skillionaire Wrote: ------------------------------------------------------- > 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”. inbead & skillionair–Thanks a lot. I feel much better now!!
So, in conclusion, use the yield beta when given? and CF when given?
Hi, Guys, I noticed your arguments for a long time but it seems no conclusion. For the sake of exam (at least), I will like to send inquiry to CFAI to get their clarification and hope their reply will be in time. However, I need your help to provide me with actual/tangible examples of calculation in CFAI’ text or exams which have discrepancies. Do you agree ?
Since not so much time is left for us to wait, I have already sent inquiry to CFAI just now to get their clarification by raising the example of Q51 of 2009 Mock exam. I will post CFAI’s reply here once I have got it.
Guys Not sure why so much confusion and not wanting to jump in and spend valuable hours explaining and re-clarifying on this already long post, but just could not resist myself 
Let me phrase it in my simple world how it works. - If you use futures to hedge, then (as a rule, it is given in exam) you need to use CF of the CTD to calculate the hedge ratio. - If you are given a yield beta then also use it as well (not so often given in exam). This is all you need to know for the exam. Now some short background: The interest rate futures mostly used is the 30 years T bond futures. To settle the futures trade, the short can choose a huge array of available bonds. To compensate for the different prices and yields, the CME exchange gives a CF for each of the eligible bonds. CF is the price that bond will have to yield the reference 6% coupon, so if coupon >6% --> CF >1 while a bond with coupon <6% --> CF<1. Why 6%, beat me. Now, different bonds because of different CF and market price will give different cost to settle the same futures --> one chooses the cheapest to settle. This bond is called CTD. So… you need to use the CF of the CTD since it is seldom the CF of the CTD is 1 Thus first rule: - If you use futures to hedge, then (as a rule, it is given in exam) you need to use CF of the CTD to calculate the hedge ratio. Now, second rule: Yield beta: Remember per def, yield on your portfolio = a + Yield Beta * Yield on the CTD. if the portfolio you want to hedge is comprised of T -bonds --> the yield beta is normally very close to 1 so it is ignored since it does not make a big difference. However, if your portfolio is comprised of corp bonds (or corp bonds and T bonds),you should use yield beta since yield beta is often different from 1. thus rule 2: - If you are given a yield beta then also use it (not so often given in exam) since yield beta (if given) is indication that your portfolio reacts significantly than the CTD used to hedge. For those who are interested, here is an intro from the exchange itself which will give you much more understanding. http://www.cmegroup.com/trading/interest-rates/files/Understanding_US_Treasury_Futures.pdf
It’s actually almost spot on with the US 10yr Note Future, so don’t think it’s the bond contract, but regardless… Do we have an answer on how to handle the CF given that the duration (not the dollar duration) is given to us? I would think that the Mod. Dur. of the futures contract (6) already incorporates the CF of the CTD, and thus, it would be meaningless in this problem.
mib20 Wrote: ------------------------------------------------------- > It’s actually almost spot on with the US 10yr Note > Future, so don’t think it’s the bond contract, but > regardless… > Agree. I meant to say ‘one of the most used’. 10 yr note futures has higher volume. > Do we have an answer on how to handle the CF given > that the duration (not the dollar duration) is > given to us? I would think that the Mod. Dur. of > the futures contract (6) already incorporates the > CF of the CTD, and thus, it would be meaningless > in this problem. Unless I miss sth critical, I believe you need to multiply with the yield beta 1.12 to get the correct contract futures, i.e., I believe the answer -287,8 is wrong. CF is independent of yield beta. Now, one small assumption: liabilities here assumed to have the same yield beta as the portfolio so that hedge is correct, otherwise you need a different (more complex) calculation.
Elcfa, Where I am a bit confused is why would the CF be necessary in the calculation. Isn’t the presence of the contract futures duration in the equation already taking the CF of the CTD into account. I would think that the equation would be the standard: # of contracts = yb*((MDt-MDp)/MDf)*((VP)/(px*mult))
Don’t think so. Check P 119 vol4 CFAI.
while we are at it, I would like to point out another ‘error’ in the text. The question for 51 says “US Treasury futures contract with a duration of 6.5 priced at $110,425.” It leads one to believe that it is the price of the ‘standard’ 6% coupon, not the price of the CTD. However, the answer uses $110,425 as the price of the CTD bonds. If $110,425 is the price of the standard bond, and 0.9177 is the CF of the CTD bond, then the price of the CTD bond is $110,425* 0.9177 = $101,337, not $110,425 Therefore, to be 100% clear, the question should have stated instead “US Treasury futures contract with a duration of 6.5. The CTD bond is priced at $110,425.”
