Measuring and Mending LP Net Profitability

Intro to paper at the SSRN

Download the full paper here.

Introduction

An AMM’s 'impermanent loss’ (IL) is the statistically certain consequence of the LP position’s negative gamma. This negative drift is not large, a few basis points per day, but it accumulates to approximately 10% annually as a percentage of the unrestricted range (v2) LP market value. LPs for the most popular capital-efficient AMMs (restricted-range or v3) pools have continually generated negative net profits since inception, which is why decentralized AMM TVL peaked shortly after they were introduced in 2020. LP net returns on the capital-inefficient v2 AMMs have been modestly profitable since 2021.

The solution presented in this paper is based on three premises outlined in this paper. First, the arbitrageurs of a constant product AMM generate a gross profit equal to the LP’s IL expense. Second, people prefer capital-efficient v3 AMMs, but their IL is generally greater than their fees, making the current status quo unsustainable. Third, a handful of players act as arbitrageurs for each AMM pool by pushing the AMM price to the CEX price.

AMM LPs can protect themselves from IL by indirectly trading with themselves. Suppose a single LP created an AMM and also created an arbitrage program that updated the AMM price to the Binance price on each 5 basis point (bp) movement. If he were the only trader and LP, he would be trading with himself in a closed system, a zero-sum game. As the asset price moved, his arbitrage account would make a profit equal to his LP position’s IL. The mechanism outlined in this paper aims to simplify, maximize profitability, and minimize capital requirements for the arbitrageur’s task. The arb’s profit can then be shared with the LP, to make both tasks profitable after all expenses, including gas and IL. With a significant fee advantage, AMM-CEX price deviations would generate a profit opportunity only for the zero-fee trader. Providing margin accounts to LPs and arbitrageurs enables them to leverage each other, as statistically, their net token changes will offset each other on average. Crediting and debiting the IL to the arb and LP collective on any one trade when it prevents a further leveraged LP token imbalance would not affect either's total expected profit, but it would significantly reduce the amount of tokens the arb and LPs need to move on chain to remain solvent.

DEX developers widely recognize LP net unprofitability, but its documentation is weak. Fee revenue is easy to calculate, but the LP’s gamma expense is not. Early estimates of v3 LP profitability did not target a stationary metric that enables comparisons across pools. For example, Crocswap (2022) presented cumulative USD losses by marking LP trades against a fixed horizon from 5 minutes to 7 days. Loesch et al. (2021), Drossos et al. (2025), Cartea et al. (2023), Heimbach et al. (2022), and Canidio and Fritsch (2025) document generally negative v3 LP returns using the returns for specific LP positions on various pools. The data are not normalized and generally presented via cumulative performance lines or scatterplots,

Cumulative net profit is a function of pool size as well as the profit rate, making comparisons difficult. There is no attempt to generate standard errors, although the different numbers by markout horizon suggest it is substantial. An LP’s rate of return varies by a factor of 50 depending on its width, which has nothing to do with the core profitability of the AMM. These empirical studies are suggestive but better classified as anecdotes rather than data.

Given the absence of any academic consensus on how to measure IL or net LP profitability, the default practice is to present gross LP profits, revenues without the expense, divided by total value locked (TVL). Crypto users have become accustomed to seeing 50% APYs on most DEXes while generally losing money as liquidity providers (LPs).

This paper demonstrates how the simplest metric, the change in pool tokens and the end-of-day price, is consistent with other estimates that utilize liquidity. For the v2 pools, it does not matter; however, for v3, the IL estimates containing ‘liquidity’ are plagued by subtle variance-liquidity correlations, although they are generally indistinguishable over several months. To avoid problems created by the ambiguity of ‘return’ applied to v3 pools of various widths, we normalize the IL with the fee revenue, generating a stationary variable that enables comparisons between all types of AMM (the IL/fee ratio was used by Fritsch and Canidio (2024), though only graphically and applied to a handful of pools). The stationary variable cost ratio applies to any time duration and has the same interpretation, whether the numeraire token is ETH or a stablecoin. Using data on 22 pools over the past five years, we document that v2 LPs make a net profit, while v3 LPs do not, at statistically significant levels; latency and fee tier do not significantly impact this outcome.

