IL, LVR and Optionality: Do AMMs Have a Future?
Automated Market Maker (AMM) is the very bedrock of all DeFi. Ever since Bancor and Uniswap v2 popularized the xy=k bonding curve, Constant Function MM (CFMM) has become almost everyone’s first experience with DeFi and crypto. Many other CFMM bonding curves have been invented after, but at the core they still share the same properties of the good old xy=k: path-independence, always-on liquidity, selling and buying tokens automatically and passively, etc. And those who provide liquidity to those AMMs share a glorious name: Liquidity Provider (LP).
LPs know from day one that they have an enemy: Impermanent Loss (IL). The art of LPing is to earn more (farming rewards & trading fees) than what you lose to IL. And degens have been fine with it. However, things started to change when bear market kicked in, bringing yield down, and new AMMs like Uniswap v3 paved the way for professional market makers and high-frequency-traders (HFT) to enter DeFi. Retail LPs are increasingly likely to lose money. And finally, the gigabrain works by thiccy, the Crocswap team, and Anthony Lee Zhang show us that LPs are losing money not because they are bad traders, but because there’s something fundamentally BROKEN in the current AMM design. Meanwhile, orderbooks are thriving on-and-off-chain. Hence we have to ask: Do AMMs still have a future?
1. IL is the past. LVR is the new inevitability
IL compares the performance of a CFMM LP position to a portfolio which holds the LP’s initial bundle of assets (ignoring fees). For example, an LP provided 1 ETH and 1000 USDC to ETH-USDC Uni v2 pool when ETH price was $1000. If later ETH price increases to $2000, the LP will be holding ~0.7 ETH and ~1414 USDC, worth a total of $2828. If the LP simply held 1 ETH and 1000 USDC in his wallet, he would still have the same assets which would be worth $3000. The $172 difference here is IL.
IL is caused by the fact that the CFMM sells asset when price goes up, and buys asset when price goes down. In our example, ETH price goes up, and the CFMM sells ETH along the way, resulting in a loss compared to holding the initial assets.
Some may ask, ‘why does the CFMM work like this? Why doesn’t it buy asset when price goes up’? The answer is passiveness: liquidity on the CFMM isn’t actively managed like on an orderbook, instead it only passively reacts to trades. When market price changes, the AMM needs to give traders a reason to trade on it and bring the AMM price in line with the market price. This reason is IL — LPs suffer from it, but traders who arbitrage the CFMM price and the market price benefit from it.
LPs do have another hope: price reversion. A nice property of CFMM is that no matter how price has changed during a period of time, as long as it goes back to the same point when the LP entered, the LP will be holding the same bundle of assets. In other words, IL equals zero.
However, new studies show that even when price reverts, LPs are still losing money. Moreover, IL isn’t the sole truth. A new benchmark is created to reveal the inherent value leakage in CFMM.
1.1 Loss-Versus-Rebalancing, the true passiveness cost
The benchmark used when calculating IL is HODL strategy: you simply hold the original assets. The problem, or feature, of this benchmark is that it mostly consists of price risk. In our example, the LP incurs a loss because he now has less ETH than HODL strategy when ETH price goes up. What if we isolate the price risk away, i.e., benchmarking LP profitability to a strategy that always has the same amount of risky asset as the LP? By doing so, we get Loss-Versus-Rebalancing (LVR).
LVR uses “rebalancing strategy” as benchmark. The rebalancing strategy replicates the CFMM’s trades by dynamically trading the underlying asset at market prices. In reality it looks like this: Whenever a trade is done on the CFMM, i.e. a trader swaps 1000 USDC for 1 ETH, a trade with same amount of the risky asset (ETH) happens on Binance (assuming Binance price is the market price, zero fee and infinite liquidity), i.e., selling 1 ETH for USDC. In this way, the rebalancing strategy will always have the same amount of risky asset as the CFMM LP, thus eliminating the price risk that’s present in the HODL strategy.
