Liquidity Fragmentation or Optimization? Analyzing Automated Market Makers Across Ethereum and Rollups
Krzysztof Gogol, Manvir Schneider, Claudio Tessone, Benjamin Livshits
TL;DR
The paper addresses whether liquidity fragmentation arises from AMMs across Ethereum and Layer-2 rollups and develops a theoretical framework to optimize cross-chain liquidity allocation with staking as the reference rate. It employs Lagrangian optimization to derive closed-form optimal allocations against a staking benchmark and empirically calibrates an elasticity-based volume model using on-chain data from WETH-USDC pools across Ethereum and rollups. Key findings show that AMM liquidity returns converge to the staking rate in equilibrium, TVL has mixed elasticity with volume on established chains and positive elasticity on newer chains, and Ethereum pools are often oversubscribed and less profitable than staking, suggesting reallocating a majority of Ethereum liquidity to L2s could maximize LP rewards. The results have practical implications for liquidity provisioning strategies and contribute to the liquidity fragmentation debate by quantifying cross-chain liquidity dynamics and staking opportunities.
Abstract
Layer-2 (L2) blockchains inherit Ethereums security guarantees while reducing gas fees. As a result, they are gaining traction among traders at Automated Market Makers (AMMs), sparking debate over whether they contribute to liquidity fragmentation of Ethereum. Our research suggests that such fragmentation is not currently occurring. However, it could emerge in the future, particularly if Liquidity Providers (LPs) recognize the higher returns available on L2s. Using Lagrangian optimization, we develop a model for optimal liquidity allocation across AMMs on Ethereum and its L2s, using staking as a benchmark. We show that, in equilibrium, AMM liquidity provision returns converge to this reference rate. Additionally, we measure the elasticity of trading volume with respect to Total Value Locked (TVL) in AMMs and find that, on well-established blockchains, an increase in TVL does not necessarily lead to higher trading volume. Finally, our empirical findings reveal that Ethereums liquidity pools are oversubscribed compared to those on L2s and often yield lower returns than staking Ether. LPs could maximize their rewards by reallocating more than two-thirds of their liquidity to L2s and staking.