Paper: Not All LPs Are Equal: The Active-Passive Gap in Automated Market Maker Liquidity Provision
Authors: Agathe Sadeghi, Dingyue Liu, Ciamac Moallemi, Xin Wan, Brian Zhu
Date: 2026-09-29
Estimated Reading Time: 15-20 minutes

Liquidity provider profitability on automated market makers is usually measured at the pool level, which treats every provider in a pool as the same participant, and the paper tests what that hides once concentrated liquidity lets some providers reposition capital around individual trades. The authors split Uniswap LP profitability into active and passive components using a fee-inclusive markout: the value a pool receives from a swap minus the value it gives up, both legs priced at the Binance mid-price 15 seconds later, with gas excluded. Two estimators carry the split. A LIFO subtraction method treats liquidity minted and burned within 20 seconds as active and assigns each swap's markout to active and passive liquidity by liquidity share, while an infinitesimal LP benchmark prices a marginal, always-in-range passive position from the pool's price path. The sample covers Uniswap v2, v3 and v4 pools on Ethereum, Arbitrum and Base from February 1st to November 30th, 2025, restricted to WETH, USDC, USDT, WBTC and cbBTC pairs with more than $10 million in volume. In v2 the method identifies no short-lived positions, so overall and passive markouts coincide, while in v3 and v4 passive LPs tend to earn less than the pool aggregate, with the gap widest on Ethereum and at the 5 bps tier. The authors read the cross-chain differences as descriptive rather than causal, and the agreement between the two estimators as cross-method evidence rather than a formal test.

Core insights

The gap points the same way in most pools, though not all (v4 Base USDC-cbBTC reverses it), and is small in size, and the way it is reported leaves the size hard to judge. Confidence intervals are printed for passive markouts, and many of them straddle zero: Ethereum v3 USDC-WETH at 30 bps has a passive LIFO estimate of -0.866415 bps inside an interval of [-2.63, 0.9]. Appendix C sets out a standard error for the difference between overall and passive markout itself, yet none of the result tables prints that interval, so whether any single pool's gap is distinguishable from zero is left to the reader. My read: the finding holds as a pattern across pools, not as a measurement of any one of them.

The more informative comparison runs between pools rather than within one. Base USDC-WETH at 5 bps carries the largest active share in v3 and a total-passive gap of only about 0.03 bps, while Ethereum USDC-WETH at 5 bps, with an active share of 1.30% to 1.36% under LIFO (Tables 7 and 5 differ), produces the move from -1.15 to -1.51 bps. On my reading, the size of the active share does not set the size of the gap; where the active liquidity sits does. On Ethereum, short-lived liquidity can see a trade coming and position for it, which leaves passive capital holding more of the flow it would rather not take (my interpretation of the paper's descriptive cross-chain result, not something it identifies causally). The share figures are not consistent across tables: Table 5's LIFO column differs from Table 7's in 12 of the 17 pools both report. For Base USDC-WETH, Table 5 gives an active LIFO share of 3.82% and 3.56% under exact matching, while Table 7 and the text give 3.56% as the LIFO figure.

For token design the relevance sits in how liquidity is paid for. The paper does not study liquidity mining, emissions or protocol-owned liquidity, and its conclusion is that TVL, volume and pool-level markout are an incomplete picture of the returns to passive capital in concentrated pools. Assumption: an incentive programme sized against pool-level fee returns is buying depth from the providers who stay in range between trades, and those are the providers whose markout is worse than the aggregate, so the emission needed to retain that depth is higher than the aggregate implies. The paper's own identity makes the adjustment explicit: passive_markout = total_markout - active_markout, aggregated over swaps. If a project funds depth with token rewards, which of those two markouts is the reward compensating, and does the answer change once active providers collect the same rewards on short-lived positions?

The fee tier is a lever a token issuer controls directly when seeding a pool, and the paper's ordering favours passive liquidity at 30 bps over 5 bps. Assumption: protocol-owned liquidity, which is typically deployed and left in place, behaves as passive liquidity in the paper's terms, so a treasury seeding a low-fee concentrated pool places its capital on the side of the gap that absorbs adverse selection. The sample limits how far that carries. It contains only WETH, USDC, USDT, WBTC and cbBTC pairs above a $10 million volume floor and excludes the noisier long tail of smaller pairs, which is where a new token's first pool sits, so the ordering is evidence about major pairs and only a hypothesis for a launch pool. Would a token's own pool, with thinner flow and a different arbitrage profile, rank the fee tiers the same way?

Two of the stated limitations point in the same direction. LIFO classification runs at the on-chain address level, so active strategies split across addresses or run through vaults are counted as passive, and the authors call the measured active share a lower bound on strategic provision. The infinitesimal benchmark is a full-range position, and finite-width passive LPs face more adverse selection per unit of liquidity, which makes it a floor on their markout cost. Both biases make passive capital look better than it is, so I would expect the reported gap to be understated rather than overstated, although the paper quantifies neither effect. The estimates also come from a single window, February to November 2025, and four of the five authors list an affiliation with Uniswap Labs (which matters less for the arithmetic than for which design interventions the paper chooses to discuss).

The decomposition survives every implementation check the authors run. At the same matching horizon, FIFO and LIFO agree to four or more decimal places in every v3 pool tested, widening the matching horizon from 20 to 60 seconds moves the Base USDC-WETH estimate from -0.709 to -0.740 bps, and the passive markout stays flat across horizons from 0 seconds to one hour before market drift dominates at four and six hours. The infinitesimal benchmark can be computed block by block from on-chain events and a reference mid-price, which the authors propose for rolling pool monitoring and ex-ante pool selection, alongside before-and-after evaluation of the active-passive gap when JIT-mitigation hooks or sequencing changes are introduced. Still open, and listed by the authors as an extension: a cross-chain comparison matched on volatility, liquidity depth and gas costs, without which the L2 result cannot be attributed to block time rather than to who is active on each chain.