So are LPs losing money compared to rebalancing strategy? Yes they are. LVR is non-negative. The loss comes from price slippage: when price on Binance changes, the price on the CFMM stays stale, therefore making it profitable for arbitragers to trade against. Let’s say at t0, price of ETH on both Binance and the CFMM is $900; at t1, price on Binance increases to $1000, while on the CFMM it stays at $900. Now a trader can buy ETH at the CFMM at a price lower than $1000 and sell ETH at Binance for profit. From LPs’ perspective, they are selling a tiny amount of ETH at every price between $900 and $1000, until price on the CFMM reaches $1000. Compared to the rebalancing strategy, which simply sells ETH at $1000, CFMM LPs take a loss.
Compared to IL, LVR is the true “passiveness cost” (or is it? We will get back to it later): even with the impact from price variation eliminated, LPs still lose money because their liquidity passively sits in the pool, without being adjusted according to market price movement. Therefore, LPs are always executing trades at worse-than-market price. In market makers’ terms, CFMM LPs are constantly “sniped” or “picked-off”.
Note that even price reversion cannot solve LVR. In the case of price reversion, CFMM LP breaks even, but the rebalancing strategy makes a profit.
Multiple empirical analyses have been done and shown that LVR is real. This conclusive piece of markout analysis of Uni LPs demonstrated LVR in real life by marking out every trade on Uniswap v2 ETH-USDC pairs using Binance price, and the result is as pessimistic as the theory predicts:
We can see that Uni v2 LPs of the ETH-USDC pairs, in aggregate, have been strictly losing money compared to the rebalancing strategy. And those who LP for the lowest fee tier (0.05%) are down BAD.
1.2 Orderflow toxicity: Understand LVR from a different (an easier) perspective
In general, there are two types of orderflows faced by market makers/liquidity providers. Uninformed flow refers to orders initiated by traders who don’t have better information on price than MMs. Those orders drive the organic price movement of assets, and are welcomed by MMs because they are usually profitable to make. Informed flow, or toxic flow, refers to orders initiated by traders who have better information on price than MMs. Arbitrage is one example, where traders have better information on price than MMs (price on market A is higher than price on market B), and make profit by buying low on market B, selling high on market A. In this case, MMs on both market A and market B take a loss. In tradfi, MMs try very hard to differentiate between informed and uninformed flow, and discriminate them by offering different spreads.
CFMM LPs are faced with both uninformed and toxic flows too. Arbitragers who bring the price on the CFMM in line with Binance are toxic flow, and incurring loss to LPs, as shown above. At the same time, on-chain naive users contribute uninformed flow — when I swapped ETH for PEPE, I obviously wasn’t arbitraging (Jaredfromsubway was), but simply just looking for a 100x. Uninformed flow doesn’t know the true price, thus could contribute gains to the MMs/LPs.
When we look at the rebalancing strategy, the benchmark for LVR, from orderflow toxicity angle, then what it is doing is very clear:
The rebalancing strategy filters out both gains from uninformed flow and losses from toxic flow.
Since all trades are executed at the true market price, orderflow toxicity, both positive and negative, is completely eliminated. With the rebalancing strategy, MMs earn/lose zero from “making markets”, instead their PnL is solely from delta (the price change of the risky asset in the portfolio).
Based on this understanding, a questions emerges: Why is LVR strictly positive? Or why are LPs always losing (before fees) against rebalancing? The rebalancing strategy eliminates losses from toxic flow, but also gives up gains from uninformed flow! Wouldn’t there be a case where the gains outweigh the losses, and LPs make higher return (before fees) than rebalancing?
Short answer is NO.
