Inefficiency of CFMs: hedging perspective and agent-based simulations

Paper: arXiv 2302.04345

Authors: Samuel Cohen, Marc Sabaté Vidales, David Šiška, Łukasz Szpruch

Abstract

We investigate whether the fee income from trades on the CFM is sufficient for the liquidity providers to hedge away the exposure to market risk. We first analyse this problem through the lens of continuous-time financial mathematics and derive an upper bound for not-arbitrage fee income that would make CFM efficient and liquidity provision fair. We then evaluate our findings by performing multi-agent simulations by varying CFM fees, market volatility, and rate of arrival of liquidity takers. We observe that, on average, fee income generated from liquidity provision is insufficient to compensate for market risk.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical framework using continuous-time finance to analyze Constant Function Market Makers (CFMMs), coupled with agent-based simulations to evaluate practical market risk for liquidity providers. It introduces novel insights into the efficiency of CFM fee structures, though full empirical backtesting on real historical blockchain data is somewhat limited by relying primarily on simulations.

Research Flowchart

  flowchart TD
    A[Research Goal: Is CFM fee income sufficient to hedge liquidity providers' market risk?] --> B[Continuous-Time Financial Mathematics]
    A --> C[Multi-Agent Simulations]
    
    B --> D[Derive Not-Arbitrage Fee Upper Bound for Fair Provision]
    
    E[Inputs: CFM Fees, Market Volatility, Trader Arrival Rates] --> C
    
    C --> F[Simulate & Compare Fee Income vs. Market Risk Exposure]
    
    D --> G[Key Finding: Fee income is on average INSUFFICIENT to compensate LPs for market risk]
    F --> G