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Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions

Author

Listed:
  • Philippe Bergault

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Louis Bertucci
  • David Bouba
  • Olivier Guéant

Abstract

We analyze the performance of Liquidity Providers (LPs) providing liquidity to different types of Automated Market Makers (AMMs). This analysis is carried out using a mean / standard deviation viewpoint \`a la Markowitz, though based on the PnL of LPs compared to that of agents holding coins outside of AMMs. We show that LPs tend to perform poorly in a wide variety of CFMMs under realistic market conditions. We then explore an alternative AMM design in which an oracle feeds the current market exchange rate to the AMM which then quotes a bid/ask spread. This allows us to define an efficient frontier for the performance of LPs in an idealized world with perfect information and to show that the smart use of oracles greatly improves LPs' risk / return profile, even in the case of a lagged oracle.

Suggested Citation

  • Philippe Bergault & Louis Bertucci & David Bouba & Olivier Guéant, 2023. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Working Papers hal-03941578, HAL.
    • Handle: RePEc:hal:wpaper:hal-03941578
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    Cited by:

    1. Alexander Lipton & Vladimir Lucic & Artur Sepp, 2024. "Unified Approach for Hedging Impermanent Loss of Liquidity Provision," Papers 2407.05146, arXiv.org.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E49 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Other
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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