target Dollar duration formula do we need to use yeild beta?? I thought yeild beta was only for the MD/ED ones but on shcweser quick sheet they use it in TDD formula.

if you are asking about adding bond position, increasing duration of portfolio, (DT-DC/DF)* (Price of portfolio/price of CTD)* Yield Beta yes, you need to use. I am not sure why you asking this question with ref to rebalancing dollar duration here…

depends what are you rebalancing with. If with futures - you do need yield beta.

csk, when using futures (MDUR - MDUR)/MDUR, etc, in cfa they do use yield beta, but in all of their examples “yield beta = 1.0” if you are not talking about this, forget what I just wrote

I think CSK is answering the part to do with “controllign position may also consist of derivatives”.

i was talking about rebalancing. If you are going to rebalance to old duration with futures, you will need to adjust for yield beta and CTD, if with bonds in your portfolio - you wont need to IMHO

(Old DD/ New DD) -1, will be the amount you have to add, do it to every position, your done. UNLESS there is a control position, then you should increase that… which would require a bit of math to figure out how much to increase that position’s DD to increase the DD of the entire portfolio back to the original. ------------------------------------------------ This means that 2 criteria of immunizing a portfolio are not there (possibly) namely (the DDa = DDl which is either a factor of the market value or the change in asset or liability duration), assuming you have a greater dispersion of DD assets then rebalancing this will re-immunize the portfolio.

jamespucyk Wrote: ------------------------------------------------------- > (Old DD/ New DD) -1, will be the amount you have > to add, do it to every position, your done. > > UNLESS there is a control position, then you > should increase that… which would require a bit > of math to figure out how much to increase that > position’s DD to increase the DD of the entire > portfolio back to the original. > > ------------------------------------------------ > > This means that 2 criteria of immunizing a > portfolio are not there (possibly) namely (the DDa > = DDl which is either a factor of the market value > or the change in asset or liability duration), > assuming you have a greater dispersion of DD > assets then rebalancing this will re-immunize the > portfolio. waaait a minute. I understand that for classical immunization we have 2 PVa = PVl and dA = dL but are you saying that DDa = DDl is sufficient? from 1 you are guaranteed to get 2 but not the other way around

Big Babbu Wrote: ------------------------------------------------------- > That makes alot of sense Volkovv. > Now I don’t remember seeing that option presented > in any of the material. > Do you know if it was?? It was, CFAI V3, p. 341, buttom of the page