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$FRAX Economics Analysis &Token Design | How to analyse token economics of stablecoins

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Frax Protocol.

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TLDR below. This is not financial advice.

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General Conclusion

$FRAX is the first fractional algorithmic stablecoin protocol with the goal of providing a highly scalable and decentralised cryptocurrency. In the FRAX protocol, there are two active tokens, $FRAX (stablecoin) and $FXS (FRAX shares).

Classifying Stablecoins

There are four main categories:

  1. Mechanism

  2. Peg

  3. Collateral Amount

  4. Collateral Type

$FRAX uses three mechanisms: dual token, reserve-based mechanism, and algorithmic mechanism. It is soft-pegged to the US dollar. $FRAX is partially collateralised so it has 100% or fewer assets or reserve backing the value of the token. It uses on-chain assets and there are two main assets in place:

  1. The stablecoin, so $USDC and $USDT, which is the collateral amount itself

  2. Collateralised by the secondary token which is the $FRAX Share Token ($FXS)

Dual Token

This means that there are two tokens in the system — $FRAX and $FXS.

$FRAX: It is soft-pegged to the US dollar and is not very volatile. It maintains the peg which is the desired outcome.

$FXS: This token captures the value that is within the ecosystem as well as being a governance token. Three types of value can be accrued by the $FXS:

  1. Value creation from seigniorage shares of the $Frax

  2. The fees collected by the ecosystem

  3. Any excess collateral amount of value that is being accrued

Reserves

$FRAX is also backed by reserves and is under collateralised. If it is 20% backed by $USDC, for example, then the other 80% needs to be $FSX. $FRAX is backed 100% by assets and a part of it is $USDC which is acknowledged by everyone and can be traded anywhere. $FSX is an asset created within the ecosystem and is more valued in the ecosystem than outside.

Reserve Backed Asset Classification

$FRAX can be used to redeem the underlying collateral which means every $FRAX that you mint or burn is linked to some amount of $USDC and some amount of $FRAX.

$FRAX

$FRAX is also an algorithmic stablecoin that is stabilised via mortgaging of assets and burning $FXS. Currently, the assets used as collateral to create $FRAX only have stablecoins such as $USDC and $USDT before in due course allowing collateral with other assets.

$FRAX is minted/redeemed to peg at $1.

The total value of $FRAX minted is guaranteed to be equal to the sum of the value of $FXS (the number of $FXS to be burned). When $FRAX is redeemed, the user will get back the collateral and $FXS at the same value (amount of $FXS minted).

For example, $USDC’s collateral rate is 99%, so to generate $1 worth of $FRAX requires $0.99 worth of $USDC and $0.1 worth of $FXS. Or, at a collateral rate of 98%, to redeem 1 $FRAX the user will receive $0.98 in $USDC and $0.2 in $FXS.

Details of the formula for calculating the amount of minting/redeem $FRAX you can find here.

Minting $FRAX

This is a four-step process:

  1. Determine how much $USDC you have: E.g 100 $USDC

  2. You want to figure out what is the collateral (C) ratio that the system has, and the C ratio is protocol wide. Let us say it is 75% which means that 75% in collateral is $USDC or $USDT and 25% is $FXS

  3. Find out how much $FXS is needed: Let’s say $FRAX is $2.6

  • $1 * 100 $USDC * 25% (1 – collateral ratio or 75%) = $2.6 * $FXS* 75%

  • $FXS= 12.82

    1. Calculate how much $FRAX is going to be minted?

  • FRAX Minted = collateral value + $FXS value

  • FRAX= 100($USDC)* $1 + 12.82($FXS)*$2.6 = 133.33 $FRAX

Maintaining Stability

Arbitrage

One of the main things in any