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Whitepaper (Core) - Frax v1
FRAX V2 - Algorithmic Market Operations (AMO)
veFXS & Gauges
Cross Chain FRAX & FXS
Frax Price Index
Token Distribution
The protocol at times will have excess collateral value or require adding collateral to reach the collateral ratio. To quickly redistribute value back to FXS holders or increase system collateral, two special swap functions are built into the protocol: buyback and recollateralize.

# Recollateralization

Anyone can call the recollateralize function which then checks if the total collateral value in USD across the system is below the current collateral ratio. If it is, then the system allows the caller to add up to the amount needed to reach the target collateral ratio in exchange for newly minted FXS at a bonus rate. The bonus rate is set to .20% to quickly incentivize arbitragers to close the gap and recollateralize the protocol to the target ratio. The bonus rate can be adjusted or changed to a dynamic PID controller adjusted variable through governance.
$FXS_{received} = \dfrac{(Y*P_y)(1+B_r)}{P_z}$
$Y$
is the units of collateral needed to reach the collateral ratio
$P_y$
is the price in USD of Y collateral
$B_r$
is the bonus rate for FXS emitted when recollateralizing
$P_z$
is the price in USD of FXS
Example A: There is 100,000,000 FRAX in circulation at a 50% collateral ratio. The total value of collateral across the USDT and USDC pools is 50m USD and the system is balanced. The price of FRAX drops to $.99 and the protocol increases the collateral ratio to 50.25%. There is now $250,000 worth of collateral needed to reach the target ratio. Anyone can call the recollateralize function and place up to $250,000 of collateral into pools to receive an equal value of FXS plus a bonus rate of .20%. Placing 250,000 USDT at a price of $1.00/USDT and a market price of $3.80/FXS is as follows: $FXS_{received} = \dfrac{(250000*1.00)(1+.0075)}{3.80}$ $FXS_{received} = 66282.89$ # Buybacks The opposite scenario occurs when there is excess collateral in the system than required to hold the target collateral ratio. This can happen a number of ways: The protocol has been lowering the collateral ratio successfully keeping the price of FRAX stable Interest bearing collateral is accepted into the protocol and its value accrues Minting and redemption fees are creating revenue In such a scenario, any FXS holder can call the buyback function to exchange the amount of excess collateral value in the system for FXS which is then burned by the protocol. This effectively redistributes any excess value back to the FXS distribution and holders don't need to actively participate in buybacks to gain value since there is no bonus rate for the buyback function. It effectively models a share buyback to the governance token distribution. $Collateral_{received} = \dfrac{Z*P_z}{P_y}$ $Z$ is units of FXS deposited to be burned $P_y$ is the price in USD of the collateral $P_z$ is the price in USD of FXS Example B: There is 150,000,000 FRAX in circulation at a 50% collateral ratio. The total value of collateral across the USDT and USDC pools is 76m USD. There is$1m worth of excess collateral available for FXS buybacks.
Anyone can call the buyback function and burn up to $1,000,000 worth of FXS to receive excess collateral. Burning 238,095.238 FXS at a price of $4.20/FXS to receive USDC at a price of \$.99/USDC is as follows:
$USDC_{received} = \dfrac{238095.238*4.20}{.99}$
$USDC_{received} = 1010101.01$