We aim to understand how the profitability of passive liquidity provision in an automated market maker (AMM) depends on the transaction fee and other market characteristics. To that end, we simulate an ecosystem where an aggregator routes order flow to a centralized exchange and the AMM. Our analysis may inform how variable fee mechanisms can be designed to mitigate systematic losses for liquidity providers. Work-in-progress with Philippe Bergault, Steven Campbell, Jason Milionis.