Challenge #4: Quantifying LVR on v3

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) across different Uniswap versions (v2 and v3) and 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].
   • Formulate and test a sound methodology for calculating LVR on v3 pools, where liquidity is concentrated across a range of prices
   • Compare LVR calculations between Uniswap v2 and v3, accounting for v3's concentrated liquidity feature. This will be tricky; calculating (and by extension, finding ways to mitigate) LVR at any given moment includes a lot of variables, and adding concentrated liquidity ranges across prices introducing more nuance to understanding the opportunity cost of rebalancing vs. holding vs. LPing.
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 and v3 across different networks.
   • Compare TAM estimates between mainnet and L2s, considering factors like trading volume, liquidity depth, and user base.
4. Uniswap v2 vs v3 Comparison:
   • Analyze how v3's concentrated liquidity model affects LVR compared to v2's constant product formula.
   • Investigate if certain pool characteristics (e.g., fee tiers, liquidity ranges) in v3 lead to higher or lower LVR compared to similar v2 pools.

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 and v3 across mainnet and/or L2 networks, with detailed comparisons and insights.
• TAM estimates for LVR across different versions and networks, including methodology and key influencing factors.
• Analysis of how v3's concentrated liquidity affects LVR compared to v2's constant product model.