Impermanent Loss and Gain of Automated Market Maker Smart Contracts

Smart contract is an important building block of blockchain. Automated market makers are working without an order book, and they determine the price of assets automatically. It is reported that he automated market makers have the impermanent loss, which causes financial damage to liquidity providers. Impermanent loss makes the liquidity providers hesitant to deposit assets in the liquidity pool. Therefore, their participation incentive from liquidity provision should be anticipated by automatic market makers inherently. However, the existence of impermanent gain has never been reported. Impermanent gain is important to attract liquidity providers without giving compensation incentives. This study shows that for some automated market makers, impermanent gain coexists with impermanent loss. Examples showing the coexistence and conditions are provided.