The reality is, CFMM LPs never get to bag the profit made from uninformed flow, instead, almost all of it is leaked to validators and searchers in the form of MEV. For example, suppose the current price on the CFMM was the same with the price on Binance, say 1 ETH = 1000 USDC. An uninformed DeFi user decided to hold more ETH on-chain, thus swapped 120,000 USDC for 100 ETH from the CFMM, or bought 100 ETH at a price of 1 ETH = 1200 USDC, significantly higher than the true market price on Binance. Right after this swap, the CFMM LPs recorded a 20,000 USDC unrealized profit, which could be realized if all liquidity was immediately withdrawn from the pool. However, this unrealized profit is ephemeral. In most cases, a “backrun” transaction by a searcher will follow right after this naive transaction from the poor DeFi user, selling 100 ETH for ~120,000 USDC, fully stripping the unrealized profit away from LPs, leaving them with only a small transaction fee. MEV, here we go again.
So from orderflow perspective, what’s happening is clear:
LPs LOSE most of the gains from uninformed flow to MEV, but FULLY BEAR the losses from informed flow.
It’s not a fair play.
2. Optionality: It’s a thing, but not everything
Thanks to Professor Lambert’s relentless effort, it’s already common knowledge that providing single-tick liquidity at Uni v3 has a payoff identical to selling a put option. LP = Short put.
Since LPs are now option sellers, they are short volatility, meaning they want to sell volatility for a high price without actually losing money to option buyers, which is a bet on volatility ends up low. With option terminologies, the ideal scenario for option sellers is to sell option when implied volatility (IV) is high and the realized volatility (RV) ends up lowers than IV when the option expires. IV > RV, option sellers win. Translated into AMM LPing language, it basically says LPs want to start to LP when a pool has low liquidity and high volume (which means high IV), and exit the position before volume/liquidity ratio becomes too low or the price deviates too much from the entry point (which means IV is now much more likely to be smaller than RV)
What’s magical is that, when looking at LPing from option perspective, everything we’ve discussed so far (IL, LVR, toxic flow…) seems to become irrelevant! IL isn’t “loss” anymore — you just unfortunately betted on the wrong side, and RV ended up bigger than IV. LVR isn’t loss either — it is the sole value that LPs provide to traders (the commitment to buy/sell assets at a pre-determined price), and traders buy it with fees. So LPs just need to make sure LVR < fees, again just like option sellers. Toxic flow becomes orthogonal to the question — as long as it contributes trading fees, why should I care about whether a trade is “toxic” or not?
Panoptic Finance is founded on those insights, enabling borrowing and lending of Uni v3 positions to help more sophisticated option traders to write options via AMM more efficiently. And normies can just deposit their money into a lending pool to provide liquidity for the professionals, earning a more stable interest rate.
Problem solved….right?
2.1 Why option premium ≠ AMM trading fee
Buying options in Panoptic is essentially “borrowing” an LP position and then selling it, thus there’s the problem of option pricing — how much should the buyer pay as premium? The parity between Uni v3 LP position and short option makes it surprisingly easy: the buyer just pays the trading fee that would’ve been earned by the LP position if it wasn’t borrowed. More intuitively, since 1) option sellers only earn option premium for selling option, and 2) LPs only earn trading fees for providing liquidity, and 3) selling option = providing liquidity, thus 4) option premium = trading fee. Indeed, option premia is called “streamia” in Panoptic and research does suggest that streamia converges to the result from Black-Scholes Model (the one people use to price options) on an equivalent traditional option.
A recap on what we’ve discovered so far:
- CFMM LPs are losing money.
- The loss arises from passiveness, embodied by LVR.
- From option perspective, LVR is in itself the good being sold, and LPs are already fairly compensated by trading fees.
This seems to suggest that no much improvement is needed for AMMs, and LPs should just accept the reality.
Is this the case though?
Let’s do a simple thought experiment: what if we auction off the right to arbitrage a CFMM pool, and give the proceed to LPs? Leave implementation details aside, this would strictly improve LP’s payoff — from orderflow toxcity perspective, it would reduce the amount of toxic flow (thus the loss), and direct part of the gains from uninformed flow to the LPs. If an LP from such a pool lends his position to an option buyer, he would obviously charge for higher premium, since LP position would have been earning a higher return than in a vanilla AMM. So now we have to price option differently, simply because the LP is earning more? Do we have to rewrite Blach-Scholes Model to fit the new result?
