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Price Stability
XUSD can always be minted and redeemed from the system for $1 of value. This allows arbitragers to balance the demand and supply of XUSD in the open market. If the market price of XUSD is above the price target of$1, then there is an arbitrage opportunity to mint XUSD tokens by placing $1 of value into the system per XUSD and sell the minted XUSD for over$1 in the open market. At all times in order to mint new XUSD a user must place $1 worth of value into the system. The difference is simply what proportion of collateral and XUS makes up that$1 of value. When XUSD is in the 100% collateral phase, 100% of the value that is put into the system to mint XUSD is collateral. As the protocol moves into the fractional phase, part of the value that enters into the system during minting becomes XUS (which is then burned from circulation). For example, in a 98% collateral ratio, every XUSD minted requires $.98 of collateral and burning$.02 of XUS. In a 97% collateral ratio, every XUSD minted requires $.97 of collateral and burning$.03 of XUS, and so on.
If the market price of XUSD is below the price range of $1, then there is an arbitrage opportunity to redeem XUSD tokens by purchasing cheaply on the open market and redeeming XUSD for$1 of value from the system. At all times, a user is able to redeem XUSD for $1 worth of value from the system. The difference is simply what proportion of the collateral and XUS is returned to the redeemer. When XUSD is in the 100% collateral phase, 100% of the value returned from redeeming XUSD is collateral. As the protocol moves into the fractional phase, part of the value that leaves the system during redemption becomes XUS (which is minted to give to the redeeming user). For example, in a 98% collateral ratio, every XUSD can be redeemed for$.98 of collateral and $.02 of minted XUS. In a 97% collateral ratio, every XUSD can be redeemed for$.97 of collateral and $.03 of minted XUS. The XUSD redemption process is seamless, easy to understand, and economically sound. During the 100% phase, it is trivially simple. During the fractional-algorithmic phase, as XUSD is minted, XUS is burned. As XUSD is redeemed, XUS is minted. As long as there is a demand for XUSD, redeeming it for collateral plus XUS simply initiates minting of a similar amount of XUSD into circulation on the other end (which burns a similar amount of XUS). Thus, the XUS token’s value is determined by the demand for XUSD. The value that accrues to the XUS market cap is the summation of the non-collateralized value of XUSD’s market cap. This is the summation of all past and future shaded areas under the curve displayed as follows. The demand-supply curve illustrates how minting and redeeming XUSD keeps the price stabilized (q is quantity, p is price). At $CD_0$ the price of XUSD is at $q_0$ . If there is more demand for XUSD, the curve shifts right to $CD_1$ and a new price, $p_1$ , for the same quantity $q_0$ . In order to recover the price to$1, new XUSD must be minted until
$q_1$
is reached and the
$p_0$
​ price is recovered. Since market capitalization is calculated as price times quantity, the market cap of XUSD at q0​ is the blue square. The market cap of XUSD at
$q_1$
​ is the sum of the areas of the blue square and green square. Notice that in this example the new market cap of XUSD would have been the same if the quantity did not increase because the increase in demand is simply reflected in the price,
$p_1$
. Given an increase in demand, the market cap increases either through an increase in price or an increase in quantity (at a stable price). This is clear because the red square and green square have the same area and thus would have added the same amount of value to the market cap. Note: the semi-shaded portion in the green square denotes the total value of XUS shares that would be burned if the new quantity of XUSD was generated at a hypothetical collateral ratio of 66%. This is important to visualize because XUS market cap is intrinsically linked to the demand for XUSD.
Lastly, it’s important to note that XUSD is an agnostic protocol. It makes no assumptions about what collateral ratio the market will settle on in the long-term. It could be the case that users simply do not have confidence in a stablecoin with 0% collateral that’s entirely algorithmic. The protocol does not make any assumptions about what that ratio is and instead keeps the ratio at what the market demands pricing XUSD at $1. It could be the case that the protocol only ever reaches, for example, a 60% collateral ratio, and only 40% of the XUSD supply is algorithmically stabilized while over half of it is backed by collateral. The protocol only adjusts the collateral ratio as a result of demand for more XUSD and changes in XUSD price. When the price of XUSD falls below$1, the protocol recollateralizes and increases the ratio until confidence is restored and the price recovers. It will not decollateralize the ratio unless demand for XUSD increases again. It could even be possible that XUSD becomes entirely algorithmic but then recollateralizes to a substantial collateral ratio should market conditions demand. We believe this deterministic and reflexive protocol is the most elegant way to measure the market’s confidence in a non-backed stablecoin. Previous algorithmic stablecoin attempts had no collateral within the system on day 1 (and never used collateral in any way). Such previous attempts did not address the lack of market confidence in an algorithmic stablecoin on day 1. It should be noted that even USD, which XUSD is pegged to, was not a fiat currency until it had global prominence.

# Collateral Ratio

The protocol adjusts the collateral ratio during times of XUSD expansion and retraction. During times of expansion, the protocol decollateralizes (lowers the ratio) the system so that less collateral and more XUS must be deposited to mint XUSD. This lowers the amount of collateral backing all XUSD. During times of retraction, the protocol recollateralizes (increases the ratio). This increases the ratio of collateral in the system as a proportion of XUSD supply, increasing market confidence in XUSD as its backing increases.
At genesis, the protocol adjusts the collateral ratio once every hour by a step of .25%. When XUSD is at or above $1, the function lowers the collateral ratio by one step per hour and when the price of XUSD is below$1, the function increases the collateral ratio by one step per hour. This means that if XUSD price is at or over $1 a majority of the time through some time frame, then the net movement of the collateral ratio is decreasing. If XUSD price is under$1 a majority of the time, then the collateral ratio is increasing toward 100% on average.
In a future protocol update, the price feeds for collateral can be deprecated and the minting process can be moved to an auction based system to limit reliance on price data and further decentralize the protocol. In such an update, the protocol would run with no price data required for any asset including XUSD and XUS. Minting and redemptions would happen through open auction blocks where bidders post the highest/lowest ratio of collateral plus XUS they are willing to mint/redeem XUSD for. This auction arrangement would lead to collateral price discovery from within the system itself and not require any price information via oracles. Another possible design instead of auctions could be using PID-controllers to provide arbitrage opportunities for minting and redeeming XUSD similar to how a Uniswap trading pair incentivizes pool assets to keep a constant ratio that converges to their open market target price.