About constant-product automated market makers

TL;DR

This paper analyzes the mathematical principles of constant-product automated market makers, demonstrating their invariance to trade splitting and highlighting the benefits of not recompounding fees for safety and profitability.

Contribution

It provides a mathematical analysis of constant-product AMMs, revealing invariance properties and advantages of fee policies not previously detailed.

Findings

Splitting trades into smaller parts does not affect the final exchange rate.

Protocols are safer when no one recompounds their fees.

Recommends fee policies for improved safety and profitability.

Abstract

Constant-product market making functions were first introduced by Hayden Adams in 2017 to create Uniswap, a decentralised exchange on Ethereum. This enables users to exchange assets at any given rate. Some variations such as Balancer and Curve were later introduced. In this paper, we analyse the maths that rule this type of protocol. We show that splitting a trade in multiple smaller trades does not impact the final exchange rate. We also show that the protocol is safer and more profitable when no one recompounds their fees.