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22nd March 2024

Elliptical Eccentricity for Capital Efficiency

Josh Guha

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Contents

A Refresher on AMMs

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Contents

A Refresher on AMMs

Gyroscope’s new E-CLP design

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Contents

A Refresher on AMMs

Gyroscope’s new E-CLP design

Use cases of the E-CLP

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Refresher: Automated Market Makers

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Foundations

First ideated by Vitalik in a blog post in 2017

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Foundations

First ideated by Vitalik in a blog post in 2017

Peer-to-pool instead of peer-to-peer

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Foundations

First ideated by Vitalik in a blog post in 2017

Peer-to-pool instead of peer-to-peer

Impermanent loss - careful incentive design necessary

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Impermanent Loss

Loss to liquidity providers (LPers) due to price variation

Relative to just holding those same assets

Graph To Be Added

Source: Finematics

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Impermanent Loss

Loss to liquidity providers (LPers) due to price variation

Relative to just holding those same assets

Change in external (market) price => AMM initially quotes stale prices

Graph To Be Added

Source: Finematics

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Impermanent Loss

Loss to liquidity providers (LPers) due to price variation

Relative to just holding those same assets

Change in external (market) price => AMM initially quotes stale prices

Form of “adverse selection” caused by information asymmetry between traders and AMM

Graph To Be Added

Source: Finematics

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xy = k (Uniswap v1/v2)

Brought Vitalik’s ideas into production in 2018

Graph To Be Added

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xy = k (Uniswap v1/v2)

Brought Vitalik’s ideas into production in 2018

First AMM with meaningful volumes

Graph To Be Added

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xy = k (Uniswap v1/v2)

Brought Vitalik’s ideas into production in 2018

First AMM with meaningful volumes

Constant Function Market Maker

Graph To Be Added

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xy = k (Uniswap v1/v2)

Brought Vitalik’s ideas into production in 2018

First AMM with meaningful volumes

Constant Function Market Maker

Provides liquidity along the entire trading range (0, ∞)

Graph To Be Added

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xy = k (Uniswap v1/v2)

Brought Vitalik’s ideas into production in 2018

First AMM with meaningful volumes

Constant Function Market Maker

Provides liquidity along the entire trading range (0, ∞)

Impermanent loss, high slippage, low capital efficiency

Graph To Be Added

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Stableswap (Curve)

Hybrid CFMM (Constant product + Constant Sum)

Graph To Be Added

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Stableswap (Curve)

Hybrid CFMM (Constant product + Constant Sum)

Constant price in a range

Graph To Be Added

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Stableswap (Curve)

Hybrid CFMM (Constant product + Constant Sum)

Constant price in a range

No / very low price slippage for trades in this range

Graph To Be Added

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Stableswap (Curve)

Hybrid CFMM (Constant product + Constant Sum)

Constant price in a range

No / very low price slippage for trades in this range

Excellent for price-related pairs (stablecoins, stETH / ETH, etc.)

Graph To Be Added

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Stableswap (Curve)

Hybrid CFMM (Constant product + Constant Sum)

Constant price in a range

No / very low price slippage for trades in this range

Excellent for price-related pairs (stablecoins, stETH / ETH, etc.)

Still underutilized capital in extremes of trading range

Graph To Be Added

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Concentrated liquidity (Uniswap v3)

Allow liquidity provision in a certain price range

Graph To Be Added

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Concentrated liquidity (Uniswap v3)

Allow liquidity provision in a certain price range

Increased returns for liquidity providers, reduced slippage for traders

Graph To Be Added

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Concentrated liquidity (Uniswap v3)

Allow liquidity provision in a certain price range

Increased returns for liquidity providers, reduced slippage for traders

No trading/fees outside of price range

Graph To Be Added

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Concentrated liquidity (Uniswap v3)

Allow liquidity provision in a certain price range

Increased returns for liquidity providers, reduced slippage for traders

No trading/fees outside of price range

Aggregate LP positions can match any liquidity profile

Graph To Be Added

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Concentrated liquidity (Uniswap v3)

Allow liquidity provision in a certain price range

Increased returns for liquidity providers, reduced slippage for traders

No trading/fees outside of price range

Aggregate LP positions can match any liquidity profile

May require more active position management by LPs

Graph To Be Added

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Combining the best of both worlds

