Whystudy…answer pls? This is really confusing me. I thought we use use yield beta whenever we are given. In this case, how do we know that the CTD bond is not different from the US Treasury futures?
sparty419 Wrote: ------------------------------------------------------- > Whystudy…answer pls? > > This is really confusing me. I thought we use use > yield beta whenever we are given. In this case, > how do we know that the CTD bond is not different > from the US Treasury futures? Sparty419, as you will see, that is exactly my question. additionally, this formula comes up in 2 sectiosn fo the book. in the Fixed Income section, where you use Dollar Duration, thus having CTD and Conversion factor! and in the Derivatives section, where you used Duration of a futures contract where there’s yield beta. But if you think intiuatively, the formula is actually the same. Cause when you muiltply the portfolio value through duration, that is the dollar duration. Gut the two formula and you will see what i am saying.
WTF is the answer
Funny, I was dealing with this same question this morning - from last year’s (2009) mock exam multiple choice, question #51. The best reason I’ve heard is if both bonds are Treasuries than we don’t need to use the yield beta, but in the question I’m referencing, the portfolio is made up of both Treasuries and corporates…and they don’t use the yield beta. I read up on it in Schweser, and couldn’t really come to an accurate conclusion. It’s 10.31.e, if anyone wants to read the CFAI text and try to come up with a concrete reasoning.
So, after reading this question, I though it was pretty easy. But then I read all the discussions after and became more confused. Here is how I would answer it. We DO NOT need to use the CF, because the duration of the futures contract (6), already has taken that into account, because its duration is derived from (duration of CTD/CF of CTD). So, the resulting formula would be: # of contracts = 1.2*((5-8)/6)*(100,000,000/100,000) = -600 contracts Because the yield beta on the futures contract is 1.2, we need to short more contracts than the -500 contracts had the yield beta been equal to 1. Am I missing something here?
I believe we still need to use Conversion Factor of 0.9. This is confusing
The duration of the futures contract already has taken the conversion factor for the CTD into account. If it hadn’t, the duration given would NOT have been the true duration of the futures contract. Assuming a 100% probability of the CTD remaining the CTD, the duration of a futures contract will always be the (duration of the CTD/CF CTD).
Can you put an example where we need to take CF in calculation?
My understanding is this: 1) You ALWAYS need your conversion factor - this is non-negotiable, and takes into account the difference(s) between the CTD bond and the bond underlying the futures contract. You need this EVERY TIME. 2) The yield beta is only necessary when there’s basis risk; i.e. the futures that you’re attempting to hedge with do not perfectly match the underlying collateral in your portfolio. If you are hedging UST (Treasuries) with UST futures, no yield beta is necessary. If hedging corporates with UST futures, then you need the yield beta.
mib20 Wrote: ------------------------------------------------------- > The duration of the futures contract already has > taken the conversion factor for the CTD into > account. If it hadn’t, the duration given would > NOT have been the true duration of the futures > contract. Assuming a 100% probability of the CTD > remaining the CTD, the duration of a futures > contract will always be the (duration of the > CTD/CF CTD). I believe what you meant to say (and where you’re getting confused) is that the DOLLAR DURATION of a futures contract has already taken the CTD conversion into account. The effective duration of said contract (to my understanding) has not taken into account the CTD conversion factor. So again, I reiterate that to my knowledge you always use the CTD CF when calculating effective duration, but not if calculating DOLLAR DURATION. Can someone who knows WTF they’re talking about (because I’m kinda shooting from the hip here) confirm or deny any of this?
skillionaire Wrote: ------------------------------------------------------- > Funny, I was dealing with this same question this > morning - from last year’s (2009) mock exam > multiple choice, question #51. > I just looked at this Q and saw yield beta was not used. I am extremely confused. > > It’s 10.31.e, if anyone wants to read the CFAI > text and try to come up with a concrete reasoning. Will look at this one tonite.
James@Houston Wrote: ------------------------------------------------------- > skillionaire Wrote: > -------------------------------------------------- > ----- > > Funny, I was dealing with this same question > this > > morning - from last year’s (2009) mock exam > > multiple choice, question #51. > > > > I just looked at this Q and saw yield beta was not > used. I am extremely confused. > > > > > > It’s 10.31.e, if anyone wants to read the CFAI > > text and try to come up with a concrete > reasoning. > > > Will look at this one tonite. Yeah, not using the yield beta when there are corporates in the underlying portfolio kinda threw me for a loop as well; that being said, there’s only so much time one can devote to these issues, so I’m just gonna go with what I typed in my previous post(s). Unless someone can confirm that’s incorrect. EDIT: I never edit posts, but this seemed like as good a time as any - that 10.31.e is from LAST year - it’s actually 10.30.e this year.
whystudy - Can you post the answer here?
I don’t have an answer, I am question it myself!! as said, there’s two formulas, one with Dollar duration that uses conversion factor and another that uses just duration and has yield beta. the formula shows up in two sections, it looks a bit different however if you put it together it’s the same formula essentially.
Before mulling over old questions over treatment of yield beta, you guys need to see this: http://www.analystforum.com/phorums/read.php?13,979999,989068#msg-989068
inbead Wrote: ------------------------------------------------------- > Before mulling over old questions over treatment > of yield beta, you guys need to see this: > > http://www.analystforum.com/phorums/read.php?13,97 > 9999,989068#msg-989068 Nice catch; in that case, I’m over this discussion and fully stand by what I wrote above. James, don’t waste your time looking at the question - seems as though CFAI made an “oopsie”.
are we sure that the answer provided is correct? the formula for changing duration does not use CF at all (except in the breakdown of $D, not IN ADDITION to duration) but is always as follows: [MD(target)-MD(current)/MD(futures)]*Value of portfolio/Value of Futures So the answer should be 600 contracts I agree that if told CTD=Treasuries and protfolio is purely treasuries then don’t need yield B but that’s only because yield beta=1 in that scenario
How can we not use the yield beta in this? I don’t care if we are hedging UST bonds with a UST futures contract. The fact that the durations are different clearly show that there is different collateral (different curve exposure) between the portfolio and the underlying CTD. Who cares that they were issued by the UST, I cannot come to grips with the fact that we would avoid using yield beta. As far as the CF is concerned, I am still lost.
mib20 Wrote: ------------------------------------------------------- > How can we not use the yield beta in this? I > don’t care if we are hedging UST bonds with a UST > futures contract. The fact that the durations are > different clearly show that there is different > collateral (different curve exposure) between the > portfolio and the underlying CTD. Who cares that > they were issued by the UST, I cannot come to > grips with the fact that we would avoid using > yield beta. As far as the CF is concerned, I am > still lost. Yield beta is a measure of the basis risk/change between the collateral underlying the portfolio being different than the collateral underlying the futures contract. For simplicity’s sake, the curriculum has us assume that all Treasuries are identical to each other, and therefore have a yield beta of 1. As far as the CF goes, you always need to use it, except when given the DOLLAR DURATION OF A FUTURES CONTRACT, which already has the CF factored in. Hope this helps.
If the curriculum is really assuming that every UST has a yield beta of 1 with one another, that is horrible. Can we confirm what the actual answer is?