Loss Versus Rebalancing (LVR) quantifies the inefficiency in liquidity provision within Automated Market Makers (AMMs) by measuring the price divergence between the AMM and the market. Essentially, it calculates the "cost" incurred by liquidity providers due to arbitrageurs exploiting price differences between the AMM's price and the market price. The two formulas used in this analysis reflect different approaches to quantifying LVR:

LVR = a(p - q) captures discrete LVR, where 'a' is the asset quantity traded, 'p' is the market price, and 'q' is the AMM price. This formula is useful for specific transactions where liquidity providers may face a loss as prices shift in favor of arbitrageurs.
LVR = σ²/8 represents a continuous-time model of LVR, where 'σ' is the price volatility. This formula focuses on measuring the effect of volatility on liquidity providers over time, particularly useful for assessing LVR in dynamic, fast-moving markets like Uniswap v2.

In the analysis, the dashboard highlights both discrete and continuous LVR calculations for the WBTC-WETH pool on Ethereum and Arbitrum. The impact of transaction fees and market price fluctuations on LVR is also visualized, emphasizing how both positive and negative LVR values affect liquidity providers and arbitrageurs. A negative LVR typically indicates a profit for liquidity providers, as arbitrageurs face losses. In contrast, a positive LVR suggests liquidity providers incur a loss as arbitrageurs profit from market inefficiencies. This analysis can help optimize liquidity strategies and minimize losses across networks.

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