# always use CTD factor?

The duration and price of the treasury futures contract were given, as well as the CTD conversion factor and yield beta. Since it did not say the price is CTD so I decided not to use the coversion factor. Apparently I was wrong and my question is: are all futures prices can be found CTD so we have to apply the conversion factor?

yes

I’ve tried to get to the bottom of this in a few other posts. In CFA-land, it appears they want us simply to use the conversion factor. Always. No matter what. It even came up in one of the questions on the free sample exam. In reality, that’s absurd. I’m not going to keep beating my head aginst the wall trying to get people to think this one through, but if you’re really interested, CBOT has a very good (and mercifully brief) paper called “A Simple Treasury Duration Adjustment” that shows that if you have the duration and price of a futures contract (and therefore its dollar duration), you don’t use the conversion factor to figure the number of contracts required. But don’t go reading that until after the exam. Apparently CFAI doesn’t want us to get confused with the facts… Can you tell I’m frustrated by this particular detail…

You should try reading that paper a little more closely. Their example is based on the following line “by the 10-year T-note futures DV01 (\$69.54)”. Where do you think they got the DV01 of the futures contract (especially since futures contracts don’t technically have a DV01)?

Joey, everything all right lately? You seem a bit more brash than usual. Maybe your just nervous for all of us, sometime I get cranky when I have a big test coming up… This one time at band camp…

Did read it already, thanks. Closely. Footnote 1: “to move from the cash DV01 to a rough estimate of the future’s DV01, simply take the cash DV01 and divide it by the conversion factor for the security.” It’s not rocket science – I get it. The problem is that in at least two examples, CFAI explicitly states that they are giving us the price and duration of the FUTURES contract. To get to the relevant dollar duration they then go and divide that FUTURES price by the conversion factor, NOT the CTD price. If you want to see why the CFA terminology, if not their actual method is screwed up, you should try reading Exmple 11, reading 29 pp 17-18 a little more closely. On p. 17, they’re using a “futures contract priced at 100,000”. Turn the page and suddenly it’s not the futures contract that’s priced at 100,000, but the CTD itself. Huh? Look, I’m an equity/derivatives guy. What I don’t know about fixed income can fill all the CFA test centers in all the world. So if you can get me to understand why that little leap from p 17 to p 18 is correct, then I’d have no problem with any of this and I’d be eternally grateful (well at least for two weeks). But in the meantime, I’m going to stubbornly persist in my belief that this is just another problem in the fixed income readings.

Hi Guys, I also struggled with this issue a while ago and logged it as a potential errata with the CFAI (assumung that they had made a mistake). I have pasted my question and their response below, it if helps: My question: “CFA level 3 curriculum, volume 4 page 17, example 11. The question states that the futures duration is 8.47 but the answer the uses 8.47 as the duration of the cheapest to deliver bond and uses the conversation factor to convert this duration. My understanding was that the duration on the future would already incorporate the conversion factor and the conversion factor is only needed if we are given only the duration of cheapest to deliver bond. I would therefore have taken the conversion factor to be a ‘red herring’ in the question and not actually required. This issue reoccurs in question 2 of the end of chapter practice problems, page 48. Again the duration given in the question is described as being that of the future but the explanation calculation uses it as the duration of the CTD bond and again applies the conversion factor. Please advise if this is correct or an errata.” Their response: “Thank you for your inquiry; the text is correct as written. An expanded definition of DCTD would be the duration of the cheapest-to-deliver-bond to satisfy the futures contract. The 8.47 in the example on page 17 then refers to the duration of the cheapest-to-deliver bond to satisfy the futures contract. The terminology and phrasing in the text is standard. The formula on page 17 is then used with the information given. This also applies for problem 2 on page 48. I hope this helps. Regards, Wanda Lauziere CFA Institute” Not sure if this helps. Seems to suggest that, even though they are referring to the futures contract, the duration provided is actually takens from the CTD bond. Still seems a bit vague to me.

