Convexity in a Long FRA and Short Eurodollar Futures Position

Summary

The document explains the convexity exposure from pairing a long forward rate agreement with a short Eurodollar futures contract that has the same fixing dates. Its answer treats the futures payoff as linear in the underlying rate, so the futures contract itself has no convexity, while the FRA has positive convexity, likened to a small bond position. The resulting combined position is therefore long convexity.

It also connects that exposure to the rate difference between the instruments: the futures rate is slightly higher than the FRA rate, reflecting the price paid for the futures contract’s lack of the FRA’s convexity. The explanation is brief and qualitative; it gives no derivation or broader discussion of contract conventions, market conditions, or the size of the adjustment.

Key ideas

• A Eurodollar futures contract has a linear value response to changes in the underlying rate.
• A forward rate agreement has positive convexity.
• Longing the FRA and shorting the matching futures contract leaves the position long convexity.
• The futures rate’s premium over the FRA rate is presented as compensation for convexity.

Tags

# long fra and a short ed future with same fixing dates, is convexivity negative or positive?


# long fra and a short ed future with same fixing dates, is convexivity negative or positive?












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?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/25376

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.

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.