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Looking at the price of 10-year note (ZN) futures, I noticed that the price of ZN futures corresponding to ~1.70% yield was ~128 today but was ~131 in March 2021.

Why is there such a huge difference between the prices for the same yield? I tried to find a calculation but I could not.

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ZN Futures is not equal to to spot price of 10-year note. If you look at the contract specs, it implies that it is ~7 years Cheapest to Deliver ("~7yr CTD").

U.S. Treasury notes with a remaining term to maturity of at least six and a half 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.

https://www.cmegroup.com/markets/interest-rates/us-treasury/10-year-us-treasury-note.contractSpecs.html

Furthermore, a minor element is that in a "continous futures" quotation / history where futures are assumed to be rolled over earlier than expiry, the historical price of ZN on 03/31/21 is actually betting on June 2021 expiry, i.e. there is a 3-month implicit financing. The same for 01/11/22 where it is actually betting on March 2022 expiry. The 3-month implicit financing rate/yield (at that time) and the market expectation of the 6.5-10yr yield for 3 months later also affects the futures price quoted.

Date 7 Yr Spot Yield 10 Yr Spot Yield 6.5-10 Yr ZN Futures Yield ZN Futures Price
03/31/21 1.40 1.74 1.43 130.9375
01/11/22 1.69 1.75 1.72 128.3906

Source of prices and yields:

https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/textview.aspx?data=yield

https://www.cmegroup.com/markets/interest-rates/us-treasury/10-year-us-treasury-note.quotes.html

https://www.nasdaq.com/market-activity/futures/zn/historical

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  • Thank you for taking the time to explain! Is the crux of the difference related to 3-month implicit financing? or is it that expiry's are different? What I'm struggling to understand is why would expiry even matter since yield is calculated only on the price of the bond, par value and coupon rate alone. Why is time even a factor? Would you be able to show the math behind these numbers, i.e., going from price the bond is traded at to the yield in a particular month? (I would greatly appreciate that!) Jan 12 at 23:41
  • @fineTuneFork the main crux is "~7yr CTD" nature of ZN Futures. The implicit financing is just a minor element. Implicit financing is the nature of all Futures products. When you buy a Futures contract, you sort of gained exposure to the underlying early, and you did not pay the full notional amount. Yes there is initial margin required but it doesn't mean you paid someone upon buying the contract. I think you can look up on "Spot–future parity" without regards to bonds. It is applicable to all Futures, including Stock Index, Gold, Oil, etc.
    – base64
    Jan 13 at 2:14

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