Convexity

Why someone would borrow liquidity.

When someone borrows AMM liquidity, they're not just borrowing the tokens but the Impermanent Loss exposure as well.

When someone liquidity provides to an AMM, they are selling their token upside potential for yield. Due to the curve equation, if the token moons, the LPer captures fewer profits. If the token dumps, the LPer captures all the losses, but during that time they'll also earn yield. The hope is that the yield outweighs the missed profits. Those missed profits are what people call Impermanent Loss or IL.

When someone borrows AMM liquidity the first thing they do is convert it into one of the two tokens in the token pair. Whichever token they convert the liquidity's assets into, the position is now back to getting all the upside exposure and downside exposure of the token. They're basically betting that those missed profits are actually greater than the yield an LP would earn. They're willing to pay the AMM the borrowed liquidity's missed swap yield plus a utilization based fee in return for capturing those missed profits for themselves. The best part of this type of position is that the borrower doesn't experience any downside from the token price dropping. If the token price goes down remember that the original LP position was willing to take on that risk anyways. So the borrower simply returns the token for no loss (besides any fees paid) if the price drops.

If this type of "borrowed" LP position sounds a lot like an option, that's because it is! They both operate off of the same financial principal of convexity which is used everyday throughout the global financial system. Without it, insurance, home loans, car loans, corporate bonds, and more would not exist.

If that was confusing, here's a step-by-step slideshow explaining convexity with an example.