Why Treasury Futures Prices May Not Show Bond Convexity

Summary

The document asks why a chart of continuous 10-year Treasury futures prices against 10-year yields does not show the familiar curved price–yield relationship of an individual bond. Its explanation is that the futures contract can be settled through delivery of different eligible Treasury notes over time, rather than one fixed bond. Changes in the deliverable’s coupon and maturity can obscure the convexity visible when tracking a single bond.

The answer notes that the contract’s deliverable range spans different maturities, and suggests a more consistent coupon and maturity would make convexity easier to observe. The discussion is qualitative: it provides no chart analysis, calculations, or empirical test, and does not quantify how much delivery choice affects the relationship. It also does not examine other factors that could affect a futures-price versus yield plot.

Key ideas

• A single bond’s price typically responds nonlinearly to yield changes because of convexity.
• A continuous Treasury futures series may represent different deliverable bonds over time.
• Changes in deliverable coupons and maturities can mask convexity in a price–yield plot.
• A more consistent deliverable bond would make the convexity relationship easier to observe.

Tags

# Bond convexity Treasuries futures


# Bond convexity Treasuries futures












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??

## Answer by adam (score 8)

https://quant.stackexchange.com/a/10316

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.