Treasury Futures Wild Card Exercise and the Gross Basis

Summary

The note explains the conversion-factor term in a Treasury futures wild card option inequality. The question concerns when a short futures holder should exercise promptly and sell the remaining bond position, comparing the gross basis cost with the price move between the relevant afternoon reference times. The response interprets the equation by splitting a starting bond position into the quantity delivered against futures and the residual tail.

If the short position covers a conversion-factor amount, gross basis is incurred only on that delivered portion. The later price change applies to the remaining fraction of the bond position. This allocation explains why the gross basis is multiplied by the conversion factor before comparing it with the tail’s price move. The response offers a simple quantity-based explanation, not a full derivation of the contract’s timing mechanics or a worked market example. Its conclusion is limited to clarifying the stated equation’s scaling.

Key ideas

• The conversion factor represents the bond quantity delivered against the futures position in the explanation.
• Gross basis applies to the delivered portion of the bond position.
• The later price change applies to the residual tail of the position.
• The equation compares the basis cost on the delivery portion with the price move on the tail.

Tags

# Treasury Futures Wild Card Option equation


# Treasury Futures Wild Card Option equation












I am confused about the equation on page 13 (upper right) from the CME: https://www.cmegroup.com/education/files/treasury-futures-basis-spreads.pdf

The equation calculates the move in the CTD that would make it worthwhile for the short futures contract holder to immediately exercise and sell the tail of the position.

In brief, the equation is

$\textrm{Gross Basis} \times (CF / (1 - CF) < P_{late} - P_{2pm}$

I understand that the 1-CF corresponds to the tail of the position. However, I don't understand why there is a CF in the numerator.

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/45523

It’s because you only lose the Gross basis on a portion of the bonds (ie the amount that you will deliver against the futures).

For example if you start with 1 bond and short CF amount of futures, you will deliver CF bonds against the contract, losing the gross basis on CF bonds. . You will pick up P(late)- P(2pm) on (1-CF) amount of bonds.

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.