# 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?

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.