Liquidity Fragmentation or Optimization? Analyzing Automated Market Makers Across Ethereum and Rollups (2410.10324v3)

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.

• The paper reveals that current AMM liquidity allocation leads to suboptimal LP returns, as oversubscribed Ethereum pools yield less than staking.
• The paper applies Lagrangian optimization to model liquidity distribution across Ethereum and L2 rollups, demonstrating yield convergence with staking rewards.
• The paper's empirical analysis shows that L2 rollups like Optimism and Arbitrum provide superior returns despite emerging security concerns.

Suboptimality in Automated Market Makers on Layer-2 Blockchains

The paper "Harvesting Layer-2 Yield: Suboptimality in Automated Market Makers" by Gogol et al. provides a detailed empirical and theoretical analysis of liquidity allocation strategies for Automated Market Makers (AMMs) across Ethereum and Layer-2 (L2) rollups. The paper identifies inefficiencies in Liquidity Providers' (LPs) current allocation strategies and proposes a method to optimize returns through Lagrangian optimization.

Key Contributions and Findings

1. Oversubscription on Ethereum: The research highlights that AMM liquidity pools on Ethereum are oversubscribed, often yielding returns lower than staking ETH. This suggests that LPs could achieve higher rewards by reallocating their liquidity to L2s or directly staking.
2. Lagrangian Optimization: The authors utilize Lagrangian optimization to develop a model that maximizes LP rewards by allocating liquidity across staking and AMM pools on Ethereum and its rollups. The derived allocation strategy shows that returns from AMM liquidity provisions should converge to the staking rate. This convergence implies that in an ideal equilibrium, returns from liquidity provision mirror those of staking rewards.
3. Impact of Layer-2 Rollups: With Ethereum's high transaction costs and slow block times, L2 rollups offer advantageous alternatives with significant reductions in fees and block production times. Rollups such as Arbitrum, Optimism, and ZKsync allow for more frequent adjustments to liquidity positions, especially beneficial for Concentrated Liquidity Market Makers (CLMM) like Uniswap (v3).
4. Empirical Analysis: The empirical data drawn from WETH-USDC pools on Uniswap v3 across Ethereum and L2s supports the theoretical findings. The paper shows that although Ethereum pools have higher trading volumes, they often do not compensate LPs adequately compared to their L2 counterparts. Notably, the pools on Optimism and Arbitrum exhibit significantly higher potential returns.
5. Security Considerations: Despite better returns on L2s, LPs may have reservations due to security concerns, such as the centralized nature of L2 sequencers and risks inherent in new technologies. This apprehension could contribute to the underutilization of L2s for liquidity provision.

Implications and Future Developments

The findings underscore the need for LPs to reassess their capital allocation strategies to enhance profitability, particularly by incorporating L2 rollups into their portfolios. As the DeFi ecosystem evolves, LPs who adapt to these more efficient liquidity environments could see improved yield outcomes.

Future advancements in L2 technologies and the potential resolution of related security issues could further facilitate the transition of liquidity from Ethereum mainnet to rollups. This shift might not only optimize LP returns but also contribute to a more efficient decentralized financial market.

Conclusion

This paper provides valuable insights into the liquidity dynamics within AMMs, emphasizing the importance of optimal liquidity allocation across Ethereum and L2s. By leveraging theoretical and empirical approaches, the paper offers a roadmap for LPs to enhance their yield potential, while also highlighting critical challenges and considerations in the current DeFi landscape.