Source: Coin98Insights

Introduction

Liquidity provision in DeFi is often promoted as a passive income strategy, where users deposit assets into Automated Market Makers (AMMs) and earn trading fees. However, beneath the surface, liquidity providers (LPs) face structural inefficiencies that impact their profitability.

One of the most overlooked inefficiencies is Loss Versus Rebalancing (LVR), a hidden cost that arises when arbitrage traders consistently extract value from LPs due to price discrepancies. Unlike impermanent loss (IL), which compares LP performance to simply holding assets, Loss versus Rebalancing provides a more accurate way to measure the true cost of providing liquidity in Automated Market Makers. This shows how LPs underperform traders who can rebalance their positions instantly. The slower an AMM updates its price, the more value arbitrageurs can extract, leaving liquidity providers (LPs) at a disadvantage.

What is Loss Versus Rebalancing (LVR)?

Loss Versus Rebalancing (LVR) is a measure of the losses incurred by LPs during liquidity provision due to the price discrepancies between assets within the AMM and external market prices.

This concept was first introduced in a 2022 research paper by Jason Milionis, Tim Roughgarden, Ciamac Moallemi, and Anthony Lee Zhang.

LVR denotes a form of arbitrage that occurs whenever an AMM has an outdated price in comparison to an external market price. Arbitrageurs exploit this difference by trading from the AMM to the more liquid exchange, correcting the arbitrage and extracting value from LPs in the process.

How Automated Market Makers are Designed

Automated Market Makers (AMMs) operate through smart contracts, enabling decentralized trading by managing liquidity pools. The liquidity pool maintains a balance of reserve tokens based on a mathematical formula, with the most common type being the constant product market maker popularized by Uniswap.

Source: Webopedia

The model is based on the equation;

x * y = k

Where;

• x = Quantity of Token A (e.g., SOL) in the liquidity pool.
• y = Quantity of Token B (e.g., a meme coin).
• k = Constant product, meaning the total liquidity remains unchanged.

This mechanism ensures that an asset’s price adjusts in response to the relative supply of the two tokens. When a user swaps one token for another, the pool’s balance shifts, altering the price. Since AMMs rely on traders to initiate swaps, prices in liquidity pools update only when market participants buy or sell. This dependency on arbitrageurs gives room for adverse selection.

Adverse Selection

Adverse selection occurs when one party in a transaction leverages an informational advantage to the detriment of the other, creating an imbalance. In traditional finance, this occurs when buyers or sellers possess superior knowledge about an asset, resulting in unfavorable outcomes for the less-informed counterparty.

In DeFi, adverse selection arises when informed traders exploit liquidity pools before AMMs update their prices. Since AMMs do not track external market movements in real time, arbitrageurs can extract value by trading against outdated prices, leading to consistent losses for liquidity providers.

Below is a simple illustration of how LVR plays out;

1. A centralized exchange (CEX) updates ETH’s price to $2,100 after a surge in demand.
2. A DeFi AMM, such as Uniswap, still prices ETH at $2,000 because no trades have occurred yet.
3. Arbitrageurs buy ETH from the AMM at $2,000 and sell it on the CEX for $2,100, capturing a $100 profit per ETH.
4. As arbitrage continues, the AMM price eventually adjusts, but LPs have already lost value, effectively “selling” ETH too cheaply.

LVR and Impermanent Loss (Loss Versus Holding)

Source: Delphi Digital

Impermanent loss (IL) occurs when the relative price of assets in a liquidity pool changes, resulting in the value of locked assets being lower than if they were held in a wallet. However, IL is “impermanent” because LPs can recover their losses if asset prices revert to their original levels.

In contrast, Loss Versus Rebalancing (LVR) persists even if prices return to their initial state. This is because arbitrageurs have already extracted value from LPs during the rebalancing process, making LVR a more fundamental cost of liquidity provision.

Illustration

Below is a step‐by‐step calculated example illustrating Liquidity Value Reduction (LVR) in an ETH-USDC pool when ETH’s price moves up and returns.

Initial Position

• Assets Deposited:
• 1 ETH (worth $1,000)

• 1,000 USDC

• Total Value:
  $1,000 (ETH)+$1,000 (USDC)=$2,000

Scenario 1: ETH Price Pumps to $2,000

Step 1: LP Rebalancing

• LP Rebalancing Mechanism:
  To maintain a 50/50 value split, the pool adjusts its holdings. (x*y=k)

• Resulting LP Position:

• Approximately 0.71 ETH

• Approximately 1,414 USDC

• Valuation at $2,000 per ETH:

• ETH value: 0.71×2,000 ≈ $1,414
• USDC: $1,414
• Total LP Value: $1,414+$1,414 ≈ $2,828

If you held your initial assets:

• 1 ETH at $2,000 = $2,000
• 1,000 USDC = $1,000
• Total Held Value: $3,000
• Impermanent Loss (IL): $3,000−$2,828 = $172

Step 2: Arbitrage Extraction During Rebalancing

• Selling Action in the LP:
• The LP’s rebalancing effectively “sells” 0.29 ETH at an internal rate of about $1,427 per ETH (worth around $414).
• Arbitrage Opportunity:
• An arbitrageur can buy that 0.29 ETH on the LP at the lower effective price, then sell it on a centralized exchange (CEX) at the true market price of $2,000 per ETH, receiving approximately $580.

