CLMM

Concentrated Liquidity AMM (CLMM)

Introduction

CLMM enhances the AMM concept by allowing liquidity providers to concentrate their capital within a specific price range. This improves capital efficiency and reduces slippage in actively traded regions. Instead of spreading liquidity evenly, CLMM focuses on targeted zones, resulting in deeper liquidity where it's most needed.

CLMM introduces the concept of virtual reserves:

(x + virtual_x) * (y + virtual_y) = k

These virtual reserves adjust dynamically based on the price range set by the liquidity provider.

Benefits

• Improved Capital Efficiency: Liquidity is focused, not wasted.

• Lower Slippage: Especially within popular trading ranges.

• Customizability: LPs can manage risk and strategy via price bounds.

Limitations

• Requires Active Management: LPs must monitor and rebalance.

• Inactive Liquidity: Out-of-range capital does not contribute to trades.

• Higher Complexity: Harder to understand for casual users.

How It Works

Let’s assume the same pool:

• 1000 BTC

• 100,000 Runes

• Liquidity is concentrated between 95 and 105 Runes per BTC

CLMM calculates liquidity depth L:

• L = sqrt(1000 * 100,000) = 10,000

• Assume the full price range spans from 50 to 150 Runes. The target range is 95–105.

• Amplification factor: (150 - 50) / (105 - 95) = 10x

• Effective liquidity: L' = 10,000 * 10 = 100,000

A user sells 50 BTC:

• The price shifts from 100 to approximately 99.014 Runes

• Runes received: ≈ 4945.23

• Average price: 98.9 Runes per BTC

• Slippage: ≈ 1.1%

This concentrated liquidity allows for deeper trades with reduced slippage, while idle capital is minimized.