Impermanent Loss Conditions: An Analysis of Decentralized Exchange Platforms

Abstract

Decentralized exchanges are widely-used platforms for trading cryptoassets. The most fundamental and openly-accessible type of decentralized exchange is based on automated market makers (AMMs), where traders transact against asset reserves managed by smart contracts. These assets are provided by liquidity providers in exchange for a fee. Unlike traditional markets, AMMs pool liquidity from numerous retail participants, and prices are determined by publicly-known mathematical functions. Static analysis shows that small price changes in one of the assets result in losses for passive liquidity providers due to arbitrage trading. However, most existing literature focuses on static effects and does not adequately address the dynamic impact of fees from arbitrageurs over time. Therefore, we investigate the impermanent loss problem in a dynamic setting using Monte Carlo simulations. We contribute to the literature by demonstrating that arbitrage fees may constitute the primary revenue driver for passive liquidity providers. Arbitrageurs exert opposing effects on profitability: they impose rebalancing costs but generate fee revenue. For passive liquidity providers, rebalancing costs are independent of the number of arbitrage trades, while fees are directly proportional to trading volume. Consequently, increased arbitrage activity enhances the profitability of passive liquidity providers. Moreover, we show that this effect is amplified when trading barriers are low and arbitrage competition is intense. As a result, in the absence of barriers,arbitrageurs emerge as the disproportionately predominant source of fee revenue.