Net Loss from Sell-Side:

• The LP only captures about $414 versus the $580 that could be obtained in the open market.
• Loss:
  $580−$414=$166

Scenario 2: ETH Price Returns to $1,000

Rebalancing to Re-align the LP

• Buy-Back Action:
• When ETH drops back to $1,000, the LP must “buy back” the 0.29 ETH to rebalance.

• Internal Rebalancing Price: The LP buys back 0.29 ETH at an effective rate of about $1,427 per ETH, costing about 414 USDC.

• Market Opportunity:

• In the open market, 0.29 ETH would cost roughly 290 USDC at the true price of $1,000 per ETH.

• Net Loss from Buy-Back:
  414 USDC (LP cost)−290 USDC (market cost) = $124

Total Loss and Final Pool Value:

• Total Arbitrage Loss: $166 (sell-side) + $124 (buy-side) = $290
• Final value: $2,000 ( 1 ETH + 1,000 USDC)

The loss does not reflect a change in the total value of the LP or a permanent capital loss on paper because it captures the opportunity cost to LPs in AMMs with stale pricing.

For any given price movement, LVR can be calculated using the formula “a(p-q),” where a is the quantity of the asset being sold, p is the “real” market price, and q is the “stale” AMM price. (Note: “a” is a positive number when selling and a negative number when buying.)

Although LVR might seem like a significant issue in theory, it doesn’t necessarily spell doom for liquidity providers (LPs) as they deposit assets into AMMs to earn a return. The fees generated from trading activity can help offset some of the LVR losses, but the overall profitability depends on several factors, including trading volume, fee structure, and market volatility. According to the report by Milionis et al., a Uniswap pool would need to turnover 10% of its total volume daily for LP fees of 30 basis points to fully cover the losses from LVR.

Measures for Reducing LVR

While there’s no perfect solution, several strategies can help minimize LVR-related losses and improve LP profitability.

Hybrid AMM Models (Oracle-Integrated & TWAMMs)

Oracle-based AMMs (e.g., Curve v2) use on-chain price oracles to dynamically adjust AMM prices, reducing the lag that arbitrageurs typically exploit. Time-weighted average Market Makers (TWAMMs) also gradually execute large trades over time, limiting the profitability of arbitrage-driven rebalancing.

Decrease Block Times

This is a theoretical approach that increases trade frequency by decreasing block times, as arbitrageurs trade more to generate the same expected pre-fee profit. With this, LPs can earn more fees to cover losses incurred by LVR.

Batch Auctions

Batch auctions process multiple orders simultaneously within fixed time intervals. All trades in a batch settle at the same price, eliminating arbitrage opportunities and reducing frequent price updates. This approach lowers rebalancing costs for LPs. Protocols like CoW Protocol and Gnosis Auction have implemented this method.

Dynamic Fee Structures

AMMs can adopt dynamic fee models that increase fees during periods of high volatility. This penalizes arbitrage trades, which rely on rapid execution, while lowering fees for trades that can wait across multiple blocks (i.e., uninformed trades).

The Function-Maximizing AMM (FM-AMM) - An alternative to CF-AMM

The Function-Maximizing Automated Market Maker (FM-AMM) is an AMM model that addresses key challenges found in traditional Automated Market Makers (AMMs), particularly those utilizing Constant Function Market Maker (CFMM) models like Uniswap. Traditional AMMs, such as those based on the CFMM model, use the constant product formula, where the product of the quantities of two tokens remains constant.

This design presents two major challenges:

Arbitrage Profits (LVR)

Price discrepancies between AMMs and external markets create opportunities for arbitrageurs to profit at the expense of liquidity providers (LPs). When external market prices shift, arbitrageurs can exploit these differences, leading to losses for LPs.

Sandwich Attacks

Malicious actors can manipulate transaction ordering by placing their transactions before and after a target transaction, profiting from the induced price changes. This not only harms the targeted traders but also undermines the integrity of the trading environment.

Benefits of FM-AMMs

FM-AMMs use frequent batch auctions to process trades in discrete time intervals rather than individually. Unlike traditional AMMs that execute trades continuously, this batch trading mechanism ensures that all transactions within a batch clear at a uniform price, neutralizing transaction ordering advantages.

Eliminates LVR

By executing all trades in a batch at the same clearing price, FM-AMMs prevent arbitrageurs from exploiting price differences between the AMM and external markets.

Prevents Sandwich Attacks

The uniform pricing within each batch means that the price is determined collectively for all trades, leaving no room for attackers to manipulate individual transaction sequences.

Improves LP Returns

By reducing losses associated with arbitrage and front-running, FM-AMMs can offer better returns to liquidity providers compared to traditional AMMs. Empirical analyses have shown that, for various token pairs, FM-AMMs provide returns that are equal to or greater than those observed in platforms like Uniswap v3.

Conclusion

LVR represents the maximal arbitrage extractable value at the cost of LPs providing liquidity in AMMs, This fault is based on structural inefficiencies of the AMM. To address these inefficiencies, various designs, including oracle-integrated AMMs, and dynamic fee structures have been adopted. While these solutions improve market efficiency and reduce arbitrage-driven losses, they do not entirely eliminate LVR. FM-AMMs leverage frequent batch auctions, to minimize front-running and arbitrage opportunities.

And while AMM designs continue to evolve, liquidity providers must navigate these structural challenges with a clear understanding of the trade-offs involved. The future of AMMs will likely depend on balancing capital efficiency, price discovery, and the incentives for both LPs and arbitrageurs.