Impermanent Loss, LVR, and Selective Analysis Does AMM Have a Future?

Can AMM Sustain its Future? Evaluating Impermanent Loss, LVR, and Selective Analysis

Author: Stanley He, MetaWeb.VC Translation: Shanooba, LianGuai

An Automated Market Maker (AMM) is the cornerstone of all DeFi. Since Bancor and Uniswap v2 popularized the x y=k bonding curve, Constant Function Market Maker (CFMM) has almost become everyone’s first encounter with DeFi and cryptocurrencies. Many other CFMM bonding curves have been invented since then, but they still have the same properties as the old x y=k curve: path independence, always online liquidity, automated and passive token buying and selling, etc. People who provide liquidity for these AMMs have a glorious name: Liquidity Providers (LPs).

Limited Partners (LPs) have known from day one that they have an enemy: Impermanent Loss (IL). The art of LPing is to earn more income than IL losses (farming rewards and trading fees). Degens are pleased with this. However, when the bear market arrives and yields decline, the situation starts to change as new AMMs like Uniswap v3 pave the way for professional market makers and high-frequency traders (HFT) to enter DeFi. The likelihood of retail LPs incurring losses increases. Finally, the Megamind designed by thiccy, Crocswap team, and Anthony Lee Zhang tells us that LPs’ losses are not because they are bad traders but because the current AMM design has fundamental issues. Meanwhile, both on-chain and off-chain order books are thriving. So we have to ask: Does AMM have a future?

1. IL is the past, LVR is the new trend

IL compares the performance of CFMM LP positions with the portfolio of LPs holding the initial asset package (ignoring fees). For example, when the price of ETH is $1000, LP provides 1 ETH and 1000 USDC to the ETH-USDC Uni v2 pool. If the price of ETH then rises to $2000, the LP will hold about 0.7 ETH and approximately 1414 USDC, with a total value of $2828. If LP only holds 1 ETH and 1000 USDC in their wallet, they still have the same assets worth $3000. The difference of $172 is IL.

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IL occurs because CFMM sells assets when the price rises and buys assets when the price falls. In our example, as the ETH price rises, CFMM sells ETH along the way, resulting in a loss compared to holding the initial assets.

Some might ask, why does CFMM work this way? Why not buy assets when the price rises? The answer is passivity: liquidity on CFMM does not actively manage like an order book but simply reacts to trades passively. When the market price changes, the AMM needs to give traders a reason to trade on it and keep the AMM price in line with the market price. This reason is IL – LPs suffer from it, but traders who arbitrage CFMM prices and market prices benefit from it.

Limited partners do have another hope: price regression. A great feature of CFMM is that no matter how the price changes over a period of time, as long as it returns to the same point when LP entered, LP will hold the same batch of assets. In other words, IL equals 0.

However, new research suggests that even if the price recovers, limited partners still suffer losses. Furthermore, IL is not the only factor. Creating a new benchmark to reveal the inherent value leakage of CFMM.

1.1 Loss and Rebalancing, the Real Passive Cost

The benchmark used to calculate IL is the HODL strategy: you just need to hold the original assets. The problem or feature of this benchmark is that it is mainly composed of price risk. In our example, LP will incur losses because when the price of ETH rises, he now owns less ETH than the HODL strategy. If we isolate the price risk and compare the profit-making ability of limited partners with the strategy that always holds the same amount of risk assets as limited partners, what will be the result? By doing this, we get the Loss and Rebalancing (LVR).

LVR is based on the “rebalancing strategy”. The rebalancing strategy replicates CFMM’s trading by dynamically trading the underlying assets at market prices. In fact, it looks like this: whenever a trade is made on CFMM, for example, a trader swaps 1000 USDC for 1 ETH, a trade of the same amount of risk assets (ETH) will occur on Binance (assuming Binance prices are market prices with no fees and unlimited liquidity), selling 1 ETH for USDC. In this way, the rebalancing strategy will always have the same amount of risk assets as CFMM LP, eliminating the price risk that exists in the HODL strategy.

