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

35 Pages Posted: 22 Nov 2022 Last revised: 19 Mar 2024

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Fayçal Drissi

University of Oxford - Oxford-Man Institute of Quantitative Finance

Marcello Monga

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: November 10, 2022

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.

Keywords: Decentralised Finance, Automated Market Making, Smart Contracts, Concentrated Liquidity, Algorithmic Trading, Market Making, Stochastic Optimal Control, Predictable Loss, Impermanent Loss

Suggested Citation

Cartea, Álvaro and Drissi, Fayçal and Monga, Marcello, Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision (November 10, 2022). Available at SSRN: https://ssrn.com/abstract=4273989 or http://dx.doi.org/10.2139/ssrn.4273989

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Fayçal Drissi (Contact Author)

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Marcello Monga

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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