Can someone explain the relationship between bond yield and bond futures quote? What I do not understand is that for many times I saw the bond yield moved about 1% while the corresponding treasury bond moved much less than 1%. For example, right now $TNX is down -0.78% while ZN M7 only up 0.25%. Even if these two numbers should not be the exact same, but at least they should be close. Help is greatly appreciated.
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Bond Yield and Bond Futures
- Thread starter clearpicks
- Start date
TNX is based on the yield-to-maturity of the most recently auctioned 10-year Treasury note. ZN is based on a basket of Treasury notes maturing from 6 1/2 years to 10 years. It's easy for them to get out of alignment.
Hah! One could spend an entire college semester studying the relation between bond yields and futures prices. There is not generally a 1:1 relation between prices and yields -- instead the change in the price is connected to the change in the yield by a measure of duration. Duration for futures is complicated by the cheapest-to-deliver option...
Hull's "Options, Futures, and other Derivatives" and Kolb's "Futures, Options, and Swaps" provide very elementary introductions to these topics. "The Treasury Bond Basis" by Burghardt, Belton, Lane, and Papa provides the most advanced and thorough discussion of this topic that I know about.
Hull's "Options, Futures, and other Derivatives" and Kolb's "Futures, Options, and Swaps" provide very elementary introductions to these topics. "The Treasury Bond Basis" by Burghardt, Belton, Lane, and Papa provides the most advanced and thorough discussion of this topic that I know about.
I use a little cheat that works well as long as there is a clear cheapest to deliver without a lot of optionality.
The futures contract will pretty closely track the cheapest to deliver issue. Right now for the June 10yr future, TYM07, the cheapest to deliver is the 4% 2/15/2014. Notice that the maturity of this issue is less than 7 years! So the contract that we are calling "the 10 year note" is actually following a 6.9 year issue. Big difference between that issue and the most recently issued 10yr, 4.625 2/15/2017 $ val of 1bp of the CTD (cheapest to deliver) is $567, while the $ val of the current 10yr is $780.
So, what I do is convert the futures contract to the cheapest to deliver. Futures price of 107-25+ times the conversion factor of .8937 plus the basis, currently -3.5 gives me a price for the note of 96-08, and my excel spreadsheet easily calculates the yield as 4.646%
I go through the same exercise for 2yr, 5yr and bond futures. Right now the current 2yr is CTD vs the June futures contract, which is kind of nice.
And one big caveat: This works very well over short periods of time and relatively small market moves. If the 10 yr yield moves up 200 bp, ie from current 4.69% to 6.69% the cheapest to deliver will shift, very likely to the current 10yr, 4.625 2/15/2017, so these futures contracts at that point will be going down faster than a 7 year, more like a 10yr!
Also, the change in the price of TNX is a direct measurement of the change in 10yr yield, while the change in the price of TYM is closer to the change in price of the bond, 2 different things.
The futures contract will pretty closely track the cheapest to deliver issue. Right now for the June 10yr future, TYM07, the cheapest to deliver is the 4% 2/15/2014. Notice that the maturity of this issue is less than 7 years! So the contract that we are calling "the 10 year note" is actually following a 6.9 year issue. Big difference between that issue and the most recently issued 10yr, 4.625 2/15/2017 $ val of 1bp of the CTD (cheapest to deliver) is $567, while the $ val of the current 10yr is $780.
So, what I do is convert the futures contract to the cheapest to deliver. Futures price of 107-25+ times the conversion factor of .8937 plus the basis, currently -3.5 gives me a price for the note of 96-08, and my excel spreadsheet easily calculates the yield as 4.646%
I go through the same exercise for 2yr, 5yr and bond futures. Right now the current 2yr is CTD vs the June futures contract, which is kind of nice.
And one big caveat: This works very well over short periods of time and relatively small market moves. If the 10 yr yield moves up 200 bp, ie from current 4.69% to 6.69% the cheapest to deliver will shift, very likely to the current 10yr, 4.625 2/15/2017, so these futures contracts at that point will be going down faster than a 7 year, more like a 10yr!
Also, the change in the price of TNX is a direct measurement of the change in 10yr yield, while the change in the price of TYM is closer to the change in price of the bond, 2 different things.
one word: DV01