Decentralized Exchanges: The Profitability Frontier of Constant Product Market Makers

Paper: arXiv 2302.05219

Authors: Tobias Bitterli, Fabian Schär

Abstract

In this paper we analyze constant product market makers (CPMMs). We formalize the liquidity providers’ profitability conditions and introduce a concept we call the profitability frontier in the xyk-space. We study the effect of mint and burn fees on the profitability frontier, consider various pool types, and compile a large data set from all Uniswap V2 transactions. We use this data to further study our theoretical framework and the profitability conditions. We show how the profitability of liquidity provision is severely affected by the costs of mint and burn events relative to the portfolio size and the characteristics of the trading pair.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a formal mathematical framework for CPMM liquidity provider returns and validates it against a comprehensive empirical dataset of Uniswap V2 transactions. It offers novel insights into how gas/fee friction impacts smaller liquidity providers, though full code availability for the empirical processing is not explicitly detailed.

Research Flowchart

  flowchart TD
    A[Analyze CPMM Liquidity Provider<br>Profitability & Conditions] --> B[Develop Theoretical Framework:<br>Define Profitability Frontier in xk-space]
    B --> C[Evaluate Impact of Fee Structures:<br>Trading, Mint, & Burn Fees]
    D[(Uniswap V2 Dataset:<br>All Historical Transactions)] --> E[Empirical Analysis:<br>Test Theory against Real Trade Data]
    B --> E
    C --> E
    E --> F[Key Finding: LP Profitability Heavily Reduced by<br>Mint/Burn Costs Relative to Pool & Pair Traits]