The answer is obviously no. And to see what there’s a discrepancy, we have to realize that although AMM LPs are indeed providing optionality, it’s not the ONLY thing they provide. The “options” sold by LPs are almost entirely consumed by arbitrageurs who already knew they are going to make a profit even before entering the trade — that’s the definition of an arbitrage and toxic flow. In other words, those “options” will only be bought in cases where LPs lose money. Yes arbitrageurs pay fees, but only when net profit is positive. Since arbs make up most of the volume on-chain right now, it’s not surprising that trading fees (that are mainly contributed by arbs) converge to option premium (that’s supposed to be paid by option buyers, again arbers) calculated by BSM.
However, that’s only part of the story — uninformed flow isn’t buying options! When those naive or degen on-chain swappers make swaps in a CFMM pool, they certainly don’t have “optionality” in their heads. Instead they just need some liquidity which allows them to get another asset, and are willing to pay for the service. Although their volume is no comparison to arbs, it is suppose to bring real gains to LPs, but fails to be captured by the option perspective.
So to sum it up, LPs are selling options AND liquidity, therefore option pricing isn’t sufficient when it comes to evaluating whether CFMM LPs are receiving fair payout.
LPs are losing money.
3. Passive liquidity and the MEV supply chain
CFMM design has entered a dead end, especially for passive liquidity providers. Uni v3 type of concentrated liquidity AMM is very similar to orderbooks, which requires active management, basically forcing LPs to become professional market makers. Automated strategies on top of concentrated liquidity AMM (i.e., Maverick) only work for pegged assets (like USDT-USDC), and you can still lose money from rebalancing, since every rebalance turns impermanent loss permanent. There are blackbox market making vaults like Hyperliquid and Elixir that basically work on a “trust me bro” model, taking users deposits and make markets on orderbooks. Also there are more oracle-based DEXes that give up price discovery to Binance, making people question why the need to build a “dex” in the first place. AMMs are losing. Just look at how many protocols have given up on AMM or virtual AMM and turned to orderbooks/RFQ (this happens more significantly with derivative protocols, like Drift, Perpetual, Lyra, etc.).
If passiveness means taking loss, the future will be dim for on-chain liquidity. But at least we now know that LVR is NOT the necessary passiveness cost, because if it was, then there shouldn’t be a way to reduce it. But our thought experiment shows that it is possible to do so with a change in market structure.
On the high level, the way to make passive liquidity provision more profitable is likely outside the CFMM design space, instead lies in MEV. You know who’s also passive? Validators. And who’s getting the most out of MEV (or the totally extractable value created on a blockchain)? Validators. PBS (Proposer-Builder Separation) has freed validators from actively building blocks and still manages to direct most of the value towards them with competitive auctions. Why can’t the same scenario happen to LPs?
The thought experiment of auctioning off the right to arbitrage a CFMM pool isn’t my invention. MEV capturing AMM (McAMM) was first proposed last year and is seeing increasing interest from the community. I believe we are very close to the first working instantiation of McAMM. The questions are mostly on the execution side: How do we conduct the auction? Is it going to add another centralized layer (just like MEVBoost for PBS) to our already quite centralized MEV supply chain? Is it possible to do it on-chain? If so will the auction itself create more MEV leakage? How to fairly return the captured MEV to LPs?
From MEV perspective, CFMM LP profitability is part of a bigger problem: How do we ensure fair representation of value created by different participants in crypto? IMO Cosmos has by far the best answer: ABCI++, the interface between application layer and consensus layer that empowers more participants (dapps, users, DAOs) to have a say in how consensus should work and how transactions should be ordered. In Ethereum we have PEPC, a more generic framework that allows proposers (validators) to enter binding commitments outside Ethereum consensus. Both designs would theoretically allow a more equitable MEV distribution since LPs would be able to express their preferences even if they stay passive when providing liquidity. McAMM, or other designs with similar principles, could then be built in a decentralized way.
