AMM Design in 2026: The Math, the Loss, and the Redesign

In July 2026, decentralized exchanges did something they had never done in the seven years The Block has kept score. They cleared roughly 24% as much spot volume as every centralized exchange combined, the highest reading in a data series that goes back to 2019, according to The Block. Almost all of that trading ran through a machine with no order book, no market maker at a desk, and no human quoting a price: the automated market maker.

An AMM is a design, not a company. It swaps the person who stands between buyers and sellers for a formula and a pool of tokens that anyone can add to. That one idea now underpins Uniswap, Curve, Balancer, PancakeSwap, and Aerodrome, and it prices everything from blue-chip pairs to the long-tail meme coins and Runes that trade nowhere else. But the design is not finished. Behind the record volume sits a quieter fight over a hard question: can the people who supply the liquidity, the LPs, actually make money? This is a story about how AMMs are built, why the design keeps changing, and who pays when it does not work.

The design problem AMMs were built to solve

Traditional markets match a buyer’s bid against a seller’s ask in an order book, a live ledger of resting offers curated by professional market makers. That model needs constant quoting, fast infrastructure, and enough traders on both sides at the same moment. On a slow blockchain in 2018, it was close to impossible: every order update cost gas, and thin books left most tokens untradeable.

The automated market maker threw the order book out. Instead of pairing two people, it lets you trade against a shared pool of two assets, with a formula setting the price from the ratio of what sits in the pool. Liquidity providers deposit both assets and earn a cut of every swap. Traders always get a quote, day or night, because the formula never sleeps. Hayden Adams built the first version of Uniswap on that premise, which is why AMMs are sometimes called constant-function market makers.

The trade-off was baked in from the start. An order book can quote a tight price and refuse a bad one. A formula quotes a price for any trade, which means it will always sell you the last token in the pool, just at a punishing price. Every AMM design since has tried to keep the always-on convenience while clawing back the efficiency an order book gets for free.

x*y=k: the invariant that started everything

The canonical AMM formula is constant product: x times y equals k, where x and y are the pool’s two token balances and k is a constant that every trade must preserve. Vitalik Buterin formalized the idea in a March 2018 ethresear.ch post about front-running resistance, crediting the formulation to the team at Gnosis. Uniswap V1 shipped it in November 2018 with a flat 0.30% fee and every pool paired against ETH.

The math is deceptively simple. Say a pool holds 10 ETH and 20,000 USDC, so k is 200,000. Buy some ETH and you remove it from the pool; to keep k constant, the formula demands proportionally more USDC, so each additional ETH costs more than the last. That rising cost is slippage, and it is a feature, not a bug: it stops a pool from being drained, and it pulls the pool’s price back toward the wider market when arbitrageurs step in.

Constant product has one great virtue. It can never run out of liquidity, because there is always a price, however bad, for the next unit. That is why it works for brand-new and long-tail tokens that no professional market maker will touch. It is also why, for two assets that should trade near a fixed ratio, it wastes almost all the money in the pool.

One curve does not fit all: StableSwap and weighted pools

A constant-product curve spreads liquidity across every price from zero to infinity. For a USDC/USDT pair that should sit at 1.00, that is close to absurd: almost none of the capital works near the peg where all the trading happens. Michael Egorov’s answer, published in a 2019 whitepaper and launched as Curve, was StableSwap: a hybrid curve that behaves like a flat, zero-slippage line close to the peg and only bends into a constant-product curve as the price runs away from it. The result is deep, cheap swaps for assets that track each other, which is why Curve became the home of stablecoins and, later, of liquid staking tokens such as stETH that trade against ETH, a market we cover in our look at Lido, Rocket Pool, and Frax.

Balancer generalized the idea in another direction. Its 2019 whitepaper replaced the two-asset, 50/50 pool with a weighted geometric mean, letting one pool hold up to eight assets in custom proportions, an 80/20 or 60/20/20 split that behaves like a self-rebalancing index fund. Where Uniswap fixed the shape and let the market fill the pool, Balancer turned the shape itself into a parameter.

The lesson that shaped the next decade of AMM design: the invariant is a choice. Pick a curve that matches how the assets actually move, and you can offer better prices with the same money. Here is how the main families compare.

Concentrated liquidity: Uniswap V3 and the efficiency leap

If StableSwap picks a better curve for pegged assets, Uniswap V3 (May 2021) let liquidity providers pick the curve themselves. Instead of spreading a deposit across all prices, an LP could concentrate it inside a chosen band, say ETH between $2,000 and $3,000, and earn fees only while the price sat inside that band. Within the range, the capital behaves like a much larger constant-product position; Uniswap reported capital-efficiency gains of up to 4,000x versus V2 for tight ranges in its V3 announcement. V3 also added fee tiers of 0.05%, 0.30%, and 1.00% and turned each position into an NFT, because positions were no longer interchangeable.

