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Optimal Fees for Geometric Mean Market Makers

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  • Alex Evans
  • Guillermo Angeris
  • Tarun Chitra

Abstract

Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. These trades impose costs on Liquidity Providers (LPs) who supply reserves to CFMMs. Trading fees have been proposed as a mechanism for compensating LPs for arbitrage losses. However, large fees reduce the accuracy of the prices reported by CFMMs and can cause reserves to deviate from desirable asset compositions. CFMM designers are therefore faced with the problem of how to optimally select fees to attract liquidity. We develop a framework for determining the value to LPs of supplying liquidity to a CFMM with fees when the underlying process follows a general diffusion. Focusing on a popular class of CFMMs which we call Geometric Mean Market Makers (G3Ms), our approach also allows one to select optimal fees for maximizing LP value. We illustrate our methodology by showing that an LP with mean-variance utility will prefer a G3M over all alternative trading strategies as fees approach zero.

Suggested Citation

  • Alex Evans & Guillermo Angeris & Tarun Chitra, 2021. "Optimal Fees for Geometric Mean Market Makers," Papers 2104.00446, arXiv.org.
    • Handle: RePEc:arx:papers:2104.00446
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    References listed on IDEAS

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    1. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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    Cited by:

    1. Guillermo Angeris & Akshay Agrawal & Alex Evans & Tarun Chitra & Stephen Boyd, 2021. "Constant Function Market Makers: Multi-Asset Trades via Convex Optimization," Papers 2107.12484, arXiv.org.
    2. Nassib Boueri, 2021. "G3M Impermanent Loss Dynamics," Papers 2108.06593, arXiv.org, revised Jun 2022.
    3. Andrea Barbon & Angelo Ranaldo, 2021. "On The Quality Of Cryptocurrency Markets: Centralized Versus Decentralized Exchanges," Papers 2112.07386, arXiv.org, revised Jul 2023.
    4. Auer, Raphael & Haslhofer, Bernhard & Kitzler, Stefan & Saggese, Pietro & Friedhelm, Victor, 2023. "The Technology of Decentralized Finance (DeFi)," CEPR Discussion Papers 18038, C.E.P.R. Discussion Papers.
    5. Guillermo Angeris & Alex Evans & Tarun Chitra, 2023. "Replicating market makers," Digital Finance, Springer, vol. 5(2), pages 367-387, June.
    6. Lioba Heimbach & Ye Wang & Roger Wattenhofer, 2021. "Behavior of Liquidity Providers in Decentralized Exchanges," Papers 2105.13822, arXiv.org, revised Oct 2021.
    7. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    8. Lioba Heimbach & Eric Schertenleib & Roger Wattenhofer, 2022. "Risks and Returns of Uniswap V3 Liquidity Providers," Papers 2205.08904, arXiv.org, revised Sep 2022.
    9. Dev Churiwala & Bhaskar Krishnamachari, 2022. "QLAMMP: A Q-Learning Agent for Optimizing Fees on Automated Market Making Protocols," Papers 2211.14977, arXiv.org.
    10. Robin Fritsch & Roger Wattenhofer, 2021. "A Note on Optimal Fees for Constant Function Market Makers," Papers 2105.13510, arXiv.org.
    11. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Monotonic Payoffs Without Oracles," Papers 2111.13740, arXiv.org.

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