G3M Impermanent Loss Dynamics

TL;DR

This paper analyzes the dynamics of impermanent loss in Geometric Mean Market Makers like Uniswap, combining theoretical bounds with empirical data, and explores how concentrated liquidity impacts impermanent loss and arbitrage opportunities.

Contribution

It establishes non-arbitrage bounds for G3M wealth processes, analyzes empirical ROI data considering impermanent loss, and demonstrates how UniswapV3's concentrated liquidity can be replicated and hedged.

Findings

Median pool ROI is near zero after impermanent loss.

High dispersion and autocorrelation in pool ROI suggest inefficiencies.

UniswapV3's concentrated liquidity can be simulated with V2 pools and hedging.

Abstract

Geometric Mean Market Makers (G3M) such as Uniswap, Sushiswap or Balancer are key building blocks of the nascent Decentralised Finance system. We establish non-arbitrage bounds for the wealth process of such Automated Market Makers in the presence of transaction fees and highlight the dynamic of their so-called Impermanent Losses, which are incurred due to negative convexity and essentially void the benefits of portfolio diversification within G3Ms. We then turn to empirical data to establish if transaction fee income has historically been high enough to offset Impermanent Losses and allow G3M investments to outperform their continually rebalanced constant-mix portfolio counterparts. It appears that the median liquidity pool had a net nil ROI when taking Impermanent Losses into account. The cross-sectional dispersion of ROI has however been high and the pool net ROI ranking has been significantly autocorrelated for several weeks. This suggests that G3M pools are not yet efficiently arbitraged as agents may access ex-ante knowledge of which G3M pools are likely to be far better investment proposals than others. We finally focus on the UniswapV3 protocol, which introduced the notion of concentrated liquidity ranges and show that such a position can be replicated by leveraging a classic UniswapV2 pool while simultaneously hedging part of the underlying token price exposition. As such, the herein described Impermanent Loss dynamics also apply to UniswapV3 pools.