# How Does a Concentrated Liquidity Pool Modify the Constant Product Formula's Impact? ⎊ Path

**Published:** 2025-12-05
**Author:** Greeks.live
**Categories:** Path

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## How Does a Concentrated Liquidity Pool Modify the Constant Product Formula’s Impact?

Concentrated liquidity pools (CLPs) allow LPs to allocate their capital within a specific price range, rather than across the entire (0, infty) range. This means the x y = k formula is only active within the chosen range.

This greatly increases capital efficiency, as the liquidity is concentrated where most trading occurs. However, it also increases the LP's exposure to impermanent loss outside their range.

- [What Is the Difference in Impermanent Loss Calculation for a Standard Pool versus a Concentrated Pool?](https://learn.greeks.live/path/what-is-the-difference-in-impermanent-loss-calculation-for-a-standard-pool-versus-a-concentrated-pool/)

- [Explain the Concept of “Concentrated Liquidity” and Its Impact on Impermanent Loss](https://learn.greeks.live/path/explain-the-concept-of-concentrated-liquidity-and-its-impact-on-impermanent-loss/)

- [How Would This Formula Change for a Liquidity Pool Governed by a Constant Mean or Constant Sum Formula?](https://learn.greeks.live/path/how-would-this-formula-change-for-a-liquidity-pool-governed-by-a-constant-mean-or-constant-sum-formula/)

- [How Does Concentrated Liquidity Differ from Traditional AMM Pools for a DAO’s Treasury?](https://learn.greeks.live/path/how-does-concentrated-liquidity-differ-from-traditional-amm-pools-for-a-daos-treasury/)

- [How Do Single-Sided Staking and Concentrated Liquidity Pools Attempt to Mitigate Impermanent Loss?](https://learn.greeks.live/path/how-do-single-sided-staking-and-concentrated-liquidity-pools-attempt-to-mitigate-impermanent-loss/)

- [How Does Regulatory Oversight Restrict the Use of Portfolio Margining in Some Jurisdictions?](https://learn.greeks.live/path/how-does-regulatory-oversight-restrict-the-use-of-portfolio-margining-in-some-jurisdictions/)

- [How Does a “Concentrated Liquidity” Model Affect Liquidation Price Impact?](https://learn.greeks.live/path/how-does-a-concentrated-liquidity-model-affect-liquidation-price-impact/)

- [How Do Concentrated Liquidity Pools Modify the Constant Product Formula’s Impact?](https://learn.greeks.live/path/how-do-concentrated-liquidity-pools-modify-the-constant-product-formulas-impact/)

## Glossar

### [Concentrated Liquidity Pool](https://learn.greeks.live/area/concentrated-liquidity-pool/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Protocol ⎊ A concentrated liquidity pool, within the context of cryptocurrency derivatives and options trading, represents a structural evolution from traditional Automated Market Makers (AMMs).

### [Capital Efficiency](https://learn.greeks.live/area/capital-efficiency/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Leverage ⎊ Capital efficiency, within cryptocurrency and derivatives, fundamentally represents the maximization of risk-adjusted returns relative to capital at risk, a metric increasingly vital given regulatory constraints and market volatility.

### [Concentrated Liquidity](https://learn.greeks.live/area/concentrated-liquidity/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Allocation ⎊ ⎊ Concentrated liquidity represents a departure from traditional automated market maker models by enabling liquidity providers to specify precise price ranges where their capital will be deployed, fundamentally altering capital efficiency.

## Discover More

### [How Does the Concept of "Virtual Reserves" Relate to the Concentrated Liquidity Formula?](https://learn.greeks.live/path/how-does-the-concept-of-virtual-reserves-relate-to-the-concentrated-liquidity-formula/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does the Concept of "Virtual Reserves" Relate to the Concentrated Liquidity Formula?](https://learn.greeks.live/wp-content/uploads/2025/10/Geometric-Abstraction-Modeling-Latent-Volatility-Surface-Structure-in-Decentralized-Finance-Ecosystem.webp)

Virtual reserves are a mathematical construct that shifts the reserve curve to simulate infinite liquidity, enabling high capital efficiency within a narrow, defined range.

### [How Does the Constant Product Formula (X Y=k) Directly Give Rise to the Impermanent Loss Phenomenon?](https://learn.greeks.live/path/how-does-the-constant-product-formula-x-yk-directly-give-rise-to-the-impermanent-loss-phenomenon/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does the Constant Product Formula (X Y=k) Directly Give Rise to the Impermanent Loss Phenomenon?](https://learn.greeks.live/wp-content/uploads/2025/10/Reflective-Metallic-Cross-Structure-Symbolizing-Intersecting-Volatility-Surface-Primes-in-Decentralized-Finance.webp)

The x y=k formula forces a rebalance during price shifts, leaving LPs with less of the valuable asset, which causes impermanent loss.

