I don't think that's necessarily true. Say Cub got listed on Coinbase. It would be very possible for the price of Cub to go up or down completely independent of what was trading in the LPs. If the price goes up, arbitrageurs would come in and equal out the LP's again with the new price so they matched. That's the part I'm not sure about. How do they do that? The arbitrage they make is what becomes the LP holders impermanent loss plus transaction fees. In other words, the arbitrageurs "skim" a little of the profit out of the LPs so the LP holders don't make as much. I agree, the asset won't go to $20 with the LP asset staying at $10. Arbitrageurs will come in way before that to even it up again. I was just using round numbers to make it easier to do the math.
To offset impermanent loss, many LPs incentivize farmers by offers rewards. In our case those rewards are Cub. The extra Cub farmed protects the LP holders from impermanent loss due to the price fluctuating on one or both assets if you're using something other than a stablecoin.
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