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Liquidity Provider Returns in Geometric Mean Markets

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  • Alex Evans

Abstract

Geometric mean market makers (G3Ms), such as Uniswap and Balancer, comprise a popular class of automated market makers (AMMs) defined by the following rule: the reserves of the AMM before and after each trade must have the same (weighted) geometric mean. This paper extends several results known for constant-weight G3Ms to the general case of G3Ms with time-varying and potentially stochastic weights. These results include the returns and no-arbitrage prices of liquidity pool (LP) shares that investors receive for supplying liquidity to G3Ms. Using these expressions, we show how to create G3Ms whose LP shares replicate the payoffs of financial derivatives. The resulting hedges are model-independent and exact for derivative contracts whose payoff functions satisfy an elasticity constraint. These strategies allow LP shares to replicate various trading strategies and financial contracts, including standard options. G3Ms are thus shown to be capable of recreating a variety of active trading strategies through passive positions in LP shares.

Suggested Citation

  • Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806, arXiv.org, revised Jul 2020.
  • Handle: RePEc:arx:papers:2006.08806
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    References listed on IDEAS

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    1. Jan Hendrik Witte, 2015. "Volatility Harvesting: Extracting Return from Randomness," Papers 1508.05241, arXiv.org, revised Nov 2015.
    2. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Citations

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    Cited by:

    1. Jiahua Xu & Krzysztof Paruch & Simon Cousaert & Yebo Feng, 2021. "SoK: Decentralized Exchanges (DEX) with Automated Market Maker (AMM) Protocols," Papers 2103.12732, arXiv.org, revised Dec 2022.
    2. Neelesh Tiruviluamala & Alexander Port & Erik Lewis, 2022. "A General Framework for Impermanent Loss in Automated Market Makers," Papers 2203.11352, arXiv.org.
    3. Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040, arXiv.org.
    4. 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.
    5. Sam M. Werner & Daniel Perez & Lewis Gudgeon & Ariah Klages-Mundt & Dominik Harz & William J. Knottenbelt, 2021. "SoK: Decentralized Finance (DeFi)," Papers 2101.08778, arXiv.org, revised Sep 2022.
    6. Andrea Barbon & Angelo Ranaldo, 2021. "On The Quality Of Cryptocurrency Markets: Centralized Versus Decentralized Exchanges," Papers 2112.07386, arXiv.org, revised Oct 2022.
    7. Johannes Rude Jensen & Mohsen Pourpouneh & Kurt Nielsen & Omri Ross, 2021. "The Homogenous Properties of Automated Market Makers," Papers 2105.02782, arXiv.org.
    8. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden & Anthony Lee Zhang, 2022. "Automated Market Making and Loss-Versus-Rebalancing," Papers 2208.06046, arXiv.org, revised Sep 2022.
    9. Lioba Heimbach & Ye Wang & Roger Wattenhofer, 2021. "Behavior of Liquidity Providers in Decentralized Exchanges," Papers 2105.13822, arXiv.org, revised Oct 2021.
    10. 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 Dec 2022.
    11. Lioba Heimbach & Eric Schertenleib & Roger Wattenhofer, 2022. "Risks and Returns of Uniswap V3 Liquidity Providers," Papers 2205.08904, arXiv.org, revised Sep 2022.
    12. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Market Makers," Papers 2103.14769, arXiv.org.
    13. Robin Fritsch & Roger Wattenhofer, 2021. "A Note on Optimal Fees for Constant Function Market Makers," Papers 2105.13510, arXiv.org.
    14. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Monotonic Payoffs Without Oracles," Papers 2111.13740, arXiv.org.

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