“Frax: Fractional-Algorithmic Stablecoin Protocol” is the 2021 documentation by Sam Kazemian and Travis Moore of Frax Finance, introducing the first fractional-algorithmic stablecoin — a design that sits between fully collateralized stablecoins (like USDC: always 100% backed) and fully algorithmic ones (like LUNA/UST: backed only by an algorithm). FRAX maintains its $1 peg by holding a collateral ratio (CR) that can range from 0–100% USDC-backed, with the remaining portion stabilized by the FXS governance token.

> Documentation: Available at docs.frax.finance/overview.

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Publication and Context

In 2021, stablecoin design was polarized:

• Fully collateralized (USDC, USDT): Stable, but require off-chain assets and regulatory trust
• Overcollateralized DeFi (DAI): Decentralized but capital-inefficient (need $150 of ETH to get $100 of DAI)
• Purely algorithmic (LUNA/UST, Empty Set Dollar): Capital-efficient in theory, catastrophically unstable in practice

Frax’s hypothesis: a partially collateralized design is optimal — enough collateral to prevent spiral instability, algorithmic component for capital efficiency, with an autonomous controller adjusting the ratio based on market demand signals.

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Collateral Ratio Mechanics

Minting 1 FRAX:

• Peg = $1
• At CR = 85%: provide $0.85 USDC + burn $0.15 worth of FXS → receive 1 FRAX
• At CR = 100%: provide $1.00 USDC → receive 1 FRAX (fully collateralized mode)
• At CR = 0%: burn $1.00 worth of FXS → receive 1 FRAX (purely algorithmic mode)

Redeeming 1 FRAX:

• At CR = 85%: return 1 FRAX → receive $0.85 USDC + $0.15 worth of FXS (newly minted)
• At CR = 100%: return 1 FRAX → receive $1.00 USDC

Autonomous Collateral Ratio Controller:

The CR adjusts automatically based on FRAX trading at its peg:

• If FRAX trades above $1 → demand exceeds supply → CR decreases (more algorithmic, less USDC needed)
• If FRAX trades below $1 → demand is weak → CR increases (more collateral, more stability)

This is implemented as a PID-style controller that adjusts CR by ±0.25% per hour in v1.

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FXS Token: Seigniorage and Governance

FXS (Frax Share) absorbs the seigniorage (profit) and volatility of the algorithmic component:

• When FRAX is minted at CR < 100%, FXS is burned (reducing supply → FXS price rises if demand for FRAX grows)
• When FRAX is redeemed at CR < 100%, FXS is minted (increasing supply → FXS price dilutes)
• FXS holders vote on: target CR, AMO strategies, collateral types, protocol fees

Contrast with LUNA/UST: UST’s algorithmic backing was 100% dependent on LUNA; a death spiral where LUNA inflation → UST depeg → more LUNA needed → hyperinflation was not adequately guarded against. Frax’s design limits the algorithmic portion via the CR floor, preventing unbounded FXS minting.

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Algorithmic Market Operations (AMOs)

Frax v2 introduced AMOs — autonomous smart contracts that deploy idle USDC collateral into yield-generating strategies while maintaining the ability to back FRAX redemptions:

• CurvAMO: Deposit USDC into Curve’s FRAX3CRV pool to earn trading fees and CRV rewards
• FraxlendAMO: Lend USDC via Fraxlend (Frax’s native lending protocol)
• ComptrollerAMO: Deposit into Compound or Aave

AMOs increase capital efficiency: collateral earns yield rather than sitting idle. AMO strategies are governed by FXS holders.

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Frax Ecosystem Expansion

Frax evolved from a single stablecoin into a DeFi ecosystem:

• Fraxswap: AMM using TWAMM (time-weighted AMM for executing large orders over time)
• Fraxlend: Isolated-market lending protocol
• frxETH / sfrxETH: Liquid staking ETH derivative (competing with stETH)
• Frax v3: Moving toward 100% collateralization (backing FRAX with US Treasuries through on-chain RWAs)

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Reality Check

Frax survived the Terra/LUNA collapse of May 2022 (which destroyed purely algorithmic stablecoins) because its collateral ratio was ~85–90% at the time — sufficient exogenous backing to prevent a death spiral. This validated the hybrid design hypothesis.

Caveats:

• FXS concentration: Early FXS distribution was concentrated among founders and investors; governance may not fully represent decentralization ideals.
• AMO strategy risk: If AMO strategies (Curve pools, lending markets) experience losses or exploits, the FRAX collateral backing decreases.
• v3 pivot to RWAs: The move toward 100% collateralization via US Treasuries (off-chain RWAs) partially abandons the algorithmic vision and reintroduces regulatory and custodian risk.

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Legacy

Frax demonstrated that a partially collateralized stablecoin could survive stress conditions where fully algorithmic stablecoins collapsed. The AMO concept (idle collateral generating yield without compromising redemption) influenced later stablecoin designs. Fraxlend’s isolated market model influenced Aave v3’s isolation mode. frxETH became one of the Top 3 Ethereum liquid staking tokens.

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Related Terms

• Algorithmic Stablecoin
• MakerDAO Whitepaper
• Curve Finance Whitepaper
• Stablecoin

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Research

• Kazemian, S., & Moore, T. (2021). Frax: Fractional-Algorithmic Stablecoin Protocol. Frax Finance.

— Primary whitepaper. Section 2 defines the minting/redemption mechanics; Section 3 covers the collateral ratio controller.

• Evans, A. (2021). Dynamical Analysis of the Terra Luna Protocol. Statespace Labs.

— Analysis of why fully algorithmic stablecoins (LUNA/UST) are structurally unstable; the context for Frax’s fractional hybrid design.

• Qin, K., et al. (2021). An Empirical Study of DeFi Liquidations: Incentives, Risks, and Instabilities. IMC 2021.

— Covers automatic liquidation and stability mechanisms in DeFi stablecoins; context for understanding how Frax’s CR adjustment compares to CDP-based over-collateralization.