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The Homogenous Properties of Automated Market Makers


  • Johannes Rude Jensen
  • Mohsen Pourpouneh
  • Kurt Nielsen
  • Omri Ross


Automated market makers (AMM) have grown to obtain significant market share within the cryptocurrency ecosystem, resulting in a proliferation of new products pursuing exotic strategies for horizontal differentiation. Yet, their theoretical properties are curiously homogeneous when a set of basic assumptions are met. In this paper, we start by presenting a universal approach to deriving a formula for liquidity provisioning for AMMs. Next, we show that the constant function market maker and token swap market maker models are theoretically equivalent when liquidity reserves are uniform. Proceeding with an examination of AMM market microstructure, we show how non-linear price effect translates into slippage for traders and impermanent losses for liquidity providers. We proceed by showing how impermanent losses are a function of both volatility and market depth and discuss the implications of these findings within the context of the literature.

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  • Johannes Rude Jensen & Mohsen Pourpouneh & Kurt Nielsen & Omri Ross, 2021. "The Homogenous Properties of Automated Market Makers," Papers 2105.02782,
  • Handle: RePEc:arx:papers:2105.02782

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    References listed on IDEAS

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    2. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001,, revised Jun 2020.
    3. Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040,
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    10. Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806,, revised Jul 2020.
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