The Gyroscope protocol

Gamified Testnet

3-CLPs

Cubic-Concentrated Liquidity Pools or 3-CLPs

Description of 3-CLPs

Given quantities of real reserves (x,y,z) in the pool and the pool's pricing parameter α, the offset a can be calculated [2]. This offset describes the amount the pool adds to real reserves to form the virtual reserves that achieve the pricing range.

Symmetric 3-CLPs use the following invariant: (x+a)(y+a)(z+a) = L^3

Like in any Balancer or Curve pool with more than two assets, the prices between different pairs of assets in the 3-CLP interact. For example, if asset x is traded against asset z, the pool’s spot price of asset y vs asset z is going to change. An implication of this is that the combinations of prices that are simultaneously offered by the pool at any point in time are constrained by a mathematical relationship.

stylistic visualization of 2-CLP price bounds

stylistic visualization of the feasible pricing region of a 3-CLP

The feasible pricing region is parameterized by the prices of asset x and y, respectively, denoted in units of asset z. The third price pair, of x denoted in units of y, is the quotient of the two prices: px/y=px/z/py/z. In the figure, each included asset is represented with a different color.

The lines indicate price combinations where the respective reserve asset x, y, or z is exhausted in the pool, and the shaded regions indicate where the respective reserve asset has a positive balance in the pool.

The region where all colors overlap is the feasible pricing region - these are combinations of prices that the pool can quote. At the corner points, the pool only holds a single asset and two of the three asset pairs realize either the minimum or the maximum price bound (i.e., they are equal to α=0.5 or 1/α=2.0) [3]. Further documentation is available here.

Benefits of 3-CLPs

*Capital efficiency**:*By concentrating liquidity between three assets, 3-CLPs achieve a 50% capital efficiency improvement from aggregating the third asset compared to a similar setup of trading pairs as 2-CLPs.: Trading among three assets is more gas efficient than connecting two trades through two different 2-CLPs.*Gas efficiency*: 3-CLPs remain comparatively simple in architecture and user experience.*User experience*

Stylized representation of capital efficiency gains of 3-CLPs

Risks of 3-CLPs

: the risk that an exploit or bug puts deposited assets at risk.*Smart contract risk*: the risk that the portfolio strategy implied by the pool has worse payoffs than a different strategy (such as just holding the assets).*Strategy risk*: the risk that permanent price changes imply a loss to LPers because arbitrageurs take stale price quotes.*Adverse selection risk*

since the 3-CLP contains an additional asset, LPers are exposed to strategy and adverse selection risk due to two additional price pairs.*Asset interaction risk:*

For example, if the price of one of the assets drops to a sufficiently low level, the pool will end up with only that least valuable asset (see the figure above). This phenomenon occurs in many multi-asset AMMs, such as the Curve stablecoin 3-pool. Just like strategy risk in the 2-pool, it can be reduced by choosing fundamentally connected assets and appropriate price bounds.

- Note that the pricing region of the 3-CLP is more complex than for other pools; this may mean that arbitrageurs need more time to get familiar with the functioning of the pool before it runs smoothly.

Technical Specification

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

Notes

[1] For technical reasons, the parameter provided to the smart contract is

$\sqrt[3]{\alpha}$

instead of α itself.[2] The offsets are computed as

$a = L \sqrt[3]{\alpha}$

[3] The figure is asymmetric, with the curve for z having a different shape than the curves for x and y, because we chose to express the relative pool prices in terms of asset z. This is only a property of how the figure was made and does not affect the functioning of the pool; within the pool, the three assets take on symmetric roles.

Last modified 25d ago

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Description of 3-CLPs

Benefits of 3-CLPs

Risks of 3-CLPs

Technical Specification

Notes