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Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision

Author

Listed:
  • 'Alvaro Cartea
  • Fayc{c}al Drissi
  • Marcello Monga

Abstract

Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP's liquidity range is determined by the profitability of the pool (provision fees minus gas fees), the predictable losses (PL) of the LP's position, and concentration risk. Concentration risk refers to the decrease in fee revenue if the marginal exchange rate (akin to the midprice in a limit order book) in the pool exits the LP's range of liquidity. When the drift in the marginal rate is stochastic, we show how to optimally skew the range of liquidity to increase fee revenue and profit from the expected changes in the marginal rate. Finally, we use Uniswap v3 data to show that, on average, LPs have traded at a significant loss, and to show that the out-of-sample performance of our strategy is superior to the historical performance of LPs in the pool we consider.

Suggested Citation

  • 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision," Papers 2309.08431, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2309.08431
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    File URL: http://arxiv.org/pdf/2309.08431
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    References listed on IDEAS

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    Cited by:

    1. Roger Lee, 2023. "All AMMs are CFMMs. All DeFi markets have invariants. A DeFi market is arbitrage-free if and only if it has an increasing invariant," Papers 2310.09782, arXiv.org, revised Dec 2023.
    2. Daniele Maria Di Nosse & Federico Gatta, 2024. "A Multi-step Approach for Minimizing Risk in Decentralized Exchanges," Papers 2406.07200, arXiv.org, revised Jun 2024.
    3. Erhan Bayraktar & Asaf Cohen & April Nellis, 2024. "DEX Specs: A Mean Field Approach to DeFi Currency Exchanges," Papers 2404.09090, arXiv.org.
    4. Robin Fritsch & Andrea Canidio, 2024. "Measuring Arbitrage Losses and Profitability of AMM Liquidity," Papers 2404.05803, arXiv.org, revised Apr 2024.

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