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

21 Pages Posted: 4 Apr 2023

See all articles by Masaaki Fukasawa

Masaaki Fukasawa

Osaka University

Basile Maire

Desma Eight, LLC; Quantena

Marcus Wunsch

ZHAW School of Management and Law

Date Written: March 23, 2023


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.

Keywords: digital currencies, automated market makers, Impermanent Loss, decentralized exchanges, divergence loss

JEL Classification: D47, D53, C02

Suggested Citation

Fukasawa, Masaaki and Maire, Basile and Wunsch, Marcus, Model-Free Hedging of Impermanent Loss in Geometric Mean Market Makers (March 23, 2023). Available at SSRN: or

Masaaki Fukasawa

Osaka University

1-1 Yamadaoka
Osaka, 565-0871

Basile Maire

Desma Eight, LLC ( email )

435 W 31st St
New York, NY 10001
United States


Quantena ( email )

Gotthardstrasse 26
Zug, 6300

Marcus Wunsch (Contact Author)

ZHAW School of Management and Law ( email )

Technoparkstrasse 2
Winterthur, 8400

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