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

TL;DR

This paper models the wealth dynamics of liquidity providers in concentrated liquidity pools, deriving an optimal strategy that balances fees, losses, and risk, and validates it with real Uniswap v3 data.

Contribution

It introduces a closed-form optimal liquidity provision strategy considering stochastic rate drift and concentration risk, improving upon prior static models.

Findings

LPs often incur significant losses in practice.

The proposed strategy outperforms historical LP performance.

Optimal skewing of liquidity ranges increases fee revenue.

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.