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X3 protocol hedges impermanent loss by splitting uniswap V3 LP into a long leveraged token and a short leveraged token

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X3 protocol hedges impermanent loss by splitting uniswap V3 LP into a long leveraged token and a short leveraged token

In the previous article, we deduced the impermanence loss of uniswap V3 in detail, so what are the characteristics of the LP token of uniswap V3? Today we will study this problem, Let’s take ETH-USDT as an example, the reserve amount of ETH is x, and the reserve amount of USDT is y. Starting with the reserves equation for V3 as followed:

V3 LP satisfies:

https://preview.redd.it/hbwfryq8eh691.png?252&format=png&auto=webp&s=78bc6f6ec3a08164352aac9b3298755374fd189f

Then the price satisfies:

https://preview.redd.it/w0rfw36aeh691.png?586&format=png&auto=webp&s=4a0df9f4b388278dd48a8560f9c3bbded5bc91bb

Obtained from the above solution:

https://preview.redd.it/971mc0jbeh691.png?167&format=png&auto=webp&s=e625c7b081d40bc080bb7d21210341e8b46f2b9c

The amount of USDT part at P:

https://preview.redd.it/n5924fjceh691.png?653&format=png&auto=webp&s=713bdbc5b2256a97f76a2982eb401c44c4e5f8a4

The amount of USDT part at Pb:

https://preview.redd.it/vv81refdeh691.png?650&format=png&auto=webp&s=0a3658b951ec8fedbd827e9c49c2c55248da9d15

The amount of USDT part at Pa:

https://preview.redd.it/x6cwkxteeh691.png?275&format=png&auto=webp&s=c69f90dff4f795bd5dcece7ed0fd69c890b7aced

Assuming USDT value of one contract size is

https://preview.redd.it/2r2wpgwfeh691.png?115&format=png&auto=webp&s=4133d3f720e025e36b76b13500c0d8a6ee26cfd9

The amount of contracts at Pb:

https://preview.redd.it/cwprcsaheh691.png?262&format=png&auto=webp&s=edb5e27c2e0333df8da4822e9bc84427e198fb77

The amount of contracts at Pb for virtual reseve is L, so the leverage of USDT part at Pb:

https://preview.redd.it/vnrsxwdieh691.png?311&format=png&auto=webp&s=00734dfdb8f1805f4f04aa6eefa1c105ac4ea067

the leverage of USDT part at P:

https://preview.redd.it/vvi7zbgjeh691.png?259&format=png&auto=webp&s=981671cb8307f41955c8a438c8659d2daceb513a

Therefore, the usdt part of V3 LP is equivalent to a long leveraged ETH asset with an initial leverage of m0.

Similarly, we can also deduce that the ETH part of V3 LP is a short ETH leveraged asset with an initial leverage ratio of m0:

https://preview.redd.it/i7v3rzlleh691.png?317&format=png&auto=webp&s=7c7338ce34c7612f21a7c05ba5bfb2b5fc8610ed

To hedge impermanent loss, X3 protocol splits uniswap V3 LP into the above long leveraged token and short leveraged token to sell to the leveraged traders.It will be a win-win for traders obtaining leveraged trading opportunities without funding fees and farmers earning LP fees with no impermanent loss risk.

https://x3finance.medium.com/x3-protocol-hedges-impermanent-loss-by-splitting-uniswap-v3-lp-into-a-long-leveraged-token-and-a-1f2adc599405

submitted by /u/x3finance
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