So do AMMs have a future? The answer is yes, but we need to move fast. Passive liquidity providers are the backbone of DeFi, and they may leave if they don’t get rewarded fairly for value they created.
Thanks to Professor Lambert’s relentless effort, it’s already common knowledge that providing single-tick liquidity at Uni v3 has a payoff identical to selling a put option. LP = Short put.
Since LPs are now option sellers, they are short volatility, meaning they want to sell volatility for a high price without actually losing money to option buyers, which is a bet on volatility ends up low. With option terminologies, the ideal scenario for option sellers is to sell option when implied volatility (IV) is high and the realized volatility (RV) ends up lowers than IV when the option expires. IV > RV, option sellers win. Translated into AMM LPing language, it basically says LPs want to start to LP when a pool has low liquidity and high volume (which means high IV), and exit the position before volume/liquidity ratio becomes too low or the price deviates too much from the entry point (which means IV is now much more likely to be smaller than RV)
What’s magical is that, when looking at LPing from option perspective, everything we’ve discussed so far (IL, LVR, toxic flow…) seems to become irrelevant! IL isn’t “loss” anymore — you just unfortunately betted on the wrong side, and RV ended up bigger than IV. LVR isn’t loss either — it is the sole value that LPs provide to traders (the commitment to buy/sell assets at a pre-determined price), and traders buy it with fees. So LPs just need to make sure LVR < fees, again just like option sellers. Toxic flow becomes orthogonal to the question — as long as it contributes trading fees, why should I care about whether a trade is “toxic” or not?
Panoptic Finance is founded on those insights, enabling borrowing and lending of Uni v3 positions to help more sophisticated option traders to write options via AMM more efficiently. And normies can just deposit their money into a lending pool to provide liquidity for the professionals, earning a more stable interest rate.
Problem solved….right?
2.1 Why option premium ≠ AMM trading fee
Buying options in Panoptic is essentially “borrowing” an LP position and then selling it, thus there’s the problem of option pricing — how much should the buyer pay as premium? The parity between Uni v3 LP position and short option makes it surprisingly easy: the buyer just pays the trading fee that would’ve been earned by the LP position if it wasn’t borrowed. More intuitively, since 1) option sellers only earn option premium for selling option, and 2) LPs only earn trading fees for providing liquidity, and 3) selling option = providing liquidity, thus 4) option premium = trading fee. Indeed, option premia is called “streamia” in Panoptic and research does suggest that streamia converges to the result from Black-Scholes Model (the one people use to price options) on an equivalent traditional option.
A recap on what we’ve discovered so far:
- CFMM LPs are losing money.
- The loss arises from passiveness, embodied by LVR.
- From option perspective, LVR is in itself the good being sold, and LPs are already fairly compensated by trading fees.
This seems to suggest that no much improvement is needed for AMMs, and LPs should just accept the reality.
Is this the case though?
Let’s do a simple thought experiment: what if we auction off the right to arbitrage a CFMM pool, and give the proceed to LPs? Leave implementation details aside, this would strictly improve LP’s payoff — from orderflow toxcity perspective, it would reduce the amount of toxic flow (thus the loss), and direct part of the gains from uninformed flow to the LPs. If an LP from such a pool lends his position to an option buyer, he would obviously charge for higher premium, since LP position would have been earning a higher return than in a vanilla AMM. So now we have to price option differently, simply because the LP is earning more? Do we have to rewrite Blach-Scholes Model to fit the new result?
