Conclusion

Frax uses ideas from Uniswap and AMMs to build a novel hybrid stablecoin design never seen before. In a Uniswap pool, the ratio of asset A and B has to be proportional due to the constant product function. The LP token is just a pro rata claim on the pool + fees so it is usually increasing in value (if fees higher than impermanent loss) or loses value (if impermanent loss greater than fees). The LP token is just passive claims on the pool. 
Frax takes that idea and turns it over to design a unique stablecoin. The LP token is the stablecoin, FRAX. It is the object of stabilization and always mintable/redeemable for $1 worth of collateral and the governance (FXS) token at the collateral ratio. This ratio of the two assets (collateral and FXS) dynamically changes based on the price of the stablecoin. If the stablecoin price is dropping, then the protocol tips the ratio in favor of collateral and less in the FXS token to regain confidence in FRAX. An arbitrage opportunity arises for people wanting to put in collateral into the pool at the new ratio for discounted FXS which the protocol mints for this "recollateralization swap." This recollateralizes the protocol to the new, higher collateral ratio. 
If FRAX is over $1, then the protocol tips the collateral ratio to the FXS token to measure the market's confidence in more FRAX supply being stabilized algorithmically. As FRAX becomes more algorithmic, the excess collateral can go back to FXS holders through a buyback shares function that anyone can call to burn their FXS tokens for an equal value of excess collateral. The "buyback swap" function always keeps value accruing to the governance token any time there is excess fees/collateral/value in the system. 
This 'Frax dance' is always happening and uses AMM game theory to test different ratios of collateralization, incentivize recollateralizing through arbitrage swaps, and redistribute excess value back to FXS holders through a buyback swap. The protocol starts at a 100% collateral ratio at genesis and might or might not ever get to purely algorithmic. The novel insight is to use market forces itself to see how much of a stablecoin can be algorithmically stabilized with its own seigniorage token so that it keeps a tight band around $1 like fiatcoins. Purely algorithmic/rebase designs like Basis, ESD, and Seigniorage Shares have wildly fluctuating prices as much as +-40% around $1 that take days/weeks to stabilize before going through another cycle. This is counterproductive and assumes the market actually wants/needs a stablecoin with 0% collateralization. Frax doesn't make this assumption. Instead, it measures the market's preference and finds the actual collateral ratio which holds a stablecoin tightly around $1, periodically testing small differences in the ratio when the price of FRAX slightly rises/drops. Frax uses AMM concepts to make a real-time fractional-algorithmic stablecoin that is as fast at price recovery as Uniswap is at keeping trading pools correctly priced. 

As this system gets more efficient and the velocity of the system increases, collateral pools can include other assets instead of stablecoins like volatile crypto such as ETH and wrapped BTC. As the price of the volatile asset rises, users will use the buy back shares function to distribute the excess value to FXS holders. When the price of the volatile collateral drops, there is an instant arbitrage opportunity to put in more crypto for discounted FXS to keep the collateral ratio at the target. Just like a Uniswap trading pair keeps its constant product function balanced, the Frax Protocol keeps its target collateral ratio balanced to what the market needs for FRAX to be $1. 
The above example uses "collateral" and "FXS" as the two assets within the protocol, but in reality, Frax can have multiple pools of collateral and multiple algorithmic token pools with weights, similar to Balancer. The protocol currently has USDC collateral pools and just 1 algorithmic token: FXS. In v2, we will release a second algorithmic token, the Frax Bond token (FXB) which represents pure debt with an interest rate attached.
We believe that the fractional-algorithmic design of Frax is paradigm shifting for stablecoins. It is fast, real-time balancing, algorithmic, governance-minimized, and extremely resilient. We strongly believe the Frax protocol can become a foil to Bitcoin's "hard money" narrative by demonstrating algorithmic monetary policy to create a trustless stablecoin that all of the crypto community can embrace

Liquidity Programs & Staking

Next - FRAX V2 - Algorithmic Market Operations (AMO)

AMO Overview

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