BNT impermanent loss protection will pay much more than impermanent loss itself

In the previous articles, we analyzed the impermanent loss of uniswap V2 and the calculation formula of BNT impermanent loss protection in detail. If you make a comparison between these two cases, you will find that BNT impermanent loss protection will pay much more than impermanent loss itself.

We know that the impermanent loss calculation formula of xyk is:

The loss rate of BNT’s impermanent loss protection is:

Wherein P0 is the price of adding liquidity, and Pn is the price of removing liquidity.

As a result ILP(BNT%) <= IL(xyk), indicating that the BNT impermanent loss protection will pay much more than the impermanent loss itself. Based on the above formula, we further know that the range of IL(xyk) is (-100%, 0) and the range of ILP(BNT%) is (-∞,0). And also we can intuitively compare the specific numbers:

When the price drops 10%, IL(xyk)=-0.14%, ILP(BNT%)=-0.29%

When the price drops 20%, IL(xyk)=-0.62%, ILP(BNT%)=-1.39%

When the price drops by 50%, IL(xyk)=-5.72%, ILP(BNT%)=-17.1%

When the price drops 75%, IL(xyk)=-20%, ILP(BNT%)=-100%

When the price drops by 90%, IL(xyk)=-42.5%, ILP(BNT%)=-467%

It can be seen from the above that the risk of impermanent loss protection provided by BNT is far greater than the impermanent loss protection itself. This is mainly because impermanent loss protection is completely exposed to the price risk of single token. Even worse, whereas any liquidity removal will accrue the loss, but impermanent loss itself does not be accrued loss due to liquidity removal.