Partially Active Automated Market Makers
This presentation introduces Partially Active Automated Market Makers (PA-AMMs), a novel approach to reducing adverse selection costs in decentralized finance. By splitting liquidity into active and passive reserves and controlling exposure through an activeness parameter, PA-AMMs offer liquidity providers a way to limit losses from arbitrage exploitation while maintaining market functionality. We explore the mechanism, theoretical foundations, and empirical results that demonstrate how this innovation reshapes the trade-off between liquidity provision and protection against stale price exploitation.Script
Automated market makers power billions in decentralized trading, yet they hemorrhage value to arbitrageurs who exploit stale prices. What if liquidity providers could shield most of their capital while still serving the market?
Current automated market makers expose all liquidity to immediate trading. When external prices shift faster than the blockchain can update, arbitrageurs strike, buying underpriced assets or selling overpriced ones. This creates systematic losses for liquidity providers, quantified as Loss-Versus-Rebalancing.
The authors propose a structural change to how liquidity itself is deployed.
Instead of offering all liquidity at once, PA-AMMs partition reserves at the start of every block. Only the active fraction trades, while the passive portion remains untouched. A single parameter, lambda, governs what fraction becomes active, letting liquidity providers dial their exposure up or down.
When lambda equals 1, you have a traditional market maker with instant full rebalancing and maximum loss. Dial lambda down, and you shield most reserves from each block's arbitrage wave. The cost is a temporary price gap, but the gain is dramatic reduction in cumulative loss.
These results from historical Ethereum price data reveal the core tension. The left panel maps the efficient frontier: lower activeness reduces instantaneous loss-versus-rebalancing but increases price gap variance. The middle panel shows cumulative loss over 5 months; lambda of 0.25 cuts losses to a fraction of the traditional pool. The right panel confirms price gaps remain bounded even at low activeness.
The authors ground their mechanism in rigorous stochastic modeling. They model external prices as geometric Brownian motion and derive closed-form expressions for expected loss. Under stationary conditions, they identify optimal activeness levels that minimize loss while keeping price gaps acceptable, giving liquidity providers concrete tuning guidance.
This theoretical analysis reveals how the optimal activeness depends on the penalty for price gap variance. The left curve shows expected loss rising with lambda for a fixed penalty weight gamma of 4. The right curve traces the optimal lambda as gamma varies; higher tolerance for price gaps favors lower activeness and thus lower loss.
The authors acknowledge key simplifications. Transaction costs, both swap fees and gas, are absent from the current model. Retail trading behavior, which differs from arbitrage, deserves its own analysis. Most intriguingly, the interplay between fee rates and activeness is uncharted territory, offering a richer design space for future market makers.
Partially active market makers offer a new lever for decentralized finance: control over liquidity exposure itself. By choosing how much capital to risk each block, liquidity providers can finally push back against the arbitrage tax. Visit EmergentMind.com to explore this paper further and create your own research video.
