Automated Market Making and Loss-Versus-Rebalancing

TL;DR

This paper develops a Black-Scholes based model for automated market makers, quantifies the adverse selection cost called loss-versus-rebalancing, and suggests protocol redesigns to mitigate these costs.

Contribution

It introduces a closed-form formula for loss-versus-rebalancing in AMMs, providing a realistic model that matches empirical LP returns and guides protocol improvements.

Findings

LVR is a significant cost for LPs in AMMs.

The model accurately matches empirical LP returns.

Redesigning CFMM protocols can reduce LVR.

Abstract

We consider the market microstructure of automated market makers (AMMs) from the perspective of liquidity providers (LPs). Our central contribution is a ``Black-Scholes formula for AMMs''. We identify the main adverse selection cost incurred by LPs, which we call ``loss-versus-rebalancing'' (LVR, pronounced ``lever''). LVR captures costs incurred by AMM LPs due to stale prices that are picked off by better informed arbitrageurs. We derive closed-form expressions for LVR applicable to all automated market makers. Our model is quantitatively realistic, matching actual LP returns empirically, and shows how CFMM protocols can be redesigned to reduce or eliminate LVR.