thanks, Damosin99. I’ll just remember this. Probably the text is “revised” regarding this next year - sticky

Damosin99 – thanks very much for sharing that. Much appreciated. I have to admit, I’m still completely befuddled by this, especially since it’s the price of the futures contract that magically transforms into the price of the CTD from p 17-18. Unfortunately, I don’t have my book with me at the moment…but when I get back into the office on this beautiful, bright sunny New England day I’ll check it out and see once again if I can get myself to understand this…

Yep, I’m with you on this MTD as it just doesn’t sound right to me and seems to conflict with the Schweser methodology (which made more sense). I still think this is an error by CFAI but, as they’re writing the exam, I’m just going to stick with their method and leave logic for another day!

MaxTheDog Wrote: ------------------------------------------------------- > Did read it already, thanks. Closely. Footnote > 1: “to move from the cash DV01 to a rough estimate > of the future’s DV01, simply take the cash DV01 > and divide it by the conversion factor for the > security.” It’s not rocket science – I get it. > > The problem is that in at least two examples, CFAI > explicitly states that they are giving us the > price and duration of the FUTURES contract. To > get to the relevant dollar duration they then go > and divide that FUTURES price by the conversion > factor, NOT the CTD price. > That would be a problem… > > If you want to see why the CFA terminology, if not > their actual method is screwed up, you should try > reading Exmple 11, reading 29 pp 17-18 a little > more closely. Don’t have CFAI books > On p. 17, they’re using a “futures > contract priced at 100,000”. > Since the futures contract are priced like bonds (i.e., numbers like 100) that’s pretty clearly a typo. On the other hand, let me get long a few contracts and then it is okay with me if they go to 100,000. > > Turn the page and > suddenly it’s not the futures contract that’s > priced at 100,000, but the CTD itself. Huh? > agree with “huh?” > > Look, I’m an equity/derivatives guy. What I don’t > know about fixed income can fill all the CFA test > centers in all the world. So if you can get me to > understand why that little leap from p 17 to p 18 > is correct, then I’d have no problem with any of > this and I’d be eternally grateful (well at least > for two weeks). But in the meantime, I’m going to > stubbornly persist in my belief that this is just > another problem in the fixed income readings.

Thanks JoeyD, that helps me get past my obsession with this detail and get on to more important things that will truly help in my particular work…you know…like memorizing the 468 GIPS requirements… Seriously, though, it scares me a bit that the same CTD terminology or calculation issue (or whatever it is) also comes up in the free sample exam and that CFA has refused to acknowledge any issue at all even though they’ve received (at least) two errata reports on this (from Damosin and myself). But for June 7 I guess I’ll just do it the CFA way… Of course whenever I need to put on a duration adjustment, I’m going to be a little suspect if the guy or gal on the other end of the line has those three little letters on their business card (kidding). And Damosin, I’m with you: in terms of the explanation CFAI gave you, it doesn’t seem to hold water. After all, if: Dollar duration = Price x Duration x .01 Futures Price = CTD Price/Conversion Factor Conversion Factor is contstant throughout life of contract, and Dollar duration of futures = Dollar Duration of CTD/Conversion Factor Then it would seem (just using algebra) that the duration of the futures contract should equal the duration of the CTD (assuming the CTD bond doesn’t change, which I’m guessing wouldn’t happen for the small changes in rates for which duration is a useful approximation of price change). Anyway, I’m officially done obsessing over this one… Thanks to everybody who has pitched in!

I havent read this whole thread, but I would take the Portfolio MV/CTD price then take that amount a multiply it by the Conversion factor.

Here’s what I think - the whole topic is silly. They should just say something like “the quant geek downstairs will tell you what the ‘duration’ of the futures contract is”. You should know that: a) The CTD can change based on interest rate changes and the repo market b) There are both quality and timing options embedded in the futures contract that make it behave differently than any bond.