Decomposing Bond Futures into CTD Bonds and Futures Basis Exposure
Summary
The document describes two ways to translate a government bond futures position into cash-bond exposure. A simple approach identifies the current cheapest-to-deliver bond and scales its value and risks by the inverse of that bond’s conversion factor. This addresses the conversion-factor question by dividing by it, rather than multiplying by it.
The simple decomposition omits exposure to the spread between the futures contract and the underlying cash bond. It can also produce jumps in measured value and risk when the cheapest-to-deliver bond changes. A more detailed approach assigns weights to eligible bonds according to their likelihood of becoming cheapest to deliver, then represents the futures as a weighted basket plus the residual futures-versus-bond spread. The discussion is framed around U.S. Treasury futures, while noting that delivery rules vary across markets; it gives no detailed calculation of the probability weights or contract-specific multipliers.
Key ideas
- A simple futures decomposition uses the current cheapest-to-deliver bond and divides its value and risks by its conversion factor.
- The simple approach omits the spread between the futures contract and the cash bond.
- The cheapest-to-deliver bond can change, causing measured exposure to shift.
- A richer decomposition weights eligible bonds by their chance of becoming cheapest to deliver and includes the residual spread.
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Full text
# Decomposing bond futures into the cheapest-to-deliver underlying bond
# Decomposing bond futures into the cheapest-to-deliver underlying bond
For a regulatory perspective, I need to decompose bonds futures into the underlying cheapest-to-deliver (CTD) government bonds on a given date.
Suppose I have a 100 bond futures position on date $d$.
How do I decompose this 100 bond futures position into the USD equivalent CTD government bond at $t$?
I am aware of the existence of the conversion factor, and it seems to me that my implied government bond exposure in USD should be something like:
$$100 \times \text{bond futures price} \times \text{conversion factor} \times \text{value multiplier}$$
Is it correct, or shall I divide by the $\text{conversion factor}$ instead?
## Answer by Dimitri Vulis (score 2)
https://quant.stackexchange.com/a/65582
There are futures contracts referencing treasury bonds in many countries. Most (U.K., German...) are very similar to the U.S. Some (Australia, South Korea) are a little different. You seem to be asking about U.S. treasury futures.
When such a futures contract is defined by the exchange, it lists some underlying bonds that can be delivered, and a conversion factor (CF) for each bond. The CFs don't change during the life of the futures contract.
Simplistic approach to decomposition: run someone's model that finds today's cheapest to deliver (CTD) bond.
Value and risks of the futures contract = value and risks of the CTD bond / conversion factor of the CTD bond.
The disadvantages are:
1 you don't see your exposure to the spread between the futures and the underlying cash bond, which can sometimes widen dramatically (like it did in March 2020, for example).
2 day to day, the CTD bond may change, and then the value and risks of the futures contract may (or may not) jump.
More sophisticated decomposition: have your model output weights for each underlying bond based on the probability of each becoming the CTD; and decompose the futures into the basket (weighted sum) of the underlying bonds, and the idiosyncratic spread between underlying bonds and the futures.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.