The answer is obviously no. And to see what there’s a discrepancy, we have to realize that although AMM LPs are indeed providing optionality, it’s not the ONLY thing they provide. The “options” sold by LPs are almost entirely consumed by arbitrageurs who already knew they are going to make a profit even before entering the trade — that’s the definition of an arbitrage and toxic flow. In other words, those “options” will only be bought in cases where LPs lose money. Yes arbitrageurs pay fees, but only when net profit is positive. Since arbs make up most of the volume on-chain right now, it’s not surprising that trading fees (that are mainly contributed by arbs) converge to option premium (that’s supposed to be paid by option buyers, again arbers) calculated by BSM.
However, that’s only part of the story — uninformed flow isn’t buying options! When those naive or degen on-chain swappers make swaps in a CFMM pool, they certainly don’t have “optionality” in their heads. Instead they just need some liquidity which allows them to get another asset, and are willing to pay for the service. Although their volume is no comparison to arbs, it is suppose to bring real gains to LPs, but fails to be captured by the option perspective.
So to sum it up, LPs are selling options AND liquidity, therefore option pricing isn’t sufficient when it comes to evaluating whether CFMM LPs are receiving fair payout.
LPs are losing money.
3. Passive liquidity and the MEV supply chain
CFMM design has entered a dead end, especially for passive liquidity providers. Uni v3 type of concentrated liquidity AMM is very similar to orderbooks, which requires active management, basically forcing LPs to become professional market makers. Automated strategies on top of concentrated liquidity AMM (i.e., Maverick) only work for pegged assets (like USDT-USDC), and you can still lose money from rebalancing, since every rebalance turns impermanent loss permanent. There are blackbox market making vaults like Hyperliquid and Elixir that basically work on a “trust me bro” model, taking users deposits and make markets on orderbooks. Also there are more oracle-based DEXes that give up price discovery to Binance, making people question why the need to build a “dex” in the first place. AMMs are losing. Just look at how many protocols have given up on AMM or virtual AMM and turned to orderbooks/RFQ (this happens more significantly with derivative protocols, like Drift, Perpetual, Lyra, etc.).
If passiveness means taking loss, the future will be dim for on-chain liquidity. But at least we now know that LVR is NOT the necessary passiveness cost, because if it was, then there shouldn’t be a way to reduce it. But our thought experiment shows that it is possible to do so with a change in market structure.
On the high level, the way to make passive liquidity provision more profitable is likely outside the CFMM design space, instead lies in MEV. You know who’s also passive? Validators. And who’s getting the most out of MEV (or the totally extractable value created on a blockchain)? Validators. PBS (Proposer-Builder Separation) has freed validators from actively building blocks and still manages to direct most of the value towards them with competitive auctions. Why can’t the same scenario happen to LPs?
The thought experiment of auctioning off the right to arbitrage a CFMM pool isn’t my invention. MEV capturing AMM (McAMM) was first proposed last year and is seeing increasing interest from the community. I believe we are very close to the first working instantiation of McAMM. The questions are mostly on the execution side: How do we conduct the auction? Is it going to add another centralized layer (just like MEVBoost for PBS) to our already quite centralized MEV supply chain? Is it possible to do it on-chain? If so will the auction itself create more MEV leakage? How to fairly return the captured MEV to LPs?
From MEV perspective, CFMM LP profitability is part of a bigger problem: How do we ensure fair representation of value created by different participants in crypto? IMO Cosmos has by far the best answer: ABCI++, the interface between application layer and consensus layer that empowers more participants (dapps, users, DAOs) to have a say in how consensus should work and how transactions should be ordered. In Ethereum we have PEPC, a more generic framework that allows proposers (validators) to enter binding commitments outside Ethereum consensus. Both designs would theoretically allow a more equitable MEV distribution since LPs would be able to express their preferences even if they stay passive when providing liquidity. McAMM, or other designs with similar principles, could then be built in a decentralized way.
So do AMMs have a future? The answer is yes, but we need to move fast. Passive liquidity providers are the backbone of DeFi, and they may leave if they don’t get rewarded fairly for value they created.
