Generalizing Impermanent Loss on Decentralized Exchanges with Constant Function Market Makers

TL;DR

This paper introduces a unified framework to analyze impermanent loss across various constant function market makers in decentralized exchanges, accounting for fees and concentrated liquidity, aiding liquidity providers in risk assessment.

Contribution

It generalizes impermanent loss analysis for any constant function market maker, incorporating fee structures and liquidity concentration, which was previously fragmented across different models.

Findings

Framework successfully applied to BalancerV2 and UniswapV3.

Identifies conditions where liquidity provisioning is profitable.

Provides insights into fee impact on impermanent loss.

Abstract

Liquidity providers are essential for the function of decentralized exchanges to ensure liquidity takers can be guaranteed a counterparty for their trades. However, liquidity providers investing in liquidity pools face many risks, the most prominent of which is impermanent loss. Currently, analysis of this metric is difficult to conduct due to different market maker algorithms, fee structures and concentrated liquidity dynamics across the various exchanges. To this end, we provide a framework to generalize impermanent loss for multiple asset pools obeying any constant function market maker with optional concentrated liquidity. We also discuss how pool fees fit into the framework, and identify the condition for which liquidity provisioning becomes profitable when earnings from trading fees exceed impermanent loss. Finally, we demonstrate the utility and generalizability of this framework with simulations in BalancerV2 and UniswapV3.