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Say we have the active German government bond future, RXH3 and we wanted to calculate a series of returns for the active contract.

Would we calculate returns on the daily price difference? And if so, what would happen on the roll day? Or would be calculate returns on the Cheapest to Deliver bond?

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    $\begingroup$ As you say results in futures are usually measured by the daily P&L (in Euros) on one contract, using RXH3 until the roll date (which is coming up in a few days) and the RXM3 contract after that. It is not standard to compute returns, but if you wanted you could divide the EUR P&L by the notional amount of 1 contract (which is 1000 times futures price) to find the return on notional amount. But why do you need a return in the first place? $\endgroup$
    – nbbo2
    Mar 2 at 14:18
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    $\begingroup$ Because I'm wanting to have daily returns which I can then use in systematic strategies. So what would you do on the roll day? Look at the return of the back contract? I have a feeling this is wrong, but I can't define why $\endgroup$
    – Fidelio
    Mar 2 at 15:49
  • $\begingroup$ @nbbo2 please see my comment above $\endgroup$
    – Fidelio
    Mar 2 at 16:54
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    $\begingroup$ I agree it is a little weird because the notional amount (and so the base for the return calculation) changes when you roll to a new contract. But that is what I do and I don't know a better way. $\endgroup$
    – nbbo2
    Mar 3 at 8:37
  • $\begingroup$ @nbbo2 let me add an additional point which disproves the back future return calculation on the roll: SCENARIO: there are no market movements except for mkt players rolling. If I choose arbitrarily roll day=roll-5 to calculate the return on the back future, and if everyone rolls their longs on that day, we will have a negative return on the front future and a positive return on the back. Given that's the day I chose to calculate the return, I would observe a positive return in my series. But in a continuous series, if the roll wasn't an issue, you would have 0 return. $\endgroup$
    – Fidelio
    Mar 3 at 12:43

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The standard approach is to create a synthetic aka adjusted price series. Usually this is done by backwards adjusting prices of older contracts to align with newer ones. This price series then mimics the price of a trading strategy. You can then create a series of returns based on this strategy. Exactly how to do the adjustments (mostly it's just a straight delta plus / minus for each contract expiry roll) is the topic of research, but bloomberg et al can give you pretty decent series directly (eg, "RX1 comdty", etc).

Exactly what the denominator for the returns calc is also kinda up to you, given the leveraged / cash paradigm of futures. Just using the notional is a weak approach though, as it's not easily comparable across contracts. Some measure of delivered risk is better. How you calculate that, is again up to you.

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