So, compared to the rebalancing strategy, will limited partners suffer losses? Yes, they will. LVR is a non-negative value. The losses come from price slippage: when the price changes on Binance, the price on CFMM remains the same, allowing arbitrageurs to profit from the trade. Assuming at t0, ETH prices on Binance and CFMM are both $900; at t1, the price on Binance rises to $1000 while the price on CFMM remains at $900. Now, a trader can buy ETH on CFMM at a price lower than $1000 and sell ETH on Binance for a profit. From the perspective of LP, they sell a small amount of ETH between $900 and $1000 until the price on CFMM reaches $1000. Compared to the simple rebalancing strategy of selling ETH at $1000, CFMM LP will suffer losses.

Compared to IL, LVR is the real “passive cost” (or is it? We’ll discuss it later): even when the impact of price fluctuations is eliminated, LP still incurs losses because their liquidity exists passively in the pool without being adjusted according to market price trends. Therefore, limited partners always execute transactions at prices lower than the market. In the words of a market maker, CFMM LP is constantly being “sniped” or “picked off.”

Please note that even if prices revert, it cannot solve LVR. In the case of price reversion, CFMM LP breaks even, but the rebalancing strategy is profitable.

Multiple empirical analyses have shown that LVR is a real phenomenon. This conclusive mark-up analysis of Uni LP demonstrates the real-life LVR by using Binance price mark-up for each transaction on Uniswap v2 ETH-USDC, and the results are as pessimistic as the theoretical predictions:

We can see that overall, the LP for the ETH-USDC currency pair on Uni v2 has been consistently in a loss compared to the rebalancing strategy. And those LPs that have the lowest fee level (0.05%) performed poorly.

1.2 Order Flow Toxicity: Understanding Leverage Ratios (LVR) from a Different (Simpler) Perspective

Generally, market makers/liquidity providers face two types of order flow. Informed flow refers to orders initiated by traders who have better price information than the MM. These orders drive organic price movements of assets and are welcomed by market makers as they are typically profitable. Toxic flow, or informed flow, refers to orders initiated by traders who have better price information than the MM. Arbitrage is an example where the trader has better price information (the price of market A is higher than market B) and profits from buying low in market B and selling high in market A. In this case, both MM in market A and B incur losses. In tradfi, MM works hard to differentiate between informed and uninformed flows and differentiates them by providing different spreads.

CFMM LPs also face uninformed and toxic flows. Arbitragers who keep the CFMM price in line with the Binance price are toxic flows, leading to losses for LPs, as shown above. At the same time, naïve users on the chain contribute uninformed flows – when I swap ETH for PEPE, I’m clearly not arbitraging (Jaredfromsubway is), I’m just looking for the 100x. Uninformed flows do not know the true price and can contribute profits to the MM/LP.

When we look at the rebalancing strategy (the benchmark for LVR) from the perspective of order flow toxicity, it becomes clear what it is doing:

The rebalancing strategy filters out profits from uninformed flow and losses from toxic flow.

Since all trades are executed at real market prices, order flow toxicity (both positive and negative) is completely eliminated. Through the rebalancing strategy, market makers earn/lose zero from “market making,” and their profit and loss only come from Delta (price changes of risky assets in the portfolio).

Based on this understanding, a question arises: why is LVR strictly positive? Or why do LPs always incur losses (excluding fees) when rebalancing? While the rebalancing strategy eliminates losses from toxic flows, it also sacrifices profits from uninformed flows! Wouldn’t there be cases where the profits exceed the losses, resulting in higher returns for LPs (excluding fees) compared to rebalancing?

