Paper: arXiv 2301.06831
Authors: Rohan Tangri, Peter Yatsyshin, Elisabeth A. Duijnstee, Danilo Mandic
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.
Complexity vs Empirical Score
- Math Complexity: 6.5/10
- Empirical Rigor: 5.5/10
- Quadrant: Holy Grail — high math complexity, high empirical rigor
Why this score: The paper presents a comprehensive theoretical framework that generalizes impermanent loss across arbitrary Constant Function Market Makers (CFMMs) and concentrated liquidity profiles. Its mathematical formulation is elegant and robust, accompanied by simulation-based validations on key protocols like Uniswap v3 and Balancer v2.
Research Flowchart
flowchart TD
A[Goal: Generalize Impermanent Loss IL for Any CFMM] --> B[Input Parameters: Pool Weights, Asset Prices, Fee Rates, Liquidity Ranges]
B --> C[Develop Mathematical Framework for IL & Fee Yields]
C --> D[Derive Profitability Condition: Fee Earnings > IL]
D --> E[Simulate & Validate Framework on BalancerV2 & UniswapV3]
E --> F[Outcome: Unified IL Model for Arbitrary CFMMs & Concentrated Liquidity]