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# "simple" explanation for 10 yr treasury note future pricing

Discussion in 'Financial Futures' started by scriabinop23, Sep 10, 2006.

1. ### scriabinop23

anyone have a simple explanation for how ZN DEC 06 is priced at 107'030 (107 6/32) ?

obviously not the same or even remotely close to the 10 year treasury price of 100-24/32 (eg bloomberg )

10 Year 4.875 08/15/2016
100-24+ / 4.77 0-03 / -.012 09/08

2. ### Surdo

Last sale on eCBOT is 107 '03.5
It closed in the pits on Friday@ 107 '05.5.

3. ### Pabst

What does that have to do with the question posed by this thread?

4. ### Pabst

The coupon on the current ten year Treasury Note 4.875

The coupon on ZN, the ten year Treasury Futures Contract is 6%.

Thus even at a similar implied yield the price between the two is different.

5. ### Surdo

Why don't you answer the question then WISEASS?

He is looking at the "Cash" price vs the Dec futures contract!

7. ### scriabinop23

lets get a little more in depth here. simplified:

if I buy 3% coupon bond for 100, then yield is 3%. If I buy 3% 1 yr coupon bond for 90, then yield is 13%.

So if coupon on 10 yr ZN is 6% and I buy it for 100. Then effective yield is 6%. If I buy it for 107 (with 1 yr maturity) ... then effective yield is -1% (107 - 6 coupon - 100 par value returned). Now I assume my mistake here is that 10 yr treasury has more than one year to maturity, so this factors into pricing. Please help provide formulas so I can have a complete understanding. I didn't add in accrual, but this must be a small portion, right? (at most 1/2 of annual coupon of 4.875)

Not making sense yet. Please help fill in the gaps for bond/note newbie. Now probably very clear why I originally asked the question.

I saw ecBOT's explanation:

http://www.ecbot.com/cbot/pub/cont_detail/0,3206,1520+14433,00.html

U.S. Treasury notes maturing at least 6 1/2 years, but not more than 10 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 note (\$1 par value) to yield 6 percent.

--- What is "invoice price"? I assume settlement price is the traded price on the exchange? And when is interest accrued from ?

My logic: a futures contract expiring 3 months from now with a coupon (and thus yield since par value=100) of 6% would have accrued interest of 1.5% and remaining interest of 1.5% (underlying note paying twice a year). So lets say par is 100, then value of the note would be 101.50. Correct?

I'm looking for something like:

future price = 10 yr note par value (underlying) + accrual + x ...

But that only gets us to something like 102 or 103, not 107.

8. ### Pabst

http://www.moneychimp.com/calculator/bond_yield_calculator.htm

Think of this as the logic. If yields are 5% then how much would you pay over par to recieve a 6% coupon? Even though I was a local in the Bond pit I'm not a math wiz so "walking" you through is difficult for me. I'm sure SOMEONE here is well versed enough on convexity to explain in layman terms.

9. ### scriabinop23

thanks. i'll learn this... but it looks like time to maturity is the factor I wasn't quite grasping.

10. ### EquityGuy4321

Buy a copy of Galen Burkhardt's book, "Treasury Bond Basis". A fixed income futures price has three components: Cash bond price, Repo rate, and Conversion factor. Using the formula given in the book you can take the futures price, repo rate, and CF and convert them to a cash price, and vice versa.

Buy the Bond Basis book and read it cover to cover. That will put you on the same page as the bond guys.

#10     Sep 10, 2006
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