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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
Combining the best of both worlds
Minimal slippage within a pre-specified price range
Capital efficiency
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Uniswap v3
Stableswap
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
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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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
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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
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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
Low operational burden on LPers
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All assets committed to ECLPs are in a ‘single tick’ with pool-wide price bounds.
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.
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.
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
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
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
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
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
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)
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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AVAILABLE NOW on app.gyro.finance
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Conclusion
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Conclusion
Future Work
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Integrated with order routers
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.
Audited by
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Supported by
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* partially true