How Treasury Futures Rolldown Relates to the Futures Curve and CTD Bond

Summary

The discussion distinguishes futures-curve roll from the price effect associated with a bond futures contract’s cheapest-to-deliver bond. In common futures terminology, roll is measured by comparing prices of successive contracts. For bond futures, however, the contract price is also linked to the CTD bond through its conversion ratio, subject to basis effects. If the yield curve’s shape remains unchanged, the CTD bond’s price can change as it ages, and that movement may flow through to the futures price.

A second answer describes measuring bond rolldown by comparing a forward bond yield with the yield of the corresponding aged spot bond, assuming the spot curve does not shift. The answers offer conceptual descriptions rather than a worked calculation or empirical evidence. The relationship depends on the bond futures basis and delivery mechanics, so CTD price rolldown and calendar-spread roll should not be treated as interchangeable without specifying the measure and assumptions.

Key ideas

• Futures roll is often measured as the price difference between successive contracts.
• Bond futures may also reflect price changes in the cheapest-to-deliver bond as it ages.
• The futures-to-CTD relationship depends on the conversion ratio and can be affected by basis.
• A forward bond yield can be compared with the aged spot bond yield to describe rolldown under a steady curve assumption.

Tags

# treasury bond futures rolldown


# treasury bond futures rolldown












Treasury futures contract has no carry, but what is its rolldown (if it exists)?

In the above answer to carry, @Helin mentioned "...bonds have expected rolldown returns that will flow through to futures..."

Does it mean that futures' rolldown is exactly the same as the rolldown of its CTD bond in spot space? Thanks.

## Answer by oronimbus (score 2)

https://quant.stackexchange.com/a/74564

Roll in futures language is typically defined in terms of the futures curve, i.e. the difference between (successive) contracts, say RXM3 minus RXH3. You can find more information on this for STIR contracts in Jha, S. (2011), Interest Rate Markets: A Practical Approach to Fixed Income. I'd say this is primarily what people refer to as "futures rolldown".

Since bond futures are a bit different to most other futures contracts, you can make an argument that the rolldown of the CTD flows through to the contract itself. In the absence of a gross/net basis, the price of the future relates to CTD price via the conversion ratio: $P_{fut}=P_{ctd}\times C$. If the shape of the yield curve stays constant, the change in the CTD bond price caused by the passage of time will then result in a profit or loss on the future.

## Answer by user68819 (score 0)

https://quant.stackexchange.com/a/76582

It should be the same as the fwd bond. You should be able to measure the fwds roll down as fwd yield minus the aged spot bonds yield (assuming the spot curve doesn't change) at term.

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