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If the the duration of a 10yr future is roughly 8 years, I simplistically think that if I go long 10% notional of my portfolio and yields rise 10bps, then my P&L is 8 x -10bps x 10% = -8 bps

In this context, what is the duration of a Eurodollar future ? Is it 1 or is it 0.25?

So, if i am long 10% notional in 10yr futures and short 10% notional in ED futures, what is the net duration of this structure ? I would have thought it's 8 - 0.25 = 7.75. So, if the yield curve rose 10bps in a parallel shift up, I would lose 7.75 bps

However, when I look at the ED future, I understand it's priced as 100 - annualised 3mth, so that means that every 1bps move in yield gives me roughly a 1bps move in price, which means the duration ( % change in price / change in yields ) is 1 and not 0.25 ?

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The duration of a bond is the percentage change in the value of the bond for a 1% change in yield. For example, a 10Y bond with a duration of 8Y will lose approximately 8% for every 1% increase in yield (equivalently 0.08% for every 1bp increase in yield).

Eurodollar futures are derivatives, not cash instruments, so they do not have a duration (their value is zero at inception so percentage increases don’t make any sense). They do have a DV01, or dollar value of a basis point, which is $25. That is, a single ED future loses \$25 for every 1bp increase in the forward rate.

If you want, you could say that the ‘value’ of an ED contract is \$2,500 x price, which is around \$250,000 and would give a ‘duration’ of 1Y or you could say that the ‘value’ is \$2,500 x price x (1/0.25) which is around \$1,000,000 and would give a ‘duration’ of 3M, but these are arbitrary choices that only loosely correspond to the duration of a cash instrument. The right way to think about ED futures is in DV01 terms.

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If your notional is 100mm, and you buy a 10Y treasury note worth 10mm (10% of 100mm) then you own 100 contracts (since each contract specification is officially a nominal of \$100,000), and the DV01 is approximately \$ 8000/bp. If you sell 10mm of a EDH0 then you have sold 10 contracts (since each contract specification is officially a \$1mm nominal) and the DV01 is \$250/bp.

You are trading an approximately 8y instrument versus a 3m instrument so that should not be surprising.

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