Minimal slippage within a pre-specified price range

Capital efficiency

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Uniswap v3

Stableswap

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Combining the best of both worlds

Minimal slippage within a pre-specified price range

Ease-of-use - minimal active position management

Capital efficiency

Liquidity provision within a given price range

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Uniswap v3

Stableswap

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Combining the best of both worlds

Minimal slippage within a pre-specified price range

Ease-of-use - minimal active position management

Compounding fees

Capital efficiency

Liquidity provision within a given price range

Higher fees for LPs

Lower slippage for traders

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Uniswap v3

Stableswap

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ECLPs: Construction

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Elliptical Trading Curve

Produced by stretching, rotating and then shifting a circle

Diagrams to be added

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Elliptical Trading Curve

Produced by stretching, rotating and then shifting a circle

Trading occurs on the decreasing ‘side’ of the ellipse

Diagrams to be added

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Elliptical Trading Curve

Produced by stretching, rotating and then shifting a circle

Trading occurs on the decreasing ‘side’ of the ellipse

Allows for more flexible design space for shaping the trading curve

Diagrams to be added

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Constructing an E-CLP

Start with a circle centered on the origin

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Constructing an E-CLP

Start with a circle centered on the origin

Stretch by factor λ in the x-axis

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2

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Constructing an E-CLP

Start with a circle centered on the origin

Stretch by factor λ in the x-axis

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Rotate by Φ

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Constructing an E-CLP

Start with a circle centered on the origin

Stretch by factor λ in the x-axis

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Rotate by Φ

Translate the ellipse by (a,b)

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E-CLP Parameters

Price Range ( α , β )

Defined by the slope of the ellipse curve where it meets the x / y axis

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E-CLP Parameters

Peg price

The price at the flattest part of the ellipse

Range of least price impact

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E-CLP Parameters

Peg price

The price at the flattest part of the ellipse

Range of least price impact

Does not have to be symmetrical about the x=y line

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E-CLP Parameters

Peg price

The price at the flattest part of the ellipse

Range of least price impact

Does not have to be symmetrical about the x=y line

= tan(Φ)

Gradient intersects x-axis at angle of Φ

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E-CLP Parameters

Peg price

Note - peg price does not have to lie within the trading range

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E-CLP Parameters

Peg price

Note - peg price does not have to lie within the trading range

Price impact of a given trade increases as you move away from the peg price

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E-CLP Parameters

Peg price

Note - peg price does not have to lie within the trading range

Price impact of a given trade increases as you move away from the peg price

(Convexity of curve increases as you move away from the peg price)

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E-CLP Parameters

E-CLP (USDC / TUSD)

0x97469e6236bd467cd147065f77752b00efadce8a

E-CLP (WMATIC / stMATIC)

0xf0ad209e2e969eaaa8c882aac71f02d8a047d5c2

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Liquidity where you need it

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Asymmetric price ranges:

Concentrate liquidity, for example, around 1 with price bounds of 0.9 and 1.01 LSD/ETH

Create custom liquidity profiles

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Asymmetric price ranges:

Concentrate liquidity, for example, around 1 with price bounds of 0.9 and 1.01 LSD/ETH

Highly flexible

E-CLPs can be calibrated to approximate most trading curves that would be desired.

Create custom liquidity profiles

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Low operational burden on LPs

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Low operational burden on LPers

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All assets committed to ECLPs are in a ‘single tick’ with pool-wide price bounds.

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Low operational burden on LPers

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Setting the shape of the trading curve on initiation transfers the burden of liquidity profile management to pool constructors away and from LPers.

All assets committed to ECLPs are in a ‘single tick’ with pool-wide price bounds.

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Low operational burden on LPers

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Setting the shape of the trading curve on initiation transfers the burden of liquidity profile management to pool constructors away and from LPers.

All assets committed to ECLPs are in a ‘single tick’ with pool-wide price bounds.

No need for active position management avoids an 'arms race' among LPers and barriers to entrance.

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Low operational burden on LPers

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Setting the shape of the trading curve on initiation transfers the burden of liquidity profile management to pool constructors away and from LPers.

All assets committed to ECLPs are in a ‘single tick’ with pool-wide price bounds.

