From TokenPost · · 1m 20s
AMM Liquidity Providers Trail Hold Strategy as Prices Shift
Liquidity providers can trail a hold strategy when token prices shift, per AMM models.
In brief
Liquidity providers can trail a hold strategy when token prices shift, per AMM models. Liquidity providers may lose value compared to holding assets if token prices change, even with increased pool value. Originally reported by TokenPost.
Impermanent loss definition
Impermanent loss compares an automated market maker position to holding original assets at a given time.
Constant-product AMM model
Traders swap directly against a token pool following x × y = k, where x and y are token amounts.
Price shift impact
If ether rises against usdc, the pool ends up with less ether and more usdc, changing the liquidity provider's position.
Simplified formula
The relative difference from holding is 2√r / (1 + r) - 1, where r is the new relative price divided by starting relative price.
Hypothetical example
One eth at $2,000 and 2,000 usdc initially worth $4,000; eth doubles to $4,000, pool holds 0.7071 eth and 2,828.43 usdc.
Price decline effect
A decline in relative price can also create a gap between the pool and holding, returning to zero if prices return to starting point.
Concentrated liquidity
Uniswap v3 and v4 let liquidity providers choose price intervals, earning fees while active within those ranges.
The bottom line
Liquidity providers may lose value compared to holding assets if token prices change, even with increased pool value.
