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Impermanent loss and Loss-vs-Rebalancing II

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  • Abe Alexander
  • Guillaume Lambert
  • Lars Fritz

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'.

Suggested Citation

  • Abe Alexander & Guillaume Lambert & Lars Fritz, 2025. "Impermanent loss and Loss-vs-Rebalancing II," Papers 2502.04097, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2502.04097
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    References listed on IDEAS

    as
    1. Abe Alexander & Lars Fritz, 2024. "A theoretical framework for dynamical fee choice in AMMs," Papers 2404.03976, arXiv.org, revised Jun 2024.
    2. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden & Anthony Lee Zhang, 2022. "Automated Market Making and Loss-Versus-Rebalancing," Papers 2208.06046, arXiv.org, revised May 2024.
    3. Robin Hanson, 2007. "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation," Journal of Prediction Markets, University of Buckingham Press, vol. 1(1), pages 3-15, February.
    4. Andrea Canidio & Robin Fritsch, 2023. "Arbitrageurs' profits, LVR, and sandwich attacks: batch trading as an AMM design response," Papers 2307.02074, arXiv.org, revised Feb 2025.
    5. Abe Alexander & Lars Fritz, 2024. "Impermanent loss and loss-vs-rebalancing I: some statistical properties," Papers 2410.00854, arXiv.org.
    6. Abe Alexander & Jesse Moestaredjo & Mart Heuvelmans & Lars Fritz, 2024. "Role of fee choice in revenue generation of AMMs: A quantitative study," Papers 2406.12417, arXiv.org.
    7. Alex Evans & Guillermo Angeris & Tarun Chitra, 2021. "Optimal Fees for Geometric Mean Market Makers," Papers 2104.00446, arXiv.org.
    8. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Automated Market Making and Arbitrage Profits in the Presence of Fees," Papers 2305.14604, arXiv.org.
    9. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
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