Decomposing bond futures into the cheapest-to-deliver underlying bond

Question

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 1

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.