Prominent solutions to rectify the LP unprofitability include lower latency (e.g., Arbitrum vs. Ethereum), dynamic fees that scale with volatility (TraderJoe), end-of-trade fill prices that eliminate IL on single trades (Thorchain), single-sided liquidity (Thorchain), and dynamic LP-range strategies (Charm’s Alpha Vaults). These have been implemented for years and have not generated capital-efficient, profitable LPs.

An oracle-updated price could mitigate LP IL (Im et al. 2024, Krishnamachari et al. 2021), but they are vulnerable to hacks, and it is non-trivial to align the oracle’s incentive with a pool’s LPs at all times. Coinbase and Chainlink are large enough companies that their franchise value would exceed any potential gain from misreporting prices, aligning their incentives as oracles with the DEX. However, these companies are susceptible to censorship, which is unacceptable for any long-run decentralized exchange (DEX).

Budish, Cramton, and Shim (2015) propose using frequent batch auctions to replace the standard centralized limit order book in traditional finance (tradFi). Auctions are intriguing solutions because classic auction theory shows that auctions maximize seller revenue in various forms (English, Dutch, and double auctions). An AMM could auction off the right to trade first in a block (Jososo, 2022), aggregate all buy and sell orders in a block to transact at a single price (Ramseyer et al. 2024; Canidio and Fritsch 2025), or the right to become the exclusive owner of fee revenue over a fixed period (Adams, Moallemi, and Robinson 2024). The intuition behind their purported efficiency is similar to that of Budish et al. (2015): competition in speed and gas payments to block builders is a deadweight cost for the exchange, leading to inefficient outcomes. Auctions transfer these activities into a competitive price environment that benefits LPs.

Centralized limit order book representatives have not publicly dismissed the frequent batch auction alternative, but they have also not made any investments in that direction. Budish, Lee, and Shim (2024) hypothesize that reluctance arises because the benefits would be immediate for the first-mover exchange, but imitators would quickly eliminate their profit bump once everyone sees the advantages, leaving the innovator to bear the large fixed costs of creating a new exchange for a fleeting reward. However, investment banks have created numerous dark pools that have minimal start-up costs, each with its unique trading protocols and order types; none have experimented with frequent batch auctions.

Tradfi’s revealed preference for CLOBs is more likely because exchanges realize that frequent auctions generate attack surfaces that not only hinder their efficiency but also expose the market to legal liability. Several papers have identified scenarios where frequent auctions increase adverse selection, allowing informed traders to manipulate auction prices (Eibelshauser et al., 2022; Ausubel et al., 2014; Kagel and Levin, 2001). As documented in this paper, AMMs have, at most, a handful of arbs who set their prices, and players are worldwide, pseudonymous, and uncensorable. An auction would elevate the level of collusion that currently exists. Arbs would have little fear of legal liability, and insiders would likely quickly manipulate any repeated blockchain auction.

For example, in the 1990s, NASDAQ market makers were found guilty of colluding on stock quotes by enforcing a collusive equilibrium that discouraged any dealer from quoting stocks in spreads below 1/4 of a point. If NASDAQ dealers could enforce an unwritten illegal equilibrium with over 20 dominant players, a handful of abs with zero legal risk would have the will and ability to collude and avoid perfectly competitive outcomes that auction models generate.

Many theoretical solutions rely on the assumption that in perfectly competitive markets, arbitrage profits would be zero. Several mechanisms would eliminate arbitrageur profits given perfectly competitive arbitrageurs: zero latency, auctioning trade blocks, and trades executed at the end-of-trade price (self-financing). As the LPs and arbitrageurs are playing a zero-sum game, a zero-profit arbitrageur implies that the LP captures the IL completely via the arb’s fees. With their IL covered by arb fees, any retail trading should generate fees, leading to positive LP profits. In practice, the low-latency blockchains, protocols where each trade is self-financing, and auctions have not generated capital-efficient, profitable LP positions. While everyone recognizes that, in practice, no market has perfect competition, and this paper outlines the limiting principle that has and will prevent AMMs from achieving this ideal.

