Paper: arXiv 2502.04097

Abstract

This paper examines the relationship between impermanent loss (IL) and loss-versus-rebalancing (LVR) in automated market makers (AMMs). Our main focus is on statistical properties, the impact of fees, the role of block times, and, related to the latter, the continuous time limit. We find there are three relevant regimes: (i) very short times where LVR and IL are identical; (ii) intermediate time where LVR and IL show distinct distribution functions but are connected via the central limit theorem exhibiting the same expectation value; (iii) long time behavior where both the distribution functions and averages are distinct. Subsequently, we study how fees change this dynamics with a special focus on competing time scales like block times and ‘arbitrage times’.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper uses advanced stochastic calculus (Brownian motion, SDEs) and statistical theory (distributions, CLT) to model AMM dynamics, but relies on conceptual numerical simulations rather than real-world data or specific backtesting protocols.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Investigate IL vs. LVR in AMMs<br>featuring fees & block times"] --> B["Methodology:<br>Theoretical Modeling &<br>Statistical Analysis"]
  B --> C["Computational Processes:<br>Simulate Discrete Block<br>vs. Continuous Time Regimes"]
  B --> D["Data Inputs:<br>Market Volatility,<br>Fee Parameters, Block Times"]
  C --> E{"Analysis of<br>Time Regimes"}
  D --> E
  E --> F["Outcome 1:<br>Three distinct regimes identified:<br>Identical (Short), Dist. but same mean (Int.),<br>Different mean (Long)"]
  E --> G["Outcome 2:<br>Fee dynamics & Arbitrage<br>Time Scales analysis"]
  F & G --> H["Key Finding:<br>LVR & IL coincide at t=0,<br>diverge over time; Fees bridge<br>block time vs. continuous limits"]

Cited References (44)

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  2. An Economic Model of a Decentralized Exchange with Concentrated Liquidity (2023)
  3. Automated Market Making and Arbitrage Profits in the Presence of Fees — → 2305.14604
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  8. The need for fees at a dex: How increases in fees can increase dex trading volume (2022)
and 36 more
  1. Uniswap v1 Core (2018) — link
  2. Uniswap v2 Core (2020) — link
  3. Uniswap v3 Core (2021) — link
  4. Uniswap v4 Core [Draft] (2023) — link
  5. JOE v2.1 Liquidity Book (2022) — link
  6. ALGEBRA Ecosystem: Decentralized exchange (2022) — link
  7. Automatic market-making with dynamic peg (2021) — link
  8. Mooniswap by 1inch.exchange (2020) — link
  9. MEV capturing AMM (McAMM) (2022) — link
  10. Censorship Resistance in On-Chain Auctions (2023) — link
  11. Flash boys 2.0: Frontrunning in decentralized exchanges, miner extractable value, and consensus instability (2020)
  12. The Costs of Swapping on the Uniswap Protocol — → 2309.13648
  13. Credible decentralized exchange design via verifiable sequencing rules (2022) — link
  14. High-frequency trading on decentralized on-chain exchanges (2021)
  15. The centralizing effects of private order flow on proposer-builder separation (2023) — link
  16. Logarithmic markets coring rules for modular combinatorial information aggregation (2007)
  17. A practical liquidity-sensitive automated market maker (2013)
  18. Twitter thread (2023) — link
  19. CEX/DEX arbitrage, transaction fees, block times, and LP profits (2024) — link
  20. UniswapX (2023) — link
  21. Radical Markets: Uprooting Capitalism and Democracy for a Just Society (2018)
  22. Triangle Fees (2023) — link
  23. Predictable Losses of Liquidity Provision in Constant Function Markets and Concentrated Liquidity Markets (2023) — link
  24. Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision (2022)
  25. Automated Market Makers Designs Beyond Constant Functions (2023)
  26. Automated Market Making and Loss-Versus-Rebalancing (2024) — link
  27. Optimal Dynamic Fees for Blockchain Resources (2023) — link
  28. Multidimensional Blockchain Fees are (Essentially) Optimal (2024) — link
  29. A theoretical framework for dynamical fee choice in AMMs (2024) — link
  30. Role of fee choice in revenue generation of AMMs: A quantitative study (2024) — link
  31. Impermanent loss and loss-vs-rebalancing I: some statistical properties (2024) — link
  32. Optimal Fees for Geometric Mean Market Makers (2021) — link
  33. A Note on Optimal Fees for Constant Function Market Makers (2021) — link
  34. Arbitrageurs’ profits, LVR, and sandwich attacks: batch trading as an AMM design response (2024) — link
  35. Measuring Arbitrage Losses and Profitability of AMM Liquidity (2024) — link
  36. MEV Capture Through Time-Advantaged Arbitrage (2024) — link

2 of 44 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.