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frost


Total Posts: 3
Joined: Aug 2017
 
Posted: 2017-08-14 11:39
Hi all,

This is my first post on this forum - I've searched quite extensively for illumination on this topic but so far I haven't found what I was looking for. So here we go.

As I understand it, conversion factors used by exchanges are ways to put all bonds in the deliverable basket on a roughly 'equal footing', which approximatively translates into computing the price at which $1 of par value would yield 6% with maturity rounded in the correct way (I'm aware the exact computation is more involved). 6% is also the 'notional coupon' of the bond.

I've been trying to gain intuition for why the conversion factor works, ie. when you multiply the futures by the CF of a bond, it gives you the correct fwd price of the bond (minus the value of the delivery option), regardless of the bond you choose.

My reasoning was as follows (talking about the CTD for now):
- it seems natural to me to say that the futures will trade at the price level the CTD would trade if it had a 6% coupon. (Hence, in the EUR world, the much above par price of the unconverted future.)
- it's approximatively equal to compute the CF as the price at which $1 par value would yield 6% or to compute it as the inverse of the price at which the coupon would be 6%
- therefore, the CF allows back and forth between futures and bond prices in an apparently seamless manner

What I can't quite grasp is how this reasoning could be valid (i.e. how CF could 'work' in the sense described above) if there's an approximation involved here (i.e. 100bp down in yield is different from 100bp up in coupon) and how it could work for other bonds than the CTD. If this reasoning is incorrect, what's your intuition about CF here?

To end this long-winded post, I know that CF are part of the contract set-up and as such are a bit arbitrary. But once they're put in a place, there is an economic meaning to them and to why they work that I think is linked to what I said.

Thanks in advance for your help, I look forward to reading you.

Dizzy


Total Posts: 247
Joined: May 2006
 
Posted: 2017-08-14 14:40
I'm not a bond expert, but it might be useful to consider that most bond futures have physical delivery.

Pricing is done in relation to what is likely to be delivered. Depending on the set of deliverable bonds, pricing may be far from any theoretical price based only on futures specifications.

This example might be of interest: Treasury Bond Futures Roll: Mind the Gap

"Although the code snippet makes taking over the earth look fairly easy, you don't see all the hard work going on behind the scenes." - Programming F#, Chris Smith

frost


Total Posts: 3
Joined: Aug 2017
 
Posted: 2017-08-15 15:35
Thanks for the article, it's very interesting. But don't you think as a rule of thumb, arbitrage pricing (ie. converted future prices will equal forward prices - delivery option) will hold most of the time?

Dizzy


Total Posts: 247
Joined: May 2006
 
Posted: 2017-08-16 08:19
The basis can be traded, so within reasonable limits, yes.

"Although the code snippet makes taking over the earth look fairly easy, you don't see all the hard work going on behind the scenes." - Programming F#, Chris Smith

Martinghoul


Total Posts: 858
Joined: Oct 2008
 
Posted: 2017-08-29 11:36
I could only add a recommendation here...

Have you read "Treasury Bond Basis" by Burghardt et al? It's sort of the seminal text on the subject.

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...

developer


Total Posts: 5
Joined: Nov 2010
 
Posted: 2017-08-29 14:12
"I've been trying to gain intuition for why the conversion factor works, ie. when you multiply the futures by the CF of a bond, it gives you the correct fwd price of the bond (minus the value of the delivery option), regardless of the bond you choose."

not sure if i understood correctly the sentence , but Price(bond) - Price(future)*CF = gross basis which is the cost of funding calculated upon the repo rate and other things . The conversion from the bond price to the future price is not seamless as you can see.

One thing is sure that the basis tends to 0 close to the delivery date

frost


Total Posts: 3
Joined: Aug 2017
 
Posted: 2017-08-30 10:56
I'm reading through it now, actually! Thanks for the recommendation.

For what it's worth, I think I found an answer to my question(s).

1° there is no approximation because talk of a '6% notional coupon' is really parasitic on the conversion factor's definition (ie. starting from the cash bond, not from the futures). So the future's price (prior to expiry) is actually CTD * 1/CF + basis. I think I was just misled by the 'coupon' talk (Hull and some other basis sources don't help saying the underlying is a 6% coupon bond).

2° converted cash prices do not give forward prices for any bonds but the CTD because some bonds are expensive to deliver.

A fascinating subject, in any case!

developer


Total Posts: 5
Joined: Nov 2010
 
Posted: 2017-08-30 13:30
most of the time, you will choose the one with the highest implied rate in basket
you might want to have a look at a bloomberg terminal, EUREX is publishing the conversion factor for Bund, bobl etc Attached File: marketdata_hedgeratios_20170829.pdf
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