T-Bond Futures

[intuit2k2]

I am confused about the settling of T-bond Futures.
My understanding is this: At maturity the seller needs to deliver a physical bond to the buyer. The seller could essentially deliver the cheapest Bond with that maturity. To circumvent that, there is a conversion factor equal to Sum over t of (C/2)/(1+y/2)^t+...+(1+C/2)/(1+y/2)^T ... which looks like a PV formula . Essentially the seller receives the futures quote times the conversion factor of the bond that he delivers and pays the price of the bond he delivered- correct?

Did I get this right?

 

[intuit2k2]

In addition; the rule of thumb from the text implies that if the relevant yield on the curve is greater than 6 then you should deliver low coupon, long maturity bonds and if its less than 6 then you have to deliver high coupon, short maturity bonds.

Could you explain the intuition for this, why the standard is 6 and how you can deliver bonds of varying maturity if the contract is based upon a bond of certain maturity. My interpretation is that 10 year Treasury Futures contract implies that at maturity, a treasury bond needs to be delivered with a 10 year maturity?

Thanks in advance.

 

[David Harper CFA FRM]

Hi intuit2k2,

Your first comment above is mostly correct, except for "maturity." The short future gets to SELECT a bond among a basket of viable choices, to deliver per the contract. Delivery price is (as you say) futures contract settlement price * CF; I think of that as the "revenue" or "benefit" to the short. She/he must purchase that bond (to deliver), and it costs its quoted price, so I think of the short as selecting the bond with the highest benefit/cost:

(futures settle price * CF) - quoted price =
(What i receive as the short) - (what i pay as the short) =
benefit/cost, which the short want to maximize; or minimize cost/benefit

…. In this way, the CTD bond is determined by the short (it's not quite like a particular T-bond is labeled CTD; the short has "free will " to select among the basket. CTD is the one that is CTD by virtue of the quoted price/CTD dynamic).

So maturity of the deliverable is not an essential criteria.
See http://www.cmegroup.com/trading/interest-rates/us-treasury/30-year-us-treasury-bond_contract_specifications.html
As the short, you might deliver a 15, 18, 20 year to maturity, etc

In regard to CF (XLS here @ http://www.bionicturtle.com/how-to/spreadsheet/3.c.4_ctd_tbonds/), again not maturity, the idea is to standardize all bonds in the available basket by assuming they all have a 6.0% yield (regardless of the prevailing yield).

Re: "My interpretation is that 10 year Treasury Futures contract implies that at maturity, a treasury bond needs to be delivered with a 10 year maturity?"
No. you could be short a contract that matures in six months or two years, and you will be able to deliver from T-bonds among the basket, with maturities of 15 years or more.



Tuckman explains the implications better than I can:
" the basic idea is to set the conversion factor of bonds with a coupon rate of 6% to one so that their delivery prices (i.e., the conversion factors times the futures price) are equal to the futures price. Bonds with a coupon rate below 6%, typically worth less than bonds with coupons equal to 6%, are assigned conversion factors less than one so that their delivery prices are below the futures price. Finally, bonds with a coupon rate above 6%, typically worth more than bonds with a coupon rate of 6%, are assigned conversion factors greater than one so that their delivery prices are above the futures price ... As yield increases above the notional coupon rate the prices of all bonds fall, but the price of the bond with the highest duration, … falls relative to the prices of the other bonds"

I hope that helps, the implication (IMO) of the 6%-anchored CF, on which maturity/coupon bond, requires a deep dive, with low testability. I recommend noting the duration implication and, unless you are curious, maybe not spend too much time on it

...David

 

[intuit2k2]

David, Thanks for the reply.

I think I have a better understanding of it now, but still confused why the short seller can deliver a bond that is not of the same maturity as the futures contract. Why would Buyer of a 10-year futures contract want a 2 year bond?

 

[David Harper CFA FRM]

Sure, if you look at the actual contract specs (http://www.cmegroup.com/trading/interest-rates/us-treasury/30-year-us-treasury-bond_contract_specifications.html)
Here is the Grade: "U.S. Treasury bonds that, if callable, are not callable for at least 15 years from the first day of the delivery month or, if not callable, have a remaining term to maturity of at least 15 years from the first day of the delivery month. Note: Beginning with the March 2011 expiry, the deliverable grade for T-Bond futures will be bonds with remaining maturity of at least 15 years, but less than 25 years, from the first day of the delivery month. The invoice price equals the futures settlement price times a conversion factor, plus accrued interest. The conversion factor is the price of the delivered bond ($1 par value) to yield 6 percent."

that's the commodity (it's just another derivative with an underlying commodity).

if you are the long and i am the short, you are committing to buying a long-term T-bond (15 years or more in maturity) with uncertainty about which exact T-bond.
note: I cannot give you a short-term T-bond, our deal is for a long-term T-bond

You can go long with a futures contract of any maturity; e.g., three months (promise to buy the above in three months), three years (promise to buy the above in three years)

So the futures contract has it's own maturity: at the end, you promise the buy
The underlying commodity (just happens to be T-bonds here) has its own maturity

David