Optimal Fees for Geometric Mean Market Makers

Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. Arbitrage trades have been shown to align the prices reported by CFMMs with those external markets. These impose costs Liquidity Providers (LPs) who supply reserves CFMMs. Trading fees proposed as mechanism for compensating LPs arbitrage losses. However, large reduce accuracy and can cause deviate from desirable asset compositions. CFMM designers therefore faced problem how optimally select attract liquidity. We develop framework determining value supplying liquidity when underlying process follows general diffusion. Focusing popular class which we call Geometric Mean (G3Ms), our approach also allows one optimal maximizing LP value. illustrate methodology showing an mean-variance utility will prefer G3M over all alternative trading strategies zero.