AMM Design and the Transmission of Impermanent Loss: Evidence from a Passive LP

This paper examines whether changes in impermanent loss (IL) are altered when the automated market maker (AMM) architecture changes. Within a framework between AMMs, we address this question by imposing a common benchmark of the passive liquidity provider (LP). We evaluate AMMs architectures active on the Ethereum mainnet and retain only the two that simultaneously satisfy all the requirements: Uniswap v2 and Uniswap v3. We then distinguish between the pool's accumulated state and price innovations to assess how both components explain future IL. The results show that Uniswap v2 and Uniswap v3 exhibit nearly identical IL transmission profiles, with differences of less than 5%. We also observed that the fee level in Uniswap v3 is not a neutral parameter. Pools with a 0.05% fee reduce the average contribution to price shocks by up to 30% in volatile-stable pools, while increasing it in volatile-volatile pairs. This difference persists even in the face of extreme shocks. Our results demonstrate that, for a passive LP in Uniswap V2 and V3, the relevant dimension of liquidity risk is not the invariant function chosen by the protocol, but rather the pair composition and the fee level at which liquidity is concentrated. JEL Classification: C22 , G15 , G23 , G32 , O33