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I know that long-duration bonds, on a a single bond basis, exhibit convexity. However, do Treasuries futures prices and the 10 year yield exhibit the same property?

Below is a plot of continuous 10 year Treasury futures (ZN contract) since 2003, where the $y$-axis is the price of ZN futures and the $x$-axis is the yield/interest rates on the 10 year. While there should be a non-linear relationship between bond price and yield for a single bond, that doesn't seem to be the case when looking at the futures price/yield relationship. Why??

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  • $\begingroup$ have you tried this plot for a different market ? Often different market exhibit different characteristix. In the US market the often mentioned mean-reverting property of the interest rate don't hold. The japanese rates however exhibit such a behaviour. $\endgroup$
    – Probilitator
    Commented Feb 19, 2014 at 20:01

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I dont think you can see convexity in such a plot, since each of these prices are not observed from a single bond deliverable, but from different coupon bond deliveries. If the delivery was always based on same coupon type bond and quite similar maturity (http://www.cmegroup.com/trading/interest-rates/us-treasury/10-year-us-treasury-note_contract_specifications.html, ZN deliverable grades go from 6.5 to 10 years), then you would have observed the convexity effect.

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    $\begingroup$ This is right, the futures' price is a function of the cheapest-to-deliver bond acceptable to settle the contract, which varies over time and may not be the 10-year benchmark US Treasury bond nor trading exactly at the interpolated generic 10-year yield/price. $\endgroup$
    – lemarin
    Commented Feb 24, 2014 at 15:44

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