🤖 AI Summary
This work addresses the losses incurred by liquidity providers in automated market makers (AMMs) due to adverse selection, commonly quantified by loss-versus-rebalancing (LVR). To mitigate this issue, the paper proposes a partially active AMM mechanism that partitions liquidity reserves into active and passive components, with only the active portion participating in trades. The proportion of active liquidity is dynamically adjusted at the beginning of each block. Drawing inspiration from index tracking optimization, this approach simultaneously reduces LVR and constrains deviations of asset weights from a target portfolio allocation. Theoretical analysis and empirical experiments demonstrate that, compared to conventional constant-function market makers (CFMMs), the proposed mechanism significantly enhances liquidity provider wealth while effectively balancing the trade-off between adverse selection costs and portfolio drift.
📝 Abstract
We introduce a new class of automated market maker (AMM), the \emph{partially active automated market maker} (PA-AMM). PA-AMM divides its reserves into two parts, the active and the passive parts, and uses only the active part for trading. At the top of every block, such a division is done again to keep the active reserves always being \(\lambda\)-portion of total reserves, where \(\lambda \in (0, 1]\) is an activeness parameter. We show that this simple mechanism reduces adverse selection costs, measured by loss-versus-rebalancing (LVR), and thereby improves the wealth of liquidity providers (LPs) relative to plain constant-function market makers (CFMMs). As a trade-off, the asset weights within a PA-AMM pool may deviate from their target weights implied by its invariant curve. Motivated by the optimal index-tracking problem literature, we also propose and solve an optimization problem that balances such deviation and the reduction of LVR.