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Automated Market Making and Loss-Versus-Rebalancing

Author

Listed:
  • Jason Milionis
  • Ciamac C. Moallemi
  • Tim Roughgarden
  • Anthony Lee Zhang

Abstract

We consider the market microstructure of automated market makers (AMMs) from the perspective of liquidity providers (LPs). Our central contribution is a ``Black-Scholes formula for AMMs''. We identify the main adverse selection cost incurred by LPs, which we call ``loss-versus-rebalancing'' (LVR, pronounced ``lever''). LVR captures costs incurred by AMM LPs due to stale prices that are picked off by better informed arbitrageurs. We derive closed-form expressions for LVR applicable to all automated market makers. Our model is quantitatively realistic, matching actual LP returns empirically, and shows how CFMM protocols can be redesigned to reduce or eliminate LVR.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2208.06046
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    File URL: http://arxiv.org/pdf/2208.06046
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    References listed on IDEAS

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    1. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    2. Peter P. Carr & Robert A. Jarrow, 2008. "The Stop-Loss Start-Gain Paradox and Option Valuation: A new Decomposition into Intrinsic and Time Value," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 4, pages 61-84, World Scientific Publishing Co. Pte. Ltd..
    3. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
    4. Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806, arXiv.org, revised Jul 2020.
    5. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
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    Cited by:

    1. Abe Alexander & Lars Fritz, 2024. "Impermanent loss and loss-vs-rebalancing I: some statistical properties," Papers 2410.00854, arXiv.org, revised May 2025.
    2. Abe Alexander & Guillaume Lambert & Lars Fritz, 2025. "Impermanent loss and Loss-vs-Rebalancing II," Papers 2502.04097, arXiv.org, revised May 2025.
    3. Tobias Bitterli & Fabian Schar, 2023. "Decentralized Exchanges: The Profitability Frontier of Constant Product Market Makers," Papers 2302.05219, arXiv.org, revised Mar 2023.

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