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arXiv · 2501.12583

Chasing price drains liquidity

Yizhou Cao·Yepeng Ding·Ruichao Jiang·Long Wen
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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.

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Yizhou Cao, Yepeng Ding, Ruichao Jiang, Long Wen. 2025-01-22. Chasing price drains liquidity. https://arxiv.org/abs/2501.12583

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