This paper illustrates how vertically integrating arbs into LPs can reduce the profit leakage to arbs. Any decentralized AMM will exist on a blockchain with latency 100 times greater than any centralized exchange. This is because decentralized blockchains require consensus mechanisms, which necessitate messaging across a sufficiently broad region to avoid country-specific censorship. For any token with liquid CEX markets, the DEX price will follow the CEX price and not vice versa. This makes the arb’s objective a straightforward technical problem as opposed to the nebulous alpha skill needed to set prices on CEX exchanges successfully. AMM arbs use liquid centralized exchanges like Binance as their target price because no other alpha is needed or adds value.

Maintaining a basic arbitrage bot requires a certain level of competence: integrating price feeds to extract the true price, generating the lowest-latency connections to RPCs, understanding how blockchain builders respond, etc. As there are only a handful of arbitrageurs for any one pool, they represent the left-tail of a power-law distribution in high-frequency trading competency. Given this barrier to entry, the handful of remaining arbitrageurs then focus primarily on non-price competition to avoid the zero-profit equilibrium.

Instead of capturing arb profits via fees or auctions, one can tax the arb’s profit directly and add this to the LP revenue. This aligns the arbs and LPs, who both want to maximize the arbitrage profit. Restrictions on arbitrage trade size can prevent ruinous competition that would eliminate arbitrage profits. The arbs need to make a sufficient post-tax APY, and the data on arb activity will show that even if you give the arbs only 10% of their profit, they have to absorb 100% of their losses; they can still generate returns of 20% or more on required capital. Such returns are sufficient to ensure a constant supply of arbs. The high tax rate and liquidation protocol only work assuming the arb engages in high-frequency tactics, discouraging traders from using the arb account to take positions without incurring a fee.

To see the feasibility intuitively, consider a standard example of how to estimate annualized IL on a v2 pool is σ^2/8. For a token with a 4% daily volatility, the IL annualizes to a 7.3% APY. An arb with 5% of the v2 pool’s market cap would have the capital to push the AMM price 10%, which would cover most days. This implies the arb uses 20 times less capital than the v2 LPs. The zero-fee arb’s return on capital would be 2 times the LP’s IL APY because his profit tax leaves him with one-tenth of his PnL but then multiplies by 20 to account for his lower need for capital. The implied arb return of 14.6% is then just the starting point.

Arb returns should be higher than the base estimate for several reasons. First, the above ignores noise trades that move the AMM price away from the CEX, providing arb profits that do not appear in the IL. Ultimately, an exchange needs noise traders to survive, as without noise traders, the best any LP can do is to lose a little money. Additionally, we can provide arb’s margin account treatment to save on capital, and apply a minimum trade size and maximum gas price to prevent competition that would eliminate their profits. The handful of successful arbs should be able to generate attractive returns sufficient for their existence.

The net result is to turn the arb into an oracle, as it effectively updates the AMM price to the CEX price, utilizing a modest amount of capital for a modest profit. Unlike an oracle, however, this mechanism has no centralization point that can be censored. If an arb maliciously pushes the AMM price away from the true price, other arbs can immediately reap profits by reverting the price. Arb accounts are pseudonymous, replaceable, and disciplined by a decentralized liquidation mechanism if insufficiently collateralized.

This paper is split into the following sections. First, it derives three different formulas for estimating the LP’s IL, which highlight the mirror nature of arb PnL and the IL. While all three metrics are consistent and highly correlated, we find the ‘markout IL’ better than alternatives because it avoids the issues created when estimating ‘liquidity’ on v3 pools. We argue that the stationary metric IL/fees is superior to rates of return and dollar estimates of IL, showing that trade size is the key to arbitrageurs (arbs) avoiding the zero-profit competitive equilibrium and highlighting the relevance of noise traders to the profitability of arbs and LPs. In Section 2, we empirically document LP performance using the ratio of IL/fees and find that LPs make a profit on v2 pools but lose money on v3 pools at a high level of statistical significance. Section 3 empirically documents the activity and profitability of current AMM arbs, their share of AMM volume, and their pre- and post-gas-fee ROEs. Section 4 uses the data on arbs and LPs to show the feasibility of this approach. We outline the unique insolvency risk introduced by leveraging LPs and how liquidators can address this. Lastly, we highlight the simplicity of extending leverage to traders, which enables perps and stablecoins.