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When does the tail wag the dog? Curvature and market making

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Listed:
  • Guillermo Angeris
  • Alex Evans
  • Tarun Chitra

Abstract

Liquidity and trading activity on constant function market makers (CFMMs) such as Uniswap, Curve, and Balancer has grown significantly in the second half of 2020. Much of the growth of these protocols has been driven by incentivized pools or 'yield farming', which reward participants in crypto assets for providing liquidity to CFMMs. As a result, CFMMs and associated protocols, which were historically very small markets, now constitute the most liquid trading venues for a large number of crypto assets. But what does it mean for a CFMM to be the most liquid market? In this paper, we propose a basic definition of price sensitivity and liquidity. We show that this definition is tightly related to the curvature of a CFMM's trading function and can be used to explain a number of heuristic results. For example, we show that low-curvature markets are good for coins whose market value is approximately fixed and that high-curvature markets are better for liquidity providers when traders have an informational edge. Additionally, the results can also be used to model interacting markets and explain the rise of incentivized liquidity provision, also known as 'yield farming.'

Suggested Citation

  • Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040, arXiv.org.
    • Handle: RePEc:arx:papers:2012.08040
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Neelesh Tiruviluamala & Alexander Port & Erik Lewis, 2022. "A General Framework for Impermanent Loss in Automated Market Makers," Papers 2203.11352, arXiv.org.
    2. 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.
    3. 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.
    4. Ariah Klages-Mundt & Steffen Schuldenzucker, 2022. "Designing Autonomous Markets for Stablecoin Monetary Policy," Papers 2212.12398, arXiv.org.
    5. Johannes Rude Jensen & Mohsen Pourpouneh & Kurt Nielsen & Omri Ross, 2021. "The Homogenous Properties of Automated Market Makers," Papers 2105.02782, arXiv.org.
    6. Tobias Bitterli & Fabian Schar, 2023. "Decentralized Exchanges: The Profitability Frontier of Constant Product Market Makers," Papers 2302.05219, arXiv.org, revised Mar 2023.
    7. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Market Makers," Papers 2103.14769, arXiv.org.
    8. Robin Fritsch & Roger Wattenhofer, 2021. "A Note on Optimal Fees for Constant Function Market Makers," Papers 2105.13510, arXiv.org.
    9. Robin Fritsch, 2021. "Concentrated Liquidity in Automated Market Makers," Papers 2110.01368, arXiv.org.
    10. de Andrés, Pablo & Arroyo, David & Correia, Ricardo & Rezola, Alvaro, 2022. "Challenges of the market for initial coin offerings," International Review of Financial Analysis, Elsevier, vol. 79(C).

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