Model-free Hedging of Impermanent Loss in Geometric Mean Market Makers

Paper: arXiv 2303.11118

Authors: Masaaki Fukasawa, Basile Maire, Marcus Wunsch

Abstract

We consider Geometric Mean Market Makers – a special type of Decentralized Exchange – with two types of users: liquidity takers and arbitrageurs. Liquidity takers trade at prices that can create arbitrage opportunities, while arbitrageurs align the exchange’s price with the external market price. We show that in Geometric Mean Market Makers charging proportional transaction fees, Impermanent Loss can be super-hedged by a model-free rebalancing strategy. Moreover, we demonstrate that in such a DEX, the exchange rate is of finite variation, so that loss-versus-rebalancing (the shortfall of providing liquidity versus the corresponding constant-weights portfolio) vanishes.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical and mathematical foundation for model-free hedging of Impermanent Loss in DEXs using finite variation analysis. However, it is purely theoretical and lacks empirical backtesting or real-world transaction data validation.

Research Flowchart

  flowchart TD
    A[Goal: Model-free Hedging of Impermanent Loss IL in GMMMs] --> B[Model Setup: GMMMs with LTs, Arbitrageurs & Fees]
    B --> C[Input: External Market Prices & Pool Weight Parameters]
    C --> D[Analysis: Rebalancing Strategy & Exchange Rate Dynamics]
    D --> E[Finding 1: IL is Super-Hedged via Model-Free Rebalancing]
    D --> F[Finding 2: Exchange Rate is Finite Variation, so LVR Vanishes]