Why Treasury Futures Implied Repo Can Rise on the Last Delivery Date

Summary

The document explains why a futures contract’s implied repo rate may be higher when the short delivers on the last eligible date rather than the first. The key detail is that the invoice price includes accrued interest in addition to the futures price adjusted by the conversion factor. Since accrued interest generally increases with time, the later delivery date can raise the invoice amount used in the implied repo calculation. A coupon received during the delivery period can also affect the return calculation.

The discussion describes the short futures position paired with ownership of the cheapest-to-deliver bond, with delivery timing as a choice available to the short. It offers a conceptual explanation rather than numerical examples or market data. The effect is described as typical, not universal: the original question notes that the stated relationship may depend on whether the implied repo rate is negative, and the answers do not fully analyze all rate, coupon, or financing scenarios.

Key ideas

• The futures invoice price includes accrued interest as well as the conversion-adjusted futures price.
• Accrued interest usually grows as the delivery date moves later, which can increase implied repo.
• A coupon paid during the delivery period can also contribute to the return from the futures and bond position.
• The short futures holder can choose when to deliver, so delivery timing affects the implied financing return.
• The explanation describes a typical effect and does not establish that the later date always produces a higher rate.

Tags

# why the implied repo rate is higher when choosing the last delivery date to deliver rather than first delivery date


# why the implied repo rate is higher when choosing the last delivery date to deliver rather than first delivery date












there must be something very basic that I did not get....

I am reading a book. And it says the implied repo rate is defined as IRR = ( invoice price / cash bond price - 1) * 360/ n, where is the number of days to the delivery date.. and this book also says the last delivery date (when n is bigger) implies a higher IRR...

The statement is only true when IRR is negative, but is this always the case?

## Answer by dm63 (score 0, accepted)

https://quant.stackexchange.com/a/40671

It's because $Invoice Price$ in your equation is the Dirty Invoice Price, meaning $$Invoice Price= Futures Price*Conversion Factor + Accrued Interest$$. The Accrued Interest grows as the delivery date lengthens, making the IRR typically more positive at month end in most situations.

## Answer by decaybeta (score 1)

https://quant.stackexchange.com/a/41319

Implied repo is the rate of return you earn by shorting the futures and buying the CTD of the security. The short exercises the right to deliver the security to the long. Essentially, the short is long this optionality. If they wait until the last delivery date, the invoice price will includes accrued interest will be higher. Secondly, if there's a coupon payment, this will also be added. These factors increases your implied repo rate.

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.