Mean-reverting Prices and Losses in Liquidity Pools

With the proliferation of decentralised finance (DeFi) protocols AMMs (automated market makers) on blockchains have also gained momentum in the past few years. This is mostly attributable to the fact that they require much weaker trust assumptions than centralised exchanges (CEXs) and that they can be utilised anonymously without requiring their users to go through a know-your-customer process. The decentralised nature of AMMs brings in some caveats, among which is the intensively researched loss-versus-rebalancing (LVR) metric, which is the dollar amount a liquidity pool (LP) loses in one unit of time compared to a rebalancing strategy that executes the same trades on CEXs. In this work, we adopt the Ornstein–Uhlenbeck stochastic differential equation to account for uncertain movements in the spot price, develop a discrete-time simulator and gauge the LVR metrics of constant function market makers (CFMMs). We demonstrate that the relative amount of losses is not as large as one would expect at first glance.