Loss-versus-Rebalancing under External Proportional Transaction Costs

01 ABSTRACT

The study analyzes loss-versus-rebalancing in automated market maker liquidity provision when external trading incurs proportional transaction costs. The author distinguishes separately collected fees from fees retained in reserves and uses a self-financing external bid-ask strategy as benchmark. Under continuous external prices and pure arbitrage, pool and benchmark have identical liquidation wealth whenever the pool fee or external spread is positive, so loss-versus-rebalancing is zero; retained-fee utility-indifference pools and geometric mean pools are constructed to implement admissible decreasing inventory schedules and feasible no-trade boundaries for portfolio weights.

02 KEY FINDINGS

1. Loss-versus-rebalancing is redefined under proportional transaction costs against a self-financing strategy holding the same total risky inventory and trading at external bid and ask.
2. Under continuous external prices and pure arbitrage, pool and benchmark have identical liquidation wealth whenever the pool fee or external spread is positive, so loss-versus-rebalancing is zero.
3. Retained-fee utility-indifference pools and geometric mean pools are constructed to implement admissible decreasing inventory schedules and feasible no-trade boundaries for portfolio weights.