Once we do LP, impermanent loss (LP) is pretty much guaranteed, it’s not a matter of if, but how much.
There’s a vivid breakdown for much better understanding:
Scenerio 1:
- Suppose we got a pool with initial liquidity of 100DAI and 1ETH
- now the
LP's position valueis 200DAI (100DAI+1ETH)
- now the
- ETH goes up
- The bot keeps arbitraging until the price gap disappears, as a result, the amount of ETH in the pool had dropped from 1 to 0.83
- x·y=k, 100·1=120*0.83
- PriceOfEth=120/0.83=144.58
- Now,
LP's position valuegot- 120DAI + 0.83* 144.58DAI= 240DAI
- we earned 240DAI-200DAI=40DAI
- But, the position of not being LP’s value is 4DAI more:
- 100DAI + 1*144.58DAI=244.58DAI
- The bot keeps arbitraging until the price gap disappears, as a result, the amount of ETH in the pool had dropped from 1 to 0.83
Conclusion:
If ETH rises, it’s profitable but you don’t capture the full gain.
Scenario 2:
- Suppose we got a pool with initial liquidity of 100DAI and 1ETH
- now the
LP's position valueis 200DAI (100DAI+1ETH)
- now the
- ETH drops
- The bot keeps arbitraging until the price gap disappears, as a result, the amount of ETH in the pool had risen from 1 to 1.25
- x·y=k, 100·1=80*1.25
- PriceOfEth=80/1.25=64
- Now,
LP's position valuegot:- 80DAI + 1.25*64DAI=160DAI
- we lost 200DAI-160DAI=40DAI
- But, the position of not being LP’s value:
- 100DAI + 64*1DAI = 164DAI
- The bot keeps arbitraging until the price gap disappears, as a result, the amount of ETH in the pool had risen from 1 to 1.25
Conclusion:
If ETH drops, we all lose money no matter whether you’re an LP or not, LP lose a bit more.