Impact of exchange fee rate parameter on impermanent loss of automatic market making systems in public blockchain networks

This article investigates the impact of the exchange fee parameter on impermanent loss of automated market making systems in public blockchain networks such as Uniswap, Balancer, and Curve. The research derives theoretical equations describing the dependence of impermanent loss on the fee rate, which allows for a deeper understanding of the mechanisms affecting the efficiency and sustainability of the considered decentralized finance protocols. Proposed analysis shows that taking into account the fees significantly affects the mechanics of the exchange, which in some cases can lead to impermanent gain of liquidity providers. The results are able to be useful both for practitioners and researchers in the field of decentralized finances seeking a deeper understanding of the dynamics of automated market making under continuously changing market conditions.