Aleph
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| Total Posts: 54 |
| Joined: Jul 2006 |
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Hey guys,
Thanks in advance for this, probably simply question:
I'm working with some Eurex Bond Future data and I want to calculate Yield to Maturities implied by the prices (on a 15min to 1 day range over the course of a few months). Since I'll be differencing these and I don't actually care about delivering anything my hunch is that it's good enough to just throw the notional terms (6% coupon, 10 year length for bund, etc...) into a yield to maturity calculator and use that.
Is that true, or do I really need to mess about with conversion factors?
Thanks! |
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| It's not really that difficult to do it right and you won't get the nonsense absolute numbers that you get with the notional 6% coupon calculation. So I'd recommend you do the right thing, even though I am not sure it's, strictly speaking, necessary in your case. |
Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness... |
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Aleph
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| Total Posts: 54 |
| Joined: Jul 2006 |
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Thank you!
It's historical, though, so I'm not sure I can get the conversion data. My expertise tops out at any phenomenon that operates on over a minute time scale, so bear with me, please:
As I (dimly) understand it, conversion factors are there to equalize the cash flows because there's usually not bonds identical to the notional bond to deliver. In a sense equating the bonds of different yields. Now, since it's the yields and not the prices I care about, I feel like that statement is telling me that the results will be the same, except for some discreteness because the basket of deliverables isn't made up of an infinite number of bonds with continuous parameters.
Carrying on on this probably wrong path: I would of thought that it's this discreteness that causes cash-and-carry trades and changes in the basis. As the basis is pretty stable on that time frame, I should be okay?
Additionally, wouldn't I need to know the CTD at every point in order to historically compute the 'perfectly accurate' YTM?
I never was very good at this sort of stuff, I'm a microstructure guy...
Thanks again, I really appreciate it. |
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Well, yes, I think you're right about the conversion factors. Specifically, if you were to do away with the conversion factors and just do the notional 6% coupon calculation, you're likely to get a self-consistent time series of YTMs. However, it's key to do this with the correct maturity, i.e. you have to fix the maturity of the contract at the start of the contract. Let me illustrate: if I am not mistaken, BBG calculates the yield for Eurex contracts by using the 6% notional coupon and a constant maturity (2y for the Schatz, etc). Yield changes that are calculated this way are not going to be consistent with the actual yield changes on the CTD, because of the slope.
So I guess you sort of need to know the CTD, at least at the contract's inception. |
Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness... |
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I suppose it depends how accurate you want/need to be.
For some of the better-known European bond futures, the cheapest-to-deliver (and so the maturity of the cheapest-to-deliver) varies quite a lot.
Having said that, I think in many cases choosing a "typical" maturity (or duration) number, as Martinghoul suggests, will suffice.
(this question, or a variation on it, has I am sure been asked a few times recently...) |
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Aleph
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| Total Posts: 54 |
| Joined: Jul 2006 |
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So, let me repeat that to be sure I understand:
Since, for example, the Shatz is talked about as a 2yr but it's really anything from a 1.75-2.25 year based on the contract specs *- I would need to know where it is at the beginning to get the correct maturity. If I assume it's 2, then my error will be bound by the difference in the yield implied by the different maturities which will get larger as I get closer to maturity. So, even if I can't find the conversions I'll at least know my error margin and then I can decide if that's acceptable or not.
Does anyone know where I could find those maturities for the U2009 and M2009 futures?
* http://www.eurexchange.com/documents/glossary_en.html?id=Euro-Schatz+Futures
Thanks again, it's really helpful. |
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I think this is possibly a viable shortcut for you: calculate the maturity date of a notional 2y bond at the contract's inception (for Schatz). Use this maturity date with the notional 6% coupon for all your yield calculations going fwd and I think you will be self-consistent to the point where yield differences, rather than outright yield levels, are valid.
From what I can see, the CTD for the M09 contract was the 1.25% 11Mar11 Schatz, while for U09 contract it was the 1.5% 10Jun11 Schatz. |
Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness... |
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Aleph
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| Total Posts: 54 |
| Joined: Jul 2006 |
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Thank you.
I suspected the fact that I was interested in differences might save me. I can see that there could be some problems with large lags in time when those differences might diverge more.
Thanks again! |
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