The short answer is no.
The reality is that CFMM LPs can never profit from uninformed flows. Instead, almost all information is leaked to arbitrageurs and frontrunners in the form of MEV. For example, let’s assume that the current price on CFMM is the same as on Binance, where 1 ETH = 1000 USDC. An uninformed DeFi user decides to acquire more ETH on-chain, so they exchange 120,000 USDC for 100 ETH on CFMM, or purchase 100 ETH at a price of 1 ETH = 1200 USDC, which is significantly higher than the actual market price on Binance. After this swap, CFMM LP records an unrealized profit of 20,000 USDC, which could be realized if all liquidity is immediately withdrawn from the pool. However, this unrealized profit is short-lived. In most cases, a frontrunning transaction by an arbitrageur follows the naive transaction of the poor DeFi user, selling 100 ETH for approximately 120,000 USDC, completely depriving the LP of their unrealized profit, while only paying a small transaction fee. And here comes MEV again.
Therefore, from the perspective of order flows, what’s happening is clear:
LPs lose most of the profit from uninformed flows to MEV, but fully bear the losses of informed flows.
This is not a fair game.

2. Optionality: It’s one thing, but not everything

Thanks to Professor Lambert’s relentless efforts, it’s well known that providing single-sided liquidity in Uni v3 is equivalent to selling put options. LP = short put options.

As LPs are now option sellers, they short volatility, meaning they hope to sell volatility at a high price, but in reality, they won’t let the option buyers lose money, which ultimately decreases the bet on volatility. In terms of options, the ideal scenario for an option seller is to sell options when the implied volatility (IV) is high and the realized volatility (RV) at expiration is ultimately lower than IV. IV > RV, Option seller wins. Translated into AMM LPing language, it basically means LPs want to start LPing when liquidity is low and trading volumes are high (meaning IV is high) and exit the position before the trading volume/liquidity ratio becomes too low or prices diverge too much. The entry point (which means IV is now more likely to be smaller than RV).
Interestingly, when looking at LPing from an options perspective, everything we have discussed so far about IL, LVR, toxic flows, etc., seems to become irrelevant! IL is no longer a “loss”—you just bet wrongly, and RV ends up being larger than IV. LVR is not a loss either—it’s the only value LPs provide to traders (a commitment to buy/sell assets at a predetermined price), for which traders have to pay a fee to buy. So LPs just need to make sure LVR < cost, just like an options seller. Toxic flows are orthogonal to the problem—why would I care if a trade is "toxic" as long as it contributes trading fees?

LianGuainoptic Finance is built on these insights, supporting borrowing and lending of Uni v3 positions to help more experienced options traders sell options more efficiently through AMMs. Regular people can deposit money into the lending pool, providing liquidity to professionals and therefore earning a more stable interest rate.

Problem solved… right?

2.1 Why Options Premium ≠ AMM Trading Fee

When buying options on LianGuainoptic, one essentially “borrows” LP positions and then sells them, hence the issue of option pricing – how much premium should the buyer pay? The parity between Uni v3 LP positions and short options makes it surprisingly easy: the buyer only needs to pay the trading fee that the LP position would have earned without borrowing. In simpler terms, since 1) options sellers earn option premiums only by selling options, 2) LPs earn trading fees only by providing liquidity, and 3) selling options = providing liquidity, therefore 4) option premiums = trading fees. In fact, the option premium convergence called “streamia” in LianGuainoptic and in research indeed indicates that Streamia converges with the Black-Scholes model (a model used to price options) on equivalent traditional options.

Let’s review what we’ve discovered so far:

1. CFMM limited partners are making losses.

2. Losses stem from passivity, manifested as LVR.

3. From the perspective of options, LVR itself is the commodity being sold, and LPs have already been fairly compensated through trading fees.

This seems to suggest that AMMs do not need much improvement and LPs should accept the reality.

But is that really the case?