No need for active position management avoids an 'arms race' among LPers and barriers to entrance.

Gyro’s E-CLPs marry the UX of Stableswap AMMs with the benefits of concentrated liquidity - the best of both worlds.

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ECLP:

Use Cases

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Within the Gyroscope ecosystem

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Maximum capital efficiency in secondary markets

Liquidity provision within mint and redemption quotes with uneven liquidity distribution concentrated around the peg

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Within the Gyroscope ecosystem

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Maximum capital efficiency in secondary markets

Liquidity provision within mint and redemption quotes with uneven liquidity distribution concentrated around the peg

Maximum fee accrual in reserve vaults

Concentrated liquidity in reserve vaults populated by stablecoins means increased fees which bolster the health of the reserve over time

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Stablecoin: GYD

Reserve assets and yield sources diversified by design.

Dynamic Stability Mechanism automatically adapts to maintain stability and liquidity.

Liquidity network: ECLPs

Elliptic Concentrated Liquidity Pools.

Highly capital efficient, highly configurable to asset pairs.

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Stablecoin: GYD

Reserve assets and yield sources diversified by design.

Dynamic Stability Mechanism automatically adapts to maintain stability and liquidity.

Liquidity network: ECLPs

Elliptic Concentrated Liquidity Pools.

Highly capital efficient, highly configurable to asset pairs.

Central asset

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Stablecoin: GYD

Reserve assets and yield sources diversified by design.

Dynamic Stability Mechanism automatically adapts to maintain stability and liquidity.

Liquidity network: ECLPs

Elliptic Concentrated Liquidity Pools.

Highly capital efficient, highly configurable to asset pairs.

Central asset

Creates efficient secondary market

LP shares (stable pairs) as collateral

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Lido’s stETH, Liquity’s LUSD

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For both Liquity’s LUSD or Lido’s stETH

Concentrated liquidity between mint price and redemption price

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Lido’s stETH, Liquity’s LUSD

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For both Liquity’s LUSD or Lido’s stETH

Concentrated liquidity between mint price and redemption price

No need for liquidity provision outside this range

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Lido’s stETH, Liquity’s LUSD

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For both Liquity’s LUSD or Lido’s stETH

Concentrated liquidity between mint price and redemption price

No need for liquidity provision outside this range

Benefits over Stableswap (wasted liquidity provision at the tail ends)

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Lido’s stETH, Liquity’s LUSD

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For both Liquity’s LUSD or Lido’s stETH

Concentrated liquidity between mint price and redemption price

No need for liquidity provision outside this range

Benefits over Stableswap (wasted liquidity provision at the tail ends)

Pool constructors can set parameters to optimize liquidity provision within the price range

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What happens to AMMs where one or more of the trading pair assets is a yield-bearing token?

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What happens to AMMs where one or more of the trading pair assets is a yield-bearing token?

Stale prices - arbitrageurs make profits, LPers lose out

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What happens to AMMs where one or more of the trading pair assets is a yield-bearing token?

Stale prices - arbitrageurs make profits, LPers lose out

LPers have to ‘re-concentrate’ liquidity periodically

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  • Aave lending yield

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  • Aave lending yield

  • Gyroscope ECLP liquidity provision yield

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  • Aave lending yield

  • Gyroscope ECLP liquidity provision yield

  • External third-party incentives for liquidity provision

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  • Aave lending yield

  • Gyroscope ECLP liquidity provision yield

  • External third-party incentives for liquidity provision

  • Earn Gyroscope SPIN

AVAILABLE NOW on app.gyro.finance

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  • ECLPs = Elliptic Concentrated Liquidity Pools
  • Configurable liquidity density curve
  • Use cases: Stablecoins, LSTs, related tokens
  • Over $25M TVL currently

Conclusion

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  • ECLPs = Elliptic Concentrated Liquidity Pools
  • Configurable liquidity density curve
  • Use cases: Stablecoins, LSTs, related tokens
  • Over $25M TVL currently

Conclusion

  • Updatable parameters
  • Dynamic ECLP

Future Work

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Integrated with order routers

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The following DEX aggregators already support Gyro’s pools.

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Aggregated 1inch, 0x, and Balancer volumes usually represent at least 70% of the total aggregated DEX volume. Source.

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Audited by

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Supported by

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* partially true