Measuring Arbitrage Losses and Profitability of AMM Liquidity

Abstract: This paper presents the results of a comprehensive empirical study of losses to arbitrageurs (following the formalization of loss-versus-rebalancing by [Milionis et al., 2022]) incurred by liquidity providers on automated market makers (AMMs). We show that those losses exceed the fees earned by liquidity providers across many of the largest AMM liquidity pools (on Uniswap). Remarkably, we also find that the Uniswap v2 pools are more profitable for passive LPs than their Uniswap v3 counterparts. We also investigate how arbitrage losses change with block times. As expected, arbitrage losses decrease when block production is faster. However, the rate of the decline varies significantly across different trading pairs. For instance, when comparing 100ms block times to Ethereum's current 12-second block times, the decrease in losses to arbitrageurs ranges between 20% to 70%, depending on the specific trading pair.

• The paper quantifies arbitrage losses by simulating LP positions across major Uniswap pools, comparing fee earnings with incurred losses.
• The analysis shows that faster block times reduce losses by 20-70%, underlining the significant impact of blockchain parameters on profitability.
• The study identifies that certain less-traded token pools allow LPs to earn fees exceeding arbitrage losses, indicating notable variability in AMM profitability.

Empirical Analysis of Arbitrage Losses and Profitability in AMM Liquidity Provision

This paper presents an empirical examination of arbitrage losses incurred by liquidity providers (LPs) in automated market makers (AMMs), focusing on their profitability. The study builds on the framework of Milionis et al. (2022), which introduces the concept of loss-versus-rebalancing (LVR), to evaluate whether the arbitrage losses exceed the fees accrued by LPs, and consequently affect their overall profitability. Employing extensive data from various Uniswap liquidity pools, the authors provide insights into arbitrage dynamics and liquidity provisioning in decentralized finance.

Key Findings

1. Widespread Arbitrage Losses in Major AMMs: The study reveals that arbitrage-induced losses often surpass the trading fees earned by LPs across a substantial number of large Uniswap pools. Specifically, passive LPs in Uniswap v2 pools generally experience higher profitability compared to those in Uniswap v3 pools. This finding underscores the latent risk dimensions associated with liquidity provisioning in prominent AMMs.
2. Impact of Block Times on Arbitrage Losses: A notable observation is the correlation between block production speed and arbitrage losses. Faster block times lead to reduced arbitrage losses; however, the magnitude of reduction varies among trading pairs. The decrease in losses ranges between 20% and 70% when comparing 100ms block times to Ethereum's typical 12-second block times. This highlights the intricate relation between network parameters and market dynamics.
3. Profitability Variability Among Less-Traded Tokens: Interestingly, the paper identifies certain less-traded token pools where LPs accrue fees exceeding arbitrage losses, suggesting opportunistic but inconsistent profitability angles for less visible market segments.

Discussion of Methodology

The authors simulate the arbitrage losses using external prices from Binance, assessing how a hypothetical AMM liquidity position would fare over a specific observation period. Fee returns are computed using historical data from significant Uniswap pools, while losses are deduced from hypothetical rebalancing actions against Binance's price records. In Uniswap v3, this empirical approach considers a full-range liquidity position, reflective of v2’s traditional setup.

Implications for AMM Design and Blockchain Parameterization

The findings on arbitrage losses versus trading fees call into question the rationale behind the substantial liquidity currently deployed in AMM pools, where fees often do not outweigh losses. This could have implications for the perceived sustainability of existing AMM designs and warrants a review of strategies to mitigate LVR. The marked profit advantage exhibited by Uniswap v2 indicates a potential flaw or feature in the concentrated liquidity mechanics of Uniswap v3, providing a basis for further innovation in AMM protocols.

Moreover, the nuanced insights into how block times affect arbitrage provide actionable intelligence for blockchain design. Particularly in scenarios where minimizing arbitrage is essential, such as enabling fairer trading conditions or aligning better with regulatory requirements, these findings could inform adjustments to block time intervals.

Conclusion and Future Directions

This paper significantly contributes to understanding the financial dynamics of LPs in AMMs by empirically quantifying the arbitrage phenomenon and fee structures across differing AMM models. Future research could explore the competitive interplay between active and passive LP strategies within variable block time environments, further refining the operational models of both AMM and LP profitability. There's ample scope for the development of AMM protocols that incorporate features such as dynamic fee models or adaptive liquidity provisioning to curtail losses and enhance overall system health.