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Automated Market Making and Loss-Versus-Rebalancing

Author

Listed:
  • Jason Milionis
  • Ciamac C. Moallemi
  • Tim Roughgarden
  • Anthony Lee Zhang

Abstract

Automated market making (AMM) protocols such as Uniswap have recently emerged as an alternative to the most common market structure for electronic trading, the limit order book. Relative to limit order books, AMMs are both more computationally efficient and do not require the participation of active market making intermediaries. As such, AMMs have emerged as the dominant market mechanism for trust-less decentralized exchanges (DEXs). We develop a model the underlying economics of AMMs from the perspective of their passive liquidity providers (LPs). Our central contribution is a "Black-Scholes formula for AMMs". Like the Black-Scholes formula, we consider the return to LPs once market risk has been hedged. We identify the main adverse selection cost incurred by LPs, which we call "loss-versus-rebalancing" (LVR, pronounced "lever"). LVR captures costs incurred by AMM LPs due to stale prices that are picked off by better informed arbitrageurs. In a continuous time Black-Scholes setting, we are able to derive closed-form expressions for this adverse selection cost, for all automated market makers, including constant function market makers and those featuring concentrated liquidity (e.g., Uniswap v3). Qualitatively, we highlight the main forces that drive AMM LP returns, including asset characteristics (volatility) and AMM characteristics (curvature/marginal liquidity). Quantitatively, we illustrate how our model's expressions for LP returns match actual LP returns for the Uniswap v2 WETH-USDC trading pair. Our model provides tradable insight into both the ex ante and ex post assessment of AMM LP investment decisions. LVR can also inform the design of the next generation of DEX market mechanisms -- in fact, in the short time since our work has been released, "LVR mitigation" has already emerged as the dominant challenge among practitioners in the AMM protocol designer community.

Suggested Citation

  • Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden & Anthony Lee Zhang, 2022. "Automated Market Making and Loss-Versus-Rebalancing," Papers 2208.06046, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2208.06046
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    References listed on IDEAS

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    1. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    2. Peter P. Carr & Robert A. Jarrow, 2008. "The Stop-Loss Start-Gain Paradox and Option Valuation: A new Decomposition into Intrinsic and Time Value," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 4, pages 61-84, World Scientific Publishing Co. Pte. Ltd..
    3. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
    4. Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806, arXiv.org, revised Jul 2020.
    5. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
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    Cited by:

    1. Tobias Bitterli & Fabian Schar, 2023. "Decentralized Exchanges: The Profitability Frontier of Constant Product Market Makers," Papers 2302.05219, arXiv.org, revised Mar 2023.

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