Is the impermanent loss of Curve V2 as computable same as uniswap V3?

Curve V2 is the biggest competitor of uniswap V3. We know that the impermanent loss of uniswap V3 can be calculated mathematically, and some people want to know how to calculate the impermanent loss of curve V2, and even ask if curve V2 will have impermanent loss? As long as there are impermanent loss in multi-token market making, even in traditional order book market making, there also exits similar impermanent loss. Can the impermanent losses of curve, be also calculated mathematically? Let’s take a look at the changes in the proportion of WETH and the swap price at two different times in the curve protocol.

We found that the proportion of WETH is different even with an almost same swap price for the two times. Surprisingly, the asset ratio of liquidity providers does not necessarily return to the original point when the price returns to the original price. Therefore, there is no unique relationship between the ratio of curve’s asset and the swap price, and it is related to the path of price change. However, the value ratio of the tokens in the liquidity pool is fixed as long as the starting point and ending point of the price are the same for uniswap. When the price returns to the original point, the asset ratio must also return to the original point for uniswap. We know that the swap price of curve V2 is related to the price of the internal oracle. We can conclude that the price of the internal oracle is related to the price path, in other words, the price path is not necessarily the same even if the price is the same due to the uncertainty of the market trend. Therefore, the impermanent loss of curve V2 cannot be quantitatively calculated mathematically. The liquidity providers of curve V2 may suffer larger or smaller impermanent loss than uniswap under different market trends.