Chasing price drains liquidity

TL;DR

This paper analyzes how liquidity in Uniswap v3-style AMMs decays when liquidity providers attempt to track price movements, and proposes strategies to counteract this decay under different market assumptions.

Contribution

It provides a theoretical proof of liquidity decay under price tracking strategies and introduces a new approach to increase liquidity without relying on fees.

Findings

Liquidity decays exponentially when tracking price in GBM models.

Price mean reversion to a CEX does not prevent liquidity decay.

Proposed strategy can increase liquidity without fees.

Abstract

Assuming that the price in a Uniswap v3 style Automated Market Maker (AMM) follows a Geometric Brownian Motion (GBM), we prove that the strategy that adjusts the position of liquidity to track the current price leads to a deterministic and exponentially fast decay of liquidity. Next, assuming that there is a Centralized Exchange (CEX), in which the price follows a GBM and the AMM price mean reverts to the CEX price, we show numerically that the same strategy still leads to decay. Last, we propose a strategy that increases the liquidity even without compounding fees earned through liquidity provision.