### [What Is the Risk for a Liquidity Provider Whose Chosen Price Range Is Exceeded in a Concentrated Liquidity Pool?](https://learn.greeks.live/path/what-is-the-risk-for-a-liquidity-provider-whose-chosen-price-range-is-exceeded-in-a-concentrated-liquidity-pool/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Risk for a Liquidity Provider Whose Chosen Price Range Is Exceeded in a Concentrated Liquidity Pool?](https://learn.greeks.live/wp-content/uploads/2025/10/Aerodynamic-Leading-Edge-Structure-Illumination-High-Frequency-Digital-Asset-Hedging-Interface.webp)

The LP's capital converts entirely to the less valuable asset, stops earning fees, and the impermanent loss is fully realized.

### [Why Is Liquidity Often Concentrated in the Nearest-Month Traditional Futures Contract?](https://learn.greeks.live/path/why-is-liquidity-often-concentrated-in-the-nearest-month-traditional-futures-contract/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Why Is Liquidity Often Concentrated in the Nearest-Month Traditional Futures Contract?](https://learn.greeks.live/wp-content/uploads/2025/10/Interoperable-Blockchain-Modularity-Traded-as-Structured-Digital-Asset-Settlement-Instruments.webp)

It is the most actively traded contract by speculators and hedgers, as they focus on the immediate future, before rolling over to the next month.

### [How Does the Constant Product Formula (X Y=k) Relate to Impermanent Loss?](https://learn.greeks.live/path/how-does-the-constant-product-formula-x-yk-relate-to-impermanent-loss/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does the Constant Product Formula (X Y=k) Relate to Impermanent Loss?](https://learn.greeks.live/wp-content/uploads/2025/10/Symmetrical-Financial-Instrument-Metaphor-Illustrating-Delta-Hedging-Dynamics-Across-Impermanent-Loss-Curves.webp)

The formula forces the asset ratio to shift following external price changes, creating a divergence from the initial deposit value, which is the loss.

### [What Role Does the "K" Constant Play in Determining the Pool's Total Liquidity Value?](https://learn.greeks.live/path/what-role-does-the-k-constant-play-in-determining-the-pools-total-liquidity-value/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Role Does the "K" Constant Play in Determining the Pool's Total Liquidity Value?](https://learn.greeks.live/wp-content/uploads/2025/10/Conceptualized-Clock-Analogy-for-Cryptocurrency-Derivatives-Strike-Price-Execution-Mechanisms.webp)

k is the product of reserves (x · y), directly measuring the pool's depth; a larger k means lower slippage for trades.

### [How Does a Concentrated Liquidity AMM like Uniswap V3 Affect Impermanent Loss Compared to V2?](https://learn.greeks.live/path/how-does-a-concentrated-liquidity-amm-like-uniswap-v3-affect-impermanent-loss-compared-to-v2/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does a Concentrated Liquidity AMM like Uniswap V3 Affect Impermanent Loss Compared to V2?](https://learn.greeks.live/wp-content/uploads/2025/10/High-Velocity-Digital-Asset-Liquidity-Provision-Penetrating-Encrypted-Ledger-Infrastructure-Boundaries.webp)

V3's concentrated liquidity increases capital efficiency but exacerbates Impermanent Loss if the price leaves the set range.

### [How Does Uniswap V3'S'concentrated Liquidity' Change the X Y = K Model?](https://learn.greeks.live/path/how-does-uniswap-v3s-concentrated-liquidity-change-the-x-y-k-model/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does Uniswap V3'S'concentrated Liquidity' Change the X Y = K Model?](https://learn.greeks.live/wp-content/uploads/2025/10/Layered-Cryptocurrency-Option-Settlement-Stack-Visualization-of-Dynamic-Strike-Price-Convergence-Mechanisms.webp)

It allows LPs to provide liquidity only within specific price ranges, making the capital more efficient than the full range x y = k model.

### [How Does Capital Efficiency Differ between a Standard AMM and a Concentrated Liquidity Pool?](https://learn.greeks.live/path/how-does-capital-efficiency-differ-between-a-standard-amm-and-a-concentrated-liquidity-pool/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does Capital Efficiency Differ between a Standard AMM and a Concentrated Liquidity Pool?](https://learn.greeks.live/wp-content/uploads/2025/10/Exposing-Latent-Digital-Asset-Bifurcation-Mechanisms-Through-Illuminated-DeFi-Protocol-Stacks.webp)

CLPs are more capital efficient because capital is concentrated in the active trading range, facilitating higher volume and fees.

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**Original URL:** https://learn.greeks.live/learn/how-does-a-concentrated-liquidity-pool-modify-the-constant-product-formulas-impact/
