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:

Then the price satisfies:

Obtained from the above solution:

The amount of USDT part at P:

The amount of USDT part at Pb:

The amount of USDT part at Pa:

Assuming USDT value of one contract size is

The amount of contracts at Pb:

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

the leverage of USDT part at P:

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：

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.