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If you are long a FRA (forward rate agreement) and short a ED (Eurodollars) future with the same fixing dates, do you have positive convexity or negative convexity? Why?

According to the following thread a Eurodollar future has no convexity and the FRA has positive convexity. Why is this true? Or if it's not true, why is it not true? Long Forward Rate Agreement, short Eurodollar futures

I think that the answer is you will have a negative convexity because the convexity adjustment would make a long future have a higher convexity than the FRA. Can anyone tell me if my logic and answer is right?

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No you are long convexity. The futures contract has no convexity (since its value is linear as the underlying rate varies, specifically it moves by $25 per bp per contract). Meanwhile, the FRA has positive convexity (it's like a mini bond). The fact that you are long convexity overall is consistent with the fact that the rate on the futures contract is slightly higher than the FRA. That is how you are paying for the convexity.

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