Let’s conduct a simple thought experiment: what if we auctioned off the arbitrage rights of the CFMM pools and distributed the proceeds to LPs? Ignoring the implementation details, this would strictly increase the profits for limited partners – from the perspective of order flow toxicity, it would decrease toxic flow (thus reducing losses) and directly channel some of the profits from uninformed liquidity providers to limited partners. If limited partners in such pools lent their positions to options buyers, they would obviously charge a higher premium because limited partner positions would yield higher returns than regular AMMs. So do we now have to price options differently just because limited partners are earning more? Do we need to rewrite the Black-Scholes model to accommodate the new results?

The answer is clearly no. To understand the differences, we must recognize that although AMM LPs do provide selectivity, it is not the only thing they provide. The “options” sold by limited partners are almost entirely consumed by arbitrageurs, who already know they will profit before entering the trade – that’s the definition of arbitrage and toxic flow. In other words, these “options” are only purchased when limited partners are at a loss. Yes, the arbitrageurs need to pay fees, but it’s on the condition that net profit is positive. Because arbitrage currently dominates most of the on-chain trading volume, it’s no surprise that the trading fees (largely contributed by arbitrageurs) tend to fall short of the option premiums calculated by BSM (which should be paid by options buyers, also arbitrageurs).

However, this is just part of the story – unsuspecting liquidity providers are not buying options! When naive or corrupt on-chain swappers swap in a CFMM pool, they don’t have “selectivity” in mind. Instead, they just need some liquidity to acquire another asset and are willing to pay for the service. Although their trading volume cannot be compared to arbitrage, it should have brought actual profits to the limited partners, but the options perspective failed to capture that.

In short, limited partners are losing money.

3. Passive Liquidity and MEV Supply Chain

The CFMM design has reached a deadlock, especially for passive liquidity providers. Uni v3 style concentrated liquidity AMMs are very similar to order books and require active management, essentially forcing LPs to become professional market makers. Automated strategies based on concentrated liquidity AMMs, such as Maverick, only work for pegged assets (e.g., USDT-USDC), and you may still incur losses due to rebalancing as each rebalance turns into a permanent loss. Black-box marketmaking treasuries like Hyperliquid and Elixir essentially operate on a “trust me, bro” mode, accepting user deposits and making markets on order books. Additionally, more oracle-based DEXs give price discovery to Binance, raising questions about why a “dex” was needed in the first place. AMMs are failing. Just look at how many protocols are ditching AMMs or virtual AMMs in favor of order books/RFQs (this is more evident in derivative protocols like Drift, Perpetual, Lyra, etc.).

If passive means loss, then the future of on-chain liquidity looks bleak. But at least now we know that LVR is not a necessary passive cost because if it were, there shouldn’t be a way to reduce it. But our thought experiment suggests that it can be done through changing market structures.

From a high-level perspective, a more profitable way to provide passive liquidity may not be within the CFMM design space, but rather through MEV. You know who else is passive? Validators. Who can profit the most from MEV (or fully-extractable value created on a blockchain)? Validators. PBS (proposer and builder separation) frees validators from actively constructing blocks and still manages to direct most of the value to them through competitive auctions. Why can’t the same happen for limited partners?

The thought experiment of auctioning CFMM pool arbitrage rights is not my invention. McAMM, a mechanism for capturing MEV in AMMs, was first proposed last year and the community’s interest is growing stronger. I believe we are very close to the first working instance of McAMM. The main focus is on the execution side: how do we conduct an auction? Will it add another centralized layer to our already fairly centralized MEV supply chain (similar to PBS’s MEVBoost)? Is it achievable on-chain? If so, will the auction itself cause more MEV leakage? How do we fairly return the captured MEV to LPs?

From the perspective of MEV, the profitability of CFMM LP is part of a bigger issue: how do we ensure a fair representation of the value created by different participants in the crypto currency? In my opinion, Cosmos has the best answer so far: ABCI++, an interface between the application layer and the consensus layer, gives more participants (dapps, users, DAOs) a say in how consensus should work and how transactions should be ordered. In Ethereum, we have PEPC, a more general framework that allows proposers (validators) to input binding commitments outside of Ethereum consensus. In theory, both designs will enable fairer MEV distribution, as LPs can express their preferences even when providing passive liquidity. McAMM or other designs based on similar principles can be built in a decentralized manner.

