Challenge #3: Quantifying LVR on Uniswap v2

Loss Versus Rebalancing (LVR) is a critical metric for assessing the efficiency of liquidity provision in Automated Market Makers (AMMs) like Uniswap. This challenge aims to quantify LVR's impact and its Total Addressable Market (TAM) on Uniswap v2 across networks (Ethereum mainnet and various L2s), exploring strategies to mitigate its effects and improve liquidity provision efficiency.

Challenge Objectives

1. LVR Quantification:
   • For discrete trades, calculate LVR using the formula: LVR = a(p - q), where 'a' is the asset quantity traded, 'p' is the market price, and 'q' is the AMM price [1].
   • For continuous-time models, especially relevant for Uniswap v2, use the instantaneous LVR formula: LVR = σ²/8, where σ represents price volatility [1].
   • Compare LVR calculations between Uniswap v2 pools. Focus on identifying an LVR value on a single pool first.
2. Cross-Network Analysis:
   • Quantify and compare LVR across Ethereum mainnet and major L2 networks (e.g., Arbitrum, Optimism, Base).
   • Investigate how network-specific factors (e.g., gas prices, block times) influence LVR.
3. TAM Estimation:
   • Develop a methodology to estimate the Total Addressable Market of LVR for both Uniswap v2 across different networks.
   • Compare TAM estimates between mainnet and L2s, considering factors like trading volume, liquidity depth, and user base.

Ultimately, these are all just options for you. Even a single chart with thoughtful analysis can be insightful. Your may feel free to explore one or a few of these objectives.

There is a ton of information out there on LVR, but here is some of the best research on the topic:

• Columbia University paper that first termed LVR:https://arxiv.org/pdf/2208.06046
• CowSwap’s batch trading solution: https://arxiv.org/pdf/2307.02074v3
• CowSwap docs: https://cow.fi/learn/what-is-loss-versus-rebalancing-lvr
• a16z (must read!) https://a16zcrypto.com/posts/article/lvr-quantifying-the-cost-of-providing-liquidity-to-automated-market-makers/
• https://medium.datadriveninvestor.com/impermanent-loss-in-defi-the-risks-involved-in-providing-liquidity-67c54fdf1cfc

Expected Outcomes & Potential Deliverables

• Comprehensive LVR calculations for Uniswap v2 across mainnet and/or L2 networks, with detailed comparisons and insights.
• TAM estimates for LVR and comparison between pools, including methodology and key influencing factors.
• Time-series analysis of LVR, identifying patterns related to time-of-day and market volatility, compared across versions and networks.
• Proposed strategies for mitigating LVR, with simulations demonstrating their potential effectiveness in reducing the TAM of LVR.