The Homogenous Properties of Automated Market Makers

TL;DR

This paper explores the fundamental theoretical properties of automated market makers (AMMs), revealing their homogeneity under basic assumptions, and analyzes their market microstructure, including slippage and impermanent loss.

Contribution

It introduces a universal formula for liquidity provisioning and demonstrates the equivalence of different AMM models under uniform reserves, advancing theoretical understanding.

Findings

AMMs exhibit homogeneous properties under basic assumptions.

Constant function and token swap AMMs are equivalent with uniform reserves.

Impermanent loss depends on volatility and market depth.

Abstract

Automated market makers (AMM) have grown to obtain significant market share within the cryptocurrency ecosystem, resulting in a proliferation of new products pursuing exotic strategies for horizontal differentiation. Yet, their theoretical properties are curiously homogeneous when a set of basic assumptions are met. In this paper, we start by presenting a universal approach to deriving a formula for liquidity provisioning for AMMs. Next, we show that the constant function market maker and token swap market maker models are theoretically equivalent when liquidity reserves are uniform. Proceeding with an examination of AMM market microstructure, we show how non-linear price effect translates into slippage for traders and impermanent losses for liquidity providers. We proceed by showing how impermanent losses are a function of both volatility and market depth and discuss the implications of these findings within the context of the literature.