So, does AMM have a future? The answer is yes, but we need to act fast. Passive liquidity providers are the cornerstone of DeFi, and if their value creation is not fairly rewarded, they may leave.

Thanks to Professor Lambert’s relentless efforts, it is well known that providing single-sided liquidity in Uni v3 is equivalent to selling put options. LP = short put options.

As limited partners are now option sellers, they are shorting volatility, meaning they want to sell volatility at high prices but won’t actually make the option buyers lose money, which ultimately reduces the bet on volatility. In terms of option jargon, the ideal situation for an option seller is to sell options when the implied volatility (IV) is high and the realized volatility (RV) at expiration is lower than IV. IV > RV, and the option sellers win. In AMM LPing language, it basically means that LPs want to start LPing when the pool has low liquidity but high trading volume (i.e., high IV), and exit before the trading volume/liquidity ratio becomes too low or the price deviates too much. The entry point (which means IV is now more likely to be smaller than RV).

Interestingly, when looking at LPing from an options perspective, all the things we’ve discussed so far (IL, LVR, toxic flow…) seem to become irrelevant! IL is no longer a “loss” – you just made an unfortunate wrong bet, and RV ends up being bigger than IV. LVR is also not a loss – it’s the only value LPs provide to traders (a commitment to buy/sell assets at predetermined prices), for which traders have to pay. So, LPs just need to make sure LVR < cost, just like option sellers. Toxic flow is orthogonal to the problem – as long as it contributes trading fees, why should I care if the trade is "toxic"?

LianGuainoptic Finance is built on these insights, supporting borrowing and lending of Uni v3 positions to help more experienced options traders sell options more efficiently through AMMs. Regular people can deposit money into the lending pool, providing liquidity to professionals and earning more stable interest rates.

The problem is solved… right?

2.1 Why is the option fee ≠ AMM transaction fee?

Buying options on LianGuainoptic essentially involves “borrowing” LP positions and then selling them, which raises the issue of option pricing – how much premium should the buyer pay? The fair value between Uni v3 LP positions and short options makes it surprisingly easy: the buyer only needs to pay the transaction fee that the LP position should have earned without borrowing. In other words, because 1) option sellers only earn option fees by selling options, 2) LPs only earn transaction fees by providing liquidity, 3) selling options = providing liquidity, therefore 4) option fees = transaction fees. In fact, the option premium known as “streamia” in LianGuainoptic and research does indicate that Streamia converges with the Black-Scholes model (the model used to price options) on equivalent traditional options.

Let’s recap what we have discovered so far:

1. CFMM LPs are experiencing losses.

2. Losses are passive and reflected in LVR.

3. From the perspective of options, LVR itself is the commodity being sold, and LPs have been fairly compensated through transaction fees.

This seems to suggest that AMM does not need much improvement and LPs should accept reality.

But is that really the case?

Let’s do a simple thought experiment: what if we auction off the arbitrage rights of the CFMM pool and give the profits to LPs? Ignoring implementation details, this would strictly increase the returns of the LPs – from the perspective of order flow toxicity, it would reduce toxic flow (thus reducing losses) and direct some of the profits from uninformed flows directly to LPs. If LPs in such pools lend their positions to option buyers, they would obviously charge a higher premium because LP positions would earn higher returns than regular AMMs. Do we then have to price options differently just because LPs are earning more? Do we have to rewrite the Black-Scholes model to accommodate the new results?

