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

ArXiv ID: 2309.08431 “View on arXiv”

Authors: Unknown

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: concentrated liquidity, automated market makers (AMM), liquidity provision, Uniswap v3, predictable losses (PL), Decentralized Finance (DeFi)

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper utilizes advanced stochastic control, continuous-time wealth dynamics, and closed-form derivations, indicating high mathematical complexity, while it validates the theoretical strategy with out-of-sample backtesting on real Uniswap v3 data, demonstrating strong empirical rigor.
  flowchart TD
    A["Research Goal:<br>Characterise LP Wealth Dynamics &<br>Develop Optimal Strategy for CL Pools"] --> B["Methodology Step 1:<br>Continuous-Time Wealth Modelling<br>(Fees, Holdings, Rebalancing Costs)"]
    B --> C["Methodology Step 2:<br>Derive Closed-Form Optimal Strategy<br>Width = f(Profitability, PL, Concentration Risk)"]
    C --> D["Methodology Step 3:<br>Stochastic Drift Extension<br>Optimal Skewing of Liquidity Range"]
    D --> E["Data Input & Validation:<br>Uniswap v3 Historical Data"]
    E --> F["Computational Process:<br>Backtesting & Out-of-Sample<br>Performance Comparison"]
    F --> G["Key Findings & Outcomes:<br>1. LPs historically traded at significant loss<br>2. Optimal strategy outperforms historical LPs"]