Gross Basis and Conversion Factors in Bond Futures Delivery

Summary

The document clarifies how gross basis relates a bond’s cash price to a bond futures contract. It gives the relationship as bond price minus futures price multiplied by the bond’s conversion factor. This frames gross basis as the difference between the bond value and its conversion-adjusted futures value, and explains why the conversion factor appears when comparing a deliverable bond with the futures contract.

The answer applies this relationship to a short futures position and a bond that is not currently cheapest to deliver, suggesting that the gross basis represents the gain or loss from buying the bond and shorting the equivalent futures exposure. The discussion is brief and comes from a question-and-answer exchange; it does not work through delivery cash flows, accrued interest, financing, or changes in the cheapest-to-deliver bond. Those details can matter in a full futures basis analysis, so the equation is a starting point rather than a complete account of delivery economics.

Key ideas

• Gross basis is the cash bond price less the futures price multiplied by the conversion factor.
• The conversion factor scales the futures price when comparing it with a specific deliverable bond.
• A cash bond and short futures position can be evaluated through their gross basis.
• The brief explanation does not detail financing, accrued interest, or delivery-option effects.

Tags

# Bond future deliveries


# Bond future deliveries












More looking for a confirmation here, if someone knowledgeable on the subject could confirm/correct I would be grateful:

I often hear authors/commentators stating that say I have to deliver a not-CTD bond into a futures contract I am short, my loss will be the gross basis of that bond (assuming basis has not converged fully). Its really conversion factor (cf) x gross basis though, isn't it, assuming I'm holding cf futures short ? (I get that it's just a notional adjustment, but assuming I can clear out the tail of my cash position at flat - I am not sure how I could lose the full gross basis).

Thank you!

Edit : basis has 'not' converged as the bond is not the CTD.

## Answer by Rowan Harley (score 0)

https://quant.stackexchange.com/a/81458

Gross basis is just the difference between the bond price and the converted futures price: $$ B_{\text{GROSS}} = P - F \times CF $$

In some cases, there can be multiple bonds which have a possibility of being the CTD at expiry. What you gain/lose will be the gross basis. It's just a simple relationship that show's what you'll gain/lose if you decided to buy a bond today and short the equivalent futures contract.

You can read more here.

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.