The answer is obviously no. To understand the difference, we must recognize that while AMM LPs do provide selectivity, that is not the only thing they provide. The “options” sold by LPs are almost entirely consumed by arbitrageurs who know they will profit before entering the trade – that is the definition of arbitrage and toxic flow. In other words, these “options” are only bought when LPs are experiencing losses. Yes, arbitrageurs have to pay fees, but only if their net profit is positive. Because arbitrage currently accounts for the majority of on-chain trading volume, it’s not surprising that transaction fees (mostly contributed by arbitrage) tend to be lower than the option premiums calculated by the BSM (which should be paid by option buyers, also arbitrageurs).

However, this is only part of the story – the unsuspecting liquidity providers are not buying options! When those naive or corrupt on-chain traders exchange in the CFMM pool, they definitely don’t have “selectivity” in their minds. Instead, they just need some liquidity to acquire another asset and are willing to pay for the service. Although their trading volume cannot compare with arbitrage, it should have brought actual profits to the limited partners. However, it fails to capture it from the perspective of options.

In summary, the limited partners are losing money while selling options and liquidity, so it is not enough to assess whether CFMM’s limited partners are receiving fair payments based solely on option pricing.

The limited partners are losing money.

3. Passive Liquidity and MEV Supply Chain

CFMM design has reached an impasse, especially for passive liquidity providers. The centralized liquidity AMM of the Uni V3 type is very similar to an order book and requires active management, essentially forcing LPs to become professional market makers. Automated strategies based on centralized liquidity AMM (i.e., Maverick) only work for paired assets (such as USDT-USDC), and you may still incur losses due to rebalancing, as each rebalance turns into a permanent loss. There are black-box market-maker vaults like Hyperliquid and Elixir that operate on a “trust me, bro” model, accepting user deposits and market-making on the order book. In addition, more oracle-based DEXs have ceded price discovery to Binance, which raises questions about why a “dex” was needed in the first place. AMMs are failing. Just look at how many protocols have abandoned AMMs or virtual AMMs and switched to order book/quoting (this situation is more obvious in derivative protocols like Drift, Perpetual, Lyra, etc.).

If passive implies losses, then the future of on-chain liquidity is bleak. But at least now we know that LVR is not a necessary passive cost because if it were, there shouldn’t be a way to reduce it. But our thought experiment indicates that it can be done by changing the market structure.

From a high-level perspective, a more profitable way to incentivize passive liquidity supply may not lie within the CFMM design space, but within MEV. You know who else is passive? Validators. Who can benefit the most from MEV (or fully extractable value created on the blockchain)? Validators. PBS (Proposers and Builders Separation) frees validators from actively constructing blocks and still manages to guide most of the value to them through competitive auctions. Why can’t the same happen to limited partners?

The thought experiment of auctioning CFMM pool arbitrage rights is not my invention. MEV-capturing AMM (McAMM) was first proposed last year, and the community’s interest is growing. I believe we are very close to the first working example of McAMM. The main focus is on the execution: how do we conduct the auction? Would it add another central layer in our already fairly centralized MEV supply chain (like MEVBoost for PBS)? Can it be implemented on-chain? If so, would the auction itself cause more MEV leakage? How do we fairly return the captured MEV to LPs?

From the perspective of MEV, the profitability of CFMM LP is a big part of the problem: how do we ensure fair representation of the value created by different participants in the cryptocurrency? IMO Cosmos has the best answer so far: ABCI++, an interface between the application layer and the consensus layer that allows more participants (dapps, users, DAOs) to have a say in how consensus should operate and how transactions should be ordered. In Ethereum, we have PEPC, a more general framework that allows proposers (validators) to input binding commitments outside of Ethereum’s consensus. In theory, both of these designs will allow for fairer distribution of MEV because LPs can express their preferences even while providing liquidity passively. McAMM or other similar designs can be built in a decentralized manner.

So, does AMM have a future? The answer is yes, but we need to act quickly. Passive liquidity providers are the backbone of DeFi, and if they don’t receive fair compensation for the value they create, they may leave.

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