From Impermanent Loss to Sustainable Gain: Quantifying Profitability Zones for Liquidity Providers on DEX
This study addresses the lack of a quantitative framework for analyzing impermanent loss risk faced by liquidity providers in automated market maker (AMM) protocols and the associated profit distribution with arbitrageurs. By constructing an empirical pool–based mathematical model that integrates on-chain data and probabilistic analysis, this work is the first to characterize the symbiotic profit region shared by both parties, derive their joint profit bounds, and quantify the probability and duration of entering the impermanent loss regime. Key contributions include a target-probability–based method for computing the lower bound of trading fees, along with estimates of the expected number of blocks before impermanent loss occurs and the minimum fee rate required to sustain positive returns. These results provide theoretical foundations for incentive alignment and market stability in AMM-based decentralized exchanges.