You guys, here’s something I wrote for a study group but seems kinda applicable…(reprinted with permission of Skillionaire). 1) You’re “mainly” right - if given the effective duration of the contract, portfolio, etc., then you use the CTD conversion factor. 2) If given the dollar duration OF THE BONDS UNDERLYING THE FUTURES CONTRACT, then you need to use the CTD as well to get the DOLLAR DURATION OF THE FUTURES CONTRACT. 3) My point, which is somewhat of a “nitpicky” one, is that if given THE DOLLAR DURATION OF THE FUTURES CONTRACT, that the CTD conversion has already taken place (see point #2 above). Just wanted to make sure people were aware that CTD has already been “accounted for” if we’re given the dollar duration of the futures CONTRACT, not the BONDS. Sorry for the caps lock, but I don’t know how to make words bold and I wanted to emphasize the difference(s).
> 2) If given the dollar duration OF THE BONDS > UNDERLYING THE FUTURES > CONTRACT, then you need to use the CTD as well to > get the DOLLAR > DURATION OF THE FUTURES CONTRACT. I agree, if you have DD of the futures contract then CF of CTD is irrelevant. Put it this way, DD futures = Futures price* Duration of Futures = (Price of CTD/CF)* Duration of CTD Duration of Futures is nearly identical to Duration of CTD (i.e.,the so called basis risk is considered to be zero), thus one normally considers them to be identical. Thus number of futures needed = hedge ratio= DD portfolio /(Futures price* Duration of Futures) =DD portfolio/ [(Price of CTD/CF)* Duration of CTD]= DD portfolio/ [(Price of CTD)* Duration of CTD]* CF See otherwise, my comment about the ‘error’ in question text above since it is related to this. Hope that it is clear.
elcfa, TKVM for your explanations. But I just have some questions which may be stupid, sorry. 1. What are the differense between the equation on P.117 of CFAI text volume 4 and the equation 4 on P.344 of CFAI text volume 5 ? Is it that the equation 4 on P.344 of CFAI text volume 5 is the general version of these equations ? 2. Is it that the equation on P.120 for hedge ratio is a version of equation on P.117 ? Is it that the only difference is that the Target Duration is set to 0 in the equation on P.120 and the “Hedge Ratio” means the number of futures required to reduce duration of the bond (or portfolio of bonds) to 0 ? TKVM in advance for your time & efforts in advance !
> 1. What are the differense between the equation on > P.117 of CFAI text volume 4 and the equation 4 on > P.344 of CFAI text volume 5 ? Is it that the > equation 4 on P.344 of CFAI text volume 5 is the > general version of these equations ? both tell you the same thing: number of contracts to buy to adjust the duration of the portfolio to target. The difference. P.117 of CFAI text volume 4 : deal primarily with info about CTD bonds and assume yield beta =1 thus ignore it P.344 of CFAI text volume 5: deal primarily with info about futures and assume yield beta <>1 thus not ignore it Thus a more general formula for both is N = (DT-DI)PI /[(Dfut * Pfut)] * Yield beta = (DT-DI)PI /[(DCTD * PCTD)] * CF * Yield beta As mentioned above DFut = DCTD (approx) > > 2. Is it that the equation on P.120 for hedge > ratio is a version of equation on P.117 ? Is it > that the only difference is that the Target > Duration is set to 0 in the equation on P.120 and > the “Hedge Ratio” means the number of futures > required to reduce duration of the bond (or > portfolio of bonds) to 0 ? > > TKVM in advance for your time & efforts in advance > ! Correct, if you set DT to be =0 in the equation above, you have the same as pg120 (with the negative sign). The reason for the lack of negative side in pg 120 is the author just focuses on the absolute value, and not worry about the direction since it is obvious that you need to sell futures to get the positive duration of a portfolio to be zero or buy futures if the duration is negative (in case of a liability like pension obligation in ALM). The author states this assumption in page 119 “taking a futures position that offsets an existing interest rate exposure” Hope it is clear.
elcfa, Thank you so much. Your help is really appreciated !