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Treasury Futures Carry, Delivery Pricing, and Expected P&L

Article Quant Q&A · Author: arna
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Summary

The discussion explains why holding a Treasury futures contract to expiration does not imply a loss equal to a simple difference between a quoted yield and a repo rate. Under the stated assumption that rates and market prices do not move, the futures price stays unchanged, so there is no futures-price P&L. A possible exception is the interest foregone on exchange margin, which applies to either position direction.

The futures price is linked by arbitrage to cash bond financing and delivery economics. The response describes offsetting strategies involving the futures contract, the deliverable bond, and repo; if one side became more attractive, arbitrage would pressure the futures price. It cautions against relying on a futures yield, described as ill-defined, and instead points to cash prices, repo rates, and conversion factors. A second answer notes that a futures buyer pays the delivery invoice price, based on accrued interest and the conversion-factor-adjusted futures price. The exchange is brief and does not quantify margin opportunity cost or model changing rates, financing, or delivery options.

Key ideas

  • With unchanged rates and prices, holding the futures contract does not create P&L from a yield-minus-repo calculation.
  • Treasury futures pricing reflects arbitrage between futures, deliverable bonds, and repo financing.
  • A futures yield is not a reliable standalone measure for calculating carry.
  • Delivery invoice value combines accrued interest with the conversion-factor-adjusted futures price.
  • Margin interest opportunity cost may affect returns even when the futures price is unchanged.

Tags

FuturesFixed incomeCarryDerivatives pricing
Full text
# Treasury futures cost of carry and P&L


# Treasury futures cost of carry and P&L












I'm looking to understand the P&L implications of holding 2YR treasury futures. Assuming no movement in interest rates through to maturity (i.e., no capital gains or losses due to interest rate moves), if I purchase a 2 YR treasury future today and hold it until expiration, what will my P&L impact be.

I have attached today's futures and CTD chart from the CME website. Using these figures, should I take:

a) The futures yield of 1.718% or the CTD yield to maturity of 1.89%,

and from this subtract...

b) The implied repo rate of 2.69% or look up an actual repo rate for the same tenor?

And once I have this number (I'm calling it cost of carry, but from other entries I know there are pure and broader definitions), if I have USD 1,000 of futures and the cost of carry is say -0.80% then my P&L at maturity will be -$8. Is this math correct?

Thanks so much in advance.

## Answer by Attack68 (score 2, accepted)

https://quant.stackexchange.com/a/46006

If you expect no market movement then there is no pnl, (except possibly the loss of interest income on the posted maintenance margin at the exchange which is true in either the case of a long or short position).

The futures price, under a no arbitrage argument, is set to be the price which at the Exchange Delivery Settlement Price (EDSP) will equate to either of the two scenarios:

A) Buying the future, selling the bond and repo-ing it in to term. B) Selling the future, buying the bong and repo-ing it out to term.

If either A) or B) were more favourable the price of the future would adjust so that it wasn't anymore.

The point being that if rates truly do not move over the lifetime of the future, all that will happen is that the futures prices remains exactly the same every day, and the price of the bond and the repo rates adjust daily to take account of their varying lengths, term structure of repo rates and pull to par.

With respect to you calculations I personally have never used the concept of a futures yield because it is ill defined and misleading. Just use the cash prices, the repo rates and the conversion factors and you have fixed financial values.

## Answer by VanillaCall (score 1)

https://quant.stackexchange.com/a/45961

You're buying a futures contract so there is no carry. It's basically a forward (assuming no optionality). Let's say you buy the TU futures contract and hold it until the last delivery date. At the end, you pay the invoice price which is Accrued Interest + Conversion Factor * Futures price.

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.