IDEAS home Printed from
   My bibliography  Save this paper

Optimal Fees for Geometric Mean Market Makers


  • Alex Evans
  • Guillermo Angeris
  • Tarun Chitra


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,
  • Handle: RePEc:arx:papers:2104.00446

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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,
    2. Nassib Boueri, 2021. "G3M Impermanent Loss Dynamics," Papers 2108.06593,, revised Jun 2022.
    3. Andrea Barbon & Angelo Ranaldo, 2021. "On The Quality Of Cryptocurrency Markets: Centralized Versus Decentralized Exchanges," Papers 2112.07386,, revised Oct 2022.
    4. Raphael Auer & Bernhard Haslhofer & Stefan Kitzler & Pietro Saggese & Friedhelm Victor, 2023. "The Technology of Decentralized Finance (DeFi)," BIS Working Papers 1066, Bank for International Settlements.
    5. Lioba Heimbach & Ye Wang & Roger Wattenhofer, 2021. "Behavior of Liquidity Providers in Decentralized Exchanges," Papers 2105.13822,, revised Oct 2021.
    6. 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,, revised Dec 2022.
    7. Lioba Heimbach & Eric Schertenleib & Roger Wattenhofer, 2022. "Risks and Returns of Uniswap V3 Liquidity Providers," Papers 2205.08904,, revised Sep 2022.
    8. Dev Churiwala & Bhaskar Krishnamachari, 2022. "QLAMMP: A Q-Learning Agent for Optimizing Fees on Automated Market Making Protocols," Papers 2211.14977,
    9. Robin Fritsch & Roger Wattenhofer, 2021. "A Note on Optimal Fees for Constant Function Market Makers," Papers 2105.13510,
    10. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Monotonic Payoffs Without Oracles," Papers 2111.13740,

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Colin Atkinson & Emmeline Storey, 2010. "Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(4), pages 323-357.
    2. Dokuchaev, Nikolai, 2010. "Optimality of myopic strategies for multi-stock discrete time market with management costs," European Journal of Operational Research, Elsevier, vol. 200(2), pages 551-556, January.
    3. Cuoco, Domenico & Liu, Hong, 2000. "Optimal consumption of a divisible durable good," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 561-613, April.
    4. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    5. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148,, revised May 2015.
    6. Christoph Belak & Lukas Mich & Frank T. Seifried, 2019. "Optimal Investment for Retail Investors with Flooredand Capped Costs," Working Paper Series 2019-06, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    7. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    8. Yen-Lin Wu & Zhi-You Chen, 2017. "On the Solutions of the Problem for a Singular Ergodic Control," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 746-762, June.
    9. Min Dai & Zuo Quan Xu & Xun Yu Zhou, 2009. "Continuous-Time Markowitz's Model with Transaction Costs," Papers 0906.0678,
    10. Villena, Marcelo J. & Reus, Lorenzo, 2016. "On the strategic behavior of large investors: A mean-variance portfolio approach," European Journal of Operational Research, Elsevier, vol. 254(2), pages 679-688.
    11. Guodong Ding & Daniele Marazzina, 2021. "Effect of Labour Income on the Optimal Bankruptcy Problem," Papers 2106.15426,
    12. Jean-Pierre Fouque & Ruimeng Hu & Ronnie Sircar, 2021. "Sub- and Super-solution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Market," Papers 2106.11510,, revised Oct 2021.
    13. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Papers 1803.05819,, revised Jul 2018.
    14. Andrew B. Abel & Janice C. Eberly & Stavros Panageas, 2013. "Optimal Inattention to the Stock Market With Information Costs and Transactions Costs," Econometrica, Econometric Society, vol. 81(4), pages 1455-1481, July.
    15. Kan Huang & David Simchi-Levi & Miao Song, 2012. "Optimal Market-Making with Risk Aversion," Operations Research, INFORMS, vol. 60(3), pages 541-565, June.
    16. Baojun Bian & Xinfu Chen & Min Dai & Shuaijie Qian, 2021. "Penalty method for portfolio selection with capital gains tax," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1013-1055, July.
    17. Cayé, Thomas & Herdegen, Martin & Muhle-Karbe, Johannes, 2020. "Scaling limits of processes with fast nonlinear mean reversion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1994-2031.
    18. Hautsch, Nikolaus & Voigt, Stefan, 2019. "Large-scale portfolio allocation under transaction costs and model uncertainty," Journal of Econometrics, Elsevier, vol. 212(1), pages 221-240.
    19. Bayraktar, Erhan & Young, Virginia R., 2007. "Minimizing the probability of lifetime ruin under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 196-221, July.
    20. Christoph Belak & Lukas Mich & Frank T. Seifried, 2022. "Optimal investment for retail investors," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 555-594, April.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2104.00446. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.