Optimal Portfolios Of Liquidity Positions

This paper introduces a novel quantitative framework for optimizing liquidity provider (LP) positions in decentralized finance (DeFi) markets, specifically focusing on Constant Product Market Makers (CPMMs). The proposed method constructs optimal mean-variance portfolios that are hedged by short positions in underlying tokens, thereby maximizing the Sharpe ratio. Unlike previous studies, which typically focus on single-pool strategies, our approach integrates multiple CPMM pools and accounts for transaction costs, offering a more comprehensive solution for risk management in DeFi. The model is rigorously tested on historical data from Uniswap V2, demonstrating significant outperformance over traditional liquidity provision strategies, with Sharpe ratios reaching up to 4. Additionally, the framework is shown to be scalable, maintaining positive returns even under high transaction costs and varying capital conditions. This work not only extends existing literature on DeFi liquidity provision but also provides a practical, implementable strategy for diversified portfolio management in volatile cryptocurrency markets.