Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions

TL;DR

This paper analyzes different Automated Market Maker mechanisms, especially oracle-based ones, using mean-variance analysis inspired by portfolio theory, showing they can outperform traditional constant function market makers under various conditions.

Contribution

It introduces an oracle-based AMM mechanism and evaluates its performance using a mean-variance framework, comparing it to existing constant function market makers.

Findings

Oracle-based mechanisms outperform CFMMs with perfect or lagged oracles.

Mean-variance analysis provides insights into LPs' risk-return profiles.

Optimized oracle mechanisms are more robust against arbitrage and adverse selection.

Abstract

With the emergence of decentralized finance, new trading mechanisms called Automated Market Makers have appeared. The most popular Automated Market Makers are Constant Function Market Makers. They have been studied both theoretically and empirically. In particular, the concept of impermanent loss has emerged and explains part of the profit and loss of liquidity providers in Constant Function Market Makers. In this paper, we propose another mechanism in which price discovery does not solely rely on liquidity takers but also on an external exchange rate or price oracle. We also propose to compare the different mechanisms from the point of view of liquidity providers by using a mean / variance analysis of their profit and loss compared to that of agents holding assets outside of Automated Market Makers. In particular, inspired by Markowitz' modern portfolio theory, we manage to obtain an efficient frontier for the performance of liquidity providers in the idealized case of a perfect oracle. Beyond that idealized case, we show that even when the oracle is lagged and in the presence of adverse selection by liquidity takers and systematic arbitrageurs, optimized oracle-based mechanisms perform better than popular Constant Function Market Makers.