The Gyroscope protocol

Gamified Testnet

2-CLPs

Quadratic-Concentrated Liquidity Pools or 2-CLPs

Description of 2-CLPs

Given quantities of real reserves (x,y) in the pool and the pool’s pricing range [α,β], offsets a and b can be calculated [2]. These offsets describe the amount the pool adds to real reserves to form the virtual reserves that achieve the pricing range. These pools use the following invariant: (x + a)(y + b) = L^2.

conceptual graphic showing liquidity concentration of 2-CLPs

Stylized representation of capital efficiency gains of 2-CLPs

2-CLPs are best understood as a simplified design of Uniswap v3 that is tailored to a specific use-case. Specializing the design for the most-traded ranges of included assets enables a pool with (i) high capital efficiency and (ii) high gas-efficiency.

Benefits of 2-CLPs

Risks of 2-CLPs

For the CLPs, this strategy risk can be higher than for a pool without concentrated liquidity because the strategy allows more trading at any price within the pool's price range.

This is a side effect of capital efficiency and low price impact for traders. In an extreme case, when the value of one of the assets goes to 0, the value of the pool goes to 0 as well. The strategy risk can be reduced by choosing fundamentally related assets for the two sides of the pool (because then severe permanent shifts in relative prices are less likely and oscillations are more likely) and by carefully selecting price ranges [8].

For the CLPs, this risk can be higher than for a pool without concentrated liquidity because the CLP design offers deeper markets within the pool's price range.

In the case of a price jump, more arbitrage is enabled. If, however, the price later returns to the initial price this loss is not realized and the pool profits from trading fees.

Technical Specification

To read about the mathematical specification and implementation, see the below resources

Notes

[1] For technical reasons, the parameters provided to the smart contract are

$\sqrt{\alpha}$

and $\sqrt{\beta}$

instead of α and β directly.[2] The offsets are computed as

$a = L / \sqrt{\beta}$

, $b = L \sqrt{\alpha}$

[3] Yield Space,’YieldSpace: An Automated Liquidity Provider for Fixed Yield Tokens’: https://yield.is/YieldSpace.pdf

[4] Uniswap, ‘Concentrated liquidity’, available at: https://docs.uniswap.org/protocol/concepts/V3-overview/concentrated-liquidity

[5] Paradigm, ‘Understanding Automated Market-Makers, Part 1: Price Impact’, available at: https://research.paradigm.xyz/amm-price-impact

[6] Balancer, ‘Smart Order Router V2’, available at: https://docs.balancer.fi/developers/smart-order-router

[7] Technically, the pool doesn't ‘sell’ any assets, but merely offers them for sale.

[8] Note that multiple CLPs with different parameters can be deployed for the same asset pair to allow LPers to choose between different risk levels. In this case, the liquidity in different pools of the same pair can be combined through smart order routing along multiple paths.

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Description of 2-CLPs

Benefits of 2-CLPs

Risks of 2-CLPs

Technical Specification

Notes