# Dollar Duration/Conversion Factor Hedge Question

Ok let me get this straight if they give you the futures contract you need to use the conversion factor for the DD calc and in the equation to get # of contracts. If they give you the CTD you do not have to use conversion factor in DD calc but you do in the equation to get # of contracts. Sorry…

The way I think about it (which may or may not be right) is that I’m always trying to figure out the dollar duration of the instrument I’m using to hedge. So if I can calculate the dollar duration of the CTD I divide it by the conversion factor to get the dollar duration of the futures contract. If I’m given the dollar duration of the futures contract, I already have the information I need. The problem is (and this is where it gets frustrating for me) is that this is NOT the way CFAI seems to do it. If you look at Example 11 in Reading 29 (I think it is) you’ll see that they give you the price and duration of the futures contract. But then on the next page they treat the problem as though they’ve given you the price and duration of the CTD. They do this same thing in the free sample exam. Which leave us where? I have no idea. If (when) I see this on the exam I’ll probably suck it up and do it the way they have in the examples. But I’ll be very hard pressed not to stand up and shout “Oh yeah, deliver this!” followed by an appropriate hand gesture…

Here’s the equation used by CFAI to solve one of the hedging problems in the freebie sample exam. …(Dtarget - Dportfolio) * Value Port # Contracts = -------------------------------------------- X Conv Factor X Yield Beta …(Dctd * Pctd) In that question, Dtarget was 0. Now, if this equation is wrong, let me know. There is an equation just like this in the curriculum, but without the yield beta on the end.

This is the correct equation. It’s exactly what I wrote earlier: Hedge ratio = (DD Portfolio/DD CTD) * CTD_conversion factor.

The equation isn’t the problem. Applying it to the given facts is.

^Agree with Max.

Back to your original question: Both problems should be solved the same way: Question 15: Dollar duration of CTD = Price of CTD * Duration. Then use the conversion factor in getting the No. of contracts. Question 18: and this is where the solution does not make sense: Duration of CTD = 10.15 ( given). Price of future = 108500 Dollar duration of CTD = 108500 * 0.1015. They should not multiply by the conversion factor here to get the DD of CTD. (I am sure of that and if in doubt check the CFAI sample question). This is a mistake in shweser. I emailed them about this problem two weeks ago and this is what they said: Dear Mo34, The conversion factor is needed twice: once to determine the DD of the CTD and the second time to determine the DD of the futures thus although we don’t show this exact calculation in our notes it is a variation of the calculation for the DD of the futures contract shown on page 75 of book 3. Regards, Kurt Schuldes, CFA

mo34 Wrote: ------------------------------------------------------- > This is the correct equation. It’s exactly what I > wrote earlier: > > Hedge ratio = (DD Portfolio/DD CTD) * > CTD_conversion factor. Just checking, but where does the yield beta fit in here? Using the numbers from the sample freebie as inputs, if you take the result of your equation and multiply it by the yield beta, you get the correct answer. So I’m assuming that we could tack on a yield beta factor at the end of your equation. Is there something wrong with that?

Mo34 thanks for the help can you clarify the below? mo34 Wrote: ------------------------------------------------------- > Back to your original question: > > Both problems should be solved the same way: > > Question 15: Dollar duration of CTD = Price of > CTD * Duration. > > Then use the conversion factor in getting the No. > of contracts. > > Question 18: and this is where the solution does > not make sense: > > Duration of CTD = 10.15 ( given). > > Price of future = 108500 > > Dollar duration of CTD = 108500 * 0.1015. So this is where Schweser times it by the conversion factor and you are saying there is no need to do that? And you still need to use the conversion factor in getting the no of contracts? > > They should not multiply by the conversion > factor here to get the DD of CTD. (I am sure of > that and if in doubt check the CFAI sample > question). This is a mistake in shweser. > > I emailed them about this problem two weeks ago > and this is what they said: > > Dear Mo34, > > The conversion factor is needed twice: once to > determine the DD of the CTD and the second time to > determine the DD of the futures thus although we > don’t show this exact calculation in our notes it > is a variation of the calculation for the DD of > the futures contract shown on page 75 of book 3. > > Regards, > > Kurt Schuldes, CFA So you are saying this guy is incorrect? -Thanks

I disagree mo. If you are given the price of the futures and the duration of the CTD you absolutely do need to use the conversion factor to get the dollar duration of the CTD. The basic formulas are: Dollar duration of CTD = Price of CTD * Duration of CTD * .01 Price of CTD = Price of Futures * Conversion Factor

In other words, schweser is (in this instance, at least) correct.

MaxTheDog Wrote: ------------------------------------------------------- > I disagree mo. If you are given the price of the > futures and the duration of the CTD you absolutely > do need to use the conversion factor to get the > dollar duration of the CTD. > > The basic formulas are: > > Dollar duration of CTD = Price of CTD * Duration > of CTD * .01 > Price of CTD = Price of Futures * Conversion > Factor You’re right. My mistake. I’ve been struggling with this problem for some time. One question remains: In the CFAI sample test, they did not calculate the DD_CTD, they used the price of the future * Duration of future. = DD_CTD

mo34 Wrote: ------------------------------------------------------- > MaxTheDog Wrote: > -------------------------------------------------- > ----- > > I disagree mo. If you are given the price of > the > > futures and the duration of the CTD you > absolutely > > do need to use the conversion factor to get the > > dollar duration of the CTD. > > > > The basic formulas are: > > > > Dollar duration of CTD = Price of CTD * > Duration > > of CTD * .01 > > Price of CTD = Price of Futures * Conversion > > Factor > > > You’re right. My mistake. I’ve been struggling > with this problem for some time. One question > remains: > > In the CFAI sample test, they did not calculate > the DD_CTD, they used the price of the future * > Duration of future. = DD_CTD Mo34 as i said, whenever they mention future, they mean duration of CTD and not future. Look at that blue box i mentioned they have example and the wording is exactly the same as in sample exam. Whenver CFAI says future duration in regards to tresuries they mean CTD duration so to get DD of futures you need to use conversion factor

Yup…and that’s exactly the problem I’ve been having with CFAI on this. Can’t tell you how many minutes and brain cells I’ve wasted on this. Same issue crops up in Example 11 of reading 29. They give you the price of the futures contract then solve the problem as though they’ve given you the price of the CTD. Even just looking at the example it’s ridiculous. On one page they give you a futures price = 100k (or something like that) and a conversion factor. On the next page the 100k magically transforms into the price of the CTD rather than the futures price. It’s just plain wrong. I’ve sent them 2 emails about it with no response… Strange because I didn’t even use any “colorful” language…

Well, I’m glad we cleared this up. I’ll print parts of this thread for future last minute reference. I was under the impression that whenever CFAI and Schweser are different, I’ll assume that the problem is from Schw. but turns out this time they were right. Thanks for your help.

mo34 Wrote: ------------------------------------------------------- > Well, I’m glad we cleared this up. I’ll print > parts of this thread for future last minute > reference. I was under the impression that > whenever CFAI and Schweser are different, I’ll > assume that the problem is from Schw. but turns > out this time they were right. > > Thanks for your help. Hull should be your guide

Thanks guys I think I got it. Hopefully they just don’t but something like this on the exam if CFAI questions have been incorrect. Max if you hear anything from CFAI let us know. -thanks.

Not to bring up a sour point with many of us… but what did we conclude here because I’m completely confused as to when I need to divide the duration by the conversion factor and when I should multiply the main formula by the conversion factor. Can someone please shed some light on this and summarize it for me… Thanks

Bump. I would appreciate some clarity on this as well.