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Estimating Bond Yield from Futures, CTD Bonds, and Repo

Article Quant Q&A · Author: lakshmen
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Summary

The document asks how to infer a yield from a Treasury bond futures price and outlines that the calculation has several possible approaches. The key instrument link is the futures contract's cheapest-to-deliver (CTD) bond: translating the futures quote into a yield requires considering the delivery bond and the relationship between its cash price and delivery economics. The cited example concerns a five-year Treasury futures contract, but the excerpt does not include the calculation steps or numerical result.

A major caveat is that the CTD bond may change before delivery. If delivery probabilities across candidate bonds matter, an average yield weighted by those probabilities may be more appropriate than assuming one CTD throughout. A follow-up answer also raises repo financing: since the futures price reflects forward financing of the bond, a yield estimate should account for repo costs. The excerpt leaves this adjustment unresolved, so it is guidance on dependencies rather than a complete yield-calculation recipe.

Key ideas

  • A bond futures yield estimate depends on the cheapest-to-deliver bond and delivery economics.
  • Assuming the current CTD remains cheapest through delivery can make the estimate unreliable.
  • Possible CTD changes can be handled by weighting yields by delivery probabilities.
  • Repo financing affects the relationship between a cash bond yield and a futures-implied measure.

Tags

Fixed incomeFutures
Full text
# How do I calculate yield from a bond futures contract?


# How do I calculate yield from a bond futures contract?












I would like to know how I can calculate the yield of a bond futures contract(say the 5 yr treasury "FVM05" is trading at 108.2)? I am not sure how to go about calculating the yield of the futures contract?

Need some guidance in doing so.

## Answer by Helin (score 11, accepted)

https://quant.stackexchange.com/a/28158

There's a lot of intracacies involved and you've got several options. Let's go through an example, using the current front-month 5-year contract FVU6 (FV expiring in September 2016).







These methods above assume that the CTD will not change between now and the delivery date. If that's not the case, you may want to calculate an average yield, weighted by CTD delivery probabilities.

## Answer by Daniel (score 0)

https://quant.stackexchange.com/a/75640

I think you can't just assume the yield of the CTD for a future. You need to also subtract the repo cost since a bond future = fwd = cash bond + repo. So i would say CTD fwd yield minus repo cost. No?

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.