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 Alex. But the P&L can't be zero as there is an embedded cost of carry - the CTD to deliver bond has an interest component and a cost to finance it. So depending on the yield curve the P&L at the end of the period must be positive or negative to capture that...?
– arna
Commented Jun 6, 2019 at 9:16
• @Helin Hi Helin, I saw your replies to a similar question from over a year ago. Do you have a view on this, or which of the yields or repo rates to use by any chance?
– arna
Commented Jun 6, 2019 at 9:22

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.

• Thanks @Attack68... that's great. I just wanted to ask a quick clarification question...: if gross basis = spot - conversion factor x futures price, then shouldn't the futures price get closer and closer to the spot price as the value of the gross basis tends towards zero as there is less and less time left for delivery -- so if interest rates truly don't change, you would still have some form of P&L determined by what your gross basis is? (ignoring option value, assuming gross basis is coupon income - financing charge)
– arna
Commented Jun 9, 2019 at 22:45
• No. In the absense of market movement the bond price changes. A bond purchased today is not the same as a bond purchased tomorrow. The bond price will move closer to the futures EDSP adjusted by CF.
– Attack68
Commented Jun 10, 2019 at 5:15

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.

• Thanks @VanillaCall. I thought the futures (forward) price converges to spot, and the P&L that you generate or lose over that period is your postive or negative carry (again assuming no change in interest rates and bond prices). So surely there has to be a positive or negative P&L associated with the embedded funding cost...? For example, if I were to buy 2 yr treasury futures today, given the present yield curve, in 3 months' time I would be out of pocket because the funding cost exceeds the interest income of the underlying... no?
– arna
Commented Jun 6, 2019 at 9:19
• If you buy 2y futures today, the price would be higher than the spot price of the underlying CTD due to the negative carry of the bond. That basically means you've locked in the futures/forward price which is HIGHER than the spot price of the bond. You need the spot price of the underlying bond to be above the futures price to be profitable. If the spot price is equal to the futures purchase price at expiration, then you break-even. If the spot price is lower than the futures purchase price at expiration, you lose money. In your example, the futures price is rolling down to spot so you lose Commented Jun 7, 2019 at 2:00
• Thanks @VanillaCall - so if I want to get an estimate in % of the annual carry, based on the CTD yield, repo rate, etc. (if you see my question), do you know which figures I should be using in my calculation -- the future yield or actual yield, and the implied repo or actual repo rate? Thanks so much again
– arna
Commented Jun 7, 2019 at 9:24