Loss-versus-rebalancing with external proportional transaction costs

By Masaaki Fukasawa

Rating

1707
Battle Count: 51

Relevance

8/10
Highly relevant for quantitative researchers and practitioners in DeFi and crypto markets. It provides a rigorous framework for understanding how AMM pools can be used as execution venues for specific trading strategies, effectively bridging the gap between passive liquidity provision and active portfolio management.

Implementation Complexity

7/10
The theoretical concepts (reflected dynamics, utility-indifference pricing) are mathematically complex. Implementing the proposed pool designs (e.g., geometric-mean pools with specific fee structures) requires sophisticated smart contract development and careful parameter calibration.

Reproducibility

3/5
The paper is purely theoretical with no empirical data or code repository provided. However, the mathematical derivations, assumptions, and constructive proofs are fully described, allowing for theoretical reproduction and verification of the logic.

Abstract

We study liquidity provision in automated market makers when trading in the external market incurs proportional transaction costs. We consider both separately collected fees and fees retained in reserves. The benchmark is a self-financing strategy holding the same total risky inventory and trading at the external bid and ask. Under continuous external prices and pure arbitrage, the pool and benchmark have identical liquidation wealth whenever the pool fee or the external spread is positive. Thus loss-versus-rebalancing relative to this transaction-cost benchmark is zero, even without a pool fee if the external spread is positive. We then construct retained-fee utility-indifference pools that implement admissible decreasing inventory schedules, and geometric mean pools that implement feasible constant no-trade boundaries for portfolio weights. These results offer an investment interpretation of liquidity provision: by choosing the pool design, a liquidity provider can specify a trading strategy whose rebalancing is carried out by arbitrageurs.

Links

arXiv:2610.21057 ยท Paper rankings

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