Concentrated liquidity is the most important AMM idea since x*y=k, and it quietly turned liquidity provision into a job. A passive V2 position needs no attention. A V3 position earns nothing the moment price leaves its band, so LPs have to move ranges as the market moves or hand the task to a manager. It also sharpened every existing risk: a tight range multiplies fee income and multiplies the loss when the price walks away.

That is the through-line of AMM design after 2021. Every gain in capital efficiency buys a new cost somewhere else, and it usually lands on the liquidity provider’s balance sheet. To see why, you have to look at the two ways an LP loses money even when nothing goes wrong.

Impermanent loss: the LP’s first tax

Impermanent loss, also called divergence loss, is the gap between holding two tokens in a pool and simply holding them in a wallet. When the pooled assets move apart in price, the AMM’s rebalancing sells the winner and buys the loser along the way, so the provider ends up with less than a passive holder. It is called impermanent because it vanishes if prices return to where they started, and it becomes permanent the instant the LP withdraws.

The numbers are unforgiving and, importantly, symmetric: a 2x move up costs exactly as much as a halving. Using the standard constant-product formula, Binance Academy lays the loss against holding out like this.

Fees are supposed to pay for this. In a calm, range-bound market, a busy pool’s trading fees can outrun impermanent loss and leave the LP ahead. In a trending market, they often cannot. But impermanent loss, for all the attention it gets, is really a symptom of a deeper problem, one the research community only named properly in 2022.

Loss-versus-rebalancing: the real cost of stale prices

Impermanent loss compares an LP to someone who did nothing. Loss-versus-rebalancing, or LVR (pronounced “lever”), compares the LP to a smarter benchmark: a trader who held the same shifting mix of assets but rebalanced it at the true market price on a real exchange. The gap between the two is what arbitrageurs pocket, and it is the cleanest measure of what it actually costs to make markets with a formula.

The mechanism is simple and brutal. An AMM only updates its price when someone trades against it, so between trades its quote goes stale. When ETH ticks up on other venues, the pool is still offering it cheap, and an arbitrageur buys from the pool until the price matches. That arbitrage profit comes straight out of the LPs’ pockets: the pool is, in effect, always selling to better-informed traders, the textbook definition of adverse selection.

The 2022 paper that named LVR, by Jason Milionis, Ciamac Moallemi, Tim Roughgarden, and Anthony Lee Zhang of Columbia and a16z crypto, put a clean number on it. For a constant-product pool, the instantaneous cost equals the asset’s variance divided by eight, written σ²/8 (arXiv). At 5% daily volatility, that is about 3.125 basis points a day, or roughly 11% a year, bled continuously to arbitrageurs before a single sandwich or hack. The authors draw the design conclusion bluntly: an AMM only survives if its liquidity providers come out ahead, so its fees have to scale with volatility, because that is what LVR scales with.

That reframed AMM design as a fight to protect the LP, not the trader. It also handed the skeptics a formula.

MEV and toxic flow: when the tax gets collected

LVR is the theory; MEV is the invoice. Maximal extractable value is the profit that searchers and block builders capture by ordering, inserting, or censoring transactions, and a large share of it is simply LVR being realized on-chain. Cumulative MEV on Ethereum runs into the billions of dollars, much of it from sandwich attacks, where a bot spots your swap waiting in the mempool, buys ahead of you, and sells into your trade. The most notorious sandwich bot, JaredfromSubway, even front-ran a Vitalik Buterin swap in 2026.

For an LP, MEV cuts both ways. Arbitrage MEV pays for the rebalancing an AMM needs, but it hands the surplus to searchers instead of the pool. Sandwich MEV is pure toxic flow: it worsens prices for the very retail traders an AMM is supposed to serve, and it does nothing for LPs. Either way, value that a well-designed market maker would keep leaks out of the pool and into the transaction-ordering supply chain.

Stack the drains together and the picture for a naive liquidity provider is grim. Here is what actually eats an LP’s return, and how modern designs try to plug each hole.

Uniswap V4 and hooks: the programmable AMM

The response to all of this is to stop treating the AMM as a fixed formula and start treating it as a platform. Uniswap V4, live since 31 January 2025, is the clearest expression of that shift, as the team laid out when it shipped the release. It keeps concentrated liquidity but adds three structural changes: a singleton contract that holds every pool (cutting the gas cost of creating pools and routing between them), flash accounting that nets balances once at the end of a transaction instead of moving tokens at every step, and, most importantly, hooks.

A hook is a smart contract that a pool calls at set points in its life, before or after a swap, or when liquidity is added or removed, so developers can bolt custom logic onto an otherwise standard pool. That turns the invariant from a fixed law into an extension point. A pool can charge a fee that changes with volatility, run its own auction, deposit idle funds into a lending market, or enforce a limit order, all without Uniswap Labs writing a line of it.

Hooks are also a new attack surface. A malicious or buggy hook can, in principle, sit between a trader and their money, which is why the audit industry treats V4 pools as a fresh class of risk and why “audited yet hacked” remains a live worry across DeFi, as we explored in our profile of Halborn. The design bet is that programmability is worth the danger. What follows is what builders are actually doing with it.

Dynamic fees and the auction-managed AMM

The LVR math says fees should rise with volatility. Static fee tiers cannot do that; a 0.30% fee is too high when markets are calm and far too low in a crash, exactly when arbitrageurs feast. Dynamic-fee hooks let a pool raise its fee automatically when volatility or order flow spikes. Arrakis Finance shipped one of the first, the Arrakis Pro Hook, aimed at token issuers who want to protect their own liquidity from arbitrage-driven MEV, and among the first whitelisted dynamic-fee hooks on V4.

A more radical idea is the auction-managed AMM, or am-AMM, proposed in 2024 by Austin Adams, Ciamac Moallemi, Sara Reynolds, and Dan Robinson (arXiv). Instead of the protocol guessing the right fee, the pool runs a continuous on-chain auction for the right to manage it: whoever bids the most, in a recurring rent, sets the swap fee and keeps the fees for a spell. The theory is elegant. The same arbitrageurs who would pick the pool off are forced to compete for the pool, so they bid away the LVR they would otherwise extract and hand it back to LPs. Bunni, a DEX built on V4, put the am-AMM into production alongside dynamic fees and the trick of routing idle pool assets into lenders like Aave for extra yield.

This is AMM design eating its own tail, in a good way. It uses the very MEV that drains LPs as the auction currency that repays them.

CoW AMM and the batch-auction escape hatch

If LVR comes from stale prices getting picked off between trades, one fix is to stop pricing continuously at all. CoW Protocol’s CoW AMM, live on Balancer, replaces the constant stream of individual swaps with batch auctions: trades are gathered over a short window and settled together at one uniform clearing price, with third-party solvers competing to fill them. Because everyone in a batch trades at the same price, and the solver rather than an arbitrageur captures any rebalancing surplus, the design aims to hand LVR back to LPs and make sandwich attacks impossible inside the batch.

CoW and Balancer market it as an AMM that eliminates LVR, and cite estimates that the cost runs to hundreds of millions of dollars a year for constant-product LPs. Those figures come from the protocols themselves, so treat them as advocacy rather than neutral accounting, but the mechanism is real and the direction of travel is clear. Batch auctions are not free: they add latency (you wait for the window to close), they lean on a competitive solver market to deliver good prices, and they move complexity from the curve to the settlement layer. Still, they show how far AMM design has traveled, from a formula that quotes every trade instantly to a system that deliberately slows down to protect the people funding it.

The order book strikes back, and the sustainability debate

All of this raises an awkward question. If the frontier of AMM design is dynamic fees, auctions, and oracles, is it just rebuilding the order book it replaced? Some of the loudest voices in DeFi think the honest answer is partly yes. Guillaume Lambert, founder of the options protocol Panoptic, has argued that AMMs can never be truly sustainable because LP fees are pegged to realized volatility while the risk LPs take on is priced by implied volatility; in effect, he says, liquidity providers are selling options far too cheaply, and no fee tweak fixes a mispriced product.

Uniswap founder Hayden Adams pushed back hard. “AMMs are only just getting started,” he wrote in a widely shared exchange, arguing that cheaper capital and composability, the ability to plug a pool into any other contract in DeFi, give AMMs a durable edge that order books cannot match, and that V4 hooks would let pools capture value for LPs the old design left on the table. The market has not settled the argument. Order-book perpetual venues such as Hyperliquid have taken real share in derivatives (they are order books, not AMMs, a distinction a lot of coverage still gets wrong), while on the spot side AMMs keep setting volume records. The likeliest outcome is convergence: AMMs that act more like order books when it helps LPs, and keep the passive, always-on liquidity that made them win in the first place.

The scoreboard backs the convergence thesis. Uniswap still leads every other DEX by volume, with roughly $52 billion in trailing-30-day turnover reported by The Block in early August, around three times its nearest rival, while its V4 deployment holds several hundred million dollars in liquidity spread across 18 chains and Curve still anchors the stablecoin trade with well over a billion dollars locked, according to DefiLlama. The spot crown is not up for grabs; the fight is over whether the people funding those pools keep enough of the yield to stay.

The fee switch: the protocol takes its cut

While designers fight to hand more value back to liquidity providers, Uniswap’s own token holders voted to take some of it for themselves. The UNIfication proposal, approved by governance in December 2025 with about 99.9% support, finally flipped Uniswap’s long-dormant fee switch. A slice of trading fees is now diverted from LPs to the protocol and used to burn UNI, and the DAO burned 100 million UNI, worth roughly $596 million at the time, from its treasury in one move. On V2 pools the mechanics cut the LP’s share from 0.30% to 0.25% and route the remaining 0.05% to the burn.

For LPs, that is a squeeze from a third side. They were already losing to impermanent loss, to LVR, and to MEV; now the protocol they provide liquidity to takes a cut off the top. It sharpens every design debate in this article, because dynamic fees, am-AMMs, and batch auctions are no longer just competing with each other. They are racing to give LPs back enough edge to outrun the protocol’s own hand in the till. Whether real yield can survive all four claims at once is the open question hanging over on-chain markets, the same tension playing out in RWA lending and other corners of DeFi where the fight is over who keeps the yield.

The SEC, and whether code can be a “dealer”

AMM design is not only an engineering problem; it is a legal one. If a pool quotes prices and fills trades with no human in the loop, is it an unregistered securities exchange, and is the code itself a “dealer”? The US Securities and Exchange Commission spent years circling that question. It sent Uniswap Labs a Wells notice in 2024, signaling likely enforcement, then closed the investigation in February 2025 with no action, under Acting Chair Mark Uyeda and Commissioner Hester Peirce.

The retreat postponed the underlying question rather than answering it. Uniswap Labs writes the front end and the contracts, but the pools run autonomously and the liquidity is other people’s; regulating a design rather than a company is genuinely hard, and it is the same puzzle at the center of the broader fight over who, if anyone, is the gatekeeper in DeFi, which we unpack in our piece on DeFi compliance. For now, US builders have more room than they expected two years ago, and much of the hook-and-auction experimentation described above is happening onshore because of it.

Where AMM design goes next

Add up the threads and a direction emerges. AMMs will keep the property that made them win, always-on liquidity that anyone can supply, while borrowing whatever they need from order books and auctions to stop bleeding their LPs. Expect more oracle-aware pools that quote closer to the real market price, more dynamic fees tuned to volatility, more batch settlement to blunt MEV, and more hooks that put idle liquidity to work in lending markets instead of sitting flat.

The measure of success is no longer trading volume, which AMMs already dominate on the spot side, but LP profitability, the boring, decisive number the LVR research forced everyone to confront. A design that pulls record volume while quietly bankrupting its liquidity providers is not sustainable, and everyone now knows it. The next generation of AMMs will be judged on a single question the first generation could ignore: after impermanent loss, after LVR, after MEV, and after the protocol’s cut, does the person who funded the pool still come out ahead?

Frequently Asked Questions

What is the difference between impermanent loss and loss-versus-rebalancing?

Impermanent loss measures a liquidity provider against simply holding the two tokens; it is symmetric and disappears if prices return to where they started. Loss-versus-rebalancing, or LVR, measures the provider against a sharper benchmark, a trader who holds the same shifting mix but rebalances at the true market price, and it captures the value arbitrageurs extract from the pool’s stale quotes. LVR is the more complete picture of what making markets with a formula actually costs.

What are Uniswap v4 hooks?

Hooks are smart contracts that a Uniswap v4 pool calls at set moments, such as before or after a swap or when liquidity changes, letting developers add custom logic to a standard pool. They can power dynamic fees, on-chain auctions, limit orders, or routing idle funds into lending markets. Hooks turn the AMM from a fixed formula into a programmable platform, at the cost of a new smart-contract attack surface.

Is providing liquidity to an AMM profitable in 2026?

It can be, but it is not automatic. A liquidity provider earns trading fees and has to beat several costs to net a profit: impermanent loss, loss-versus-rebalancing, MEV, and, on Uniswap, the new protocol fee that burns UNI. Passive positions in volatile, trending pairs often lose to a simple hold, while active management, correlated-asset pools, and newer designs such as dynamic fees and batch auctions try to tilt the odds back toward the provider.

Which AMM design is best for stablecoin trading?

StableSwap, the hybrid curve pioneered by Curve, is the standard for assets that should trade near a fixed ratio, such as USDC/USDT or stETH/ETH. It concentrates liquidity around the peg to offer very low slippage where nearly all the trading happens, then bends into a constant-product curve if the peg breaks. Plain constant-product pools waste most of their capital on prices a pegged pair never reaches.

What did the Uniswap UNIfication fee switch change for liquidity providers?

Approved by Uniswap governance in December 2025, UNIfication turned on protocol fees for the first time and burned 100 million UNI from the treasury. It diverts a slice of trading fees, for example cutting a v2 provider’s share from 0.30% to 0.25% and routing 0.05% to buy and burn UNI, away from liquidity providers and toward the protocol. For LPs it is another cost to overcome on top of impermanent loss, LVR, and MEV.

By Marcus Lindqvist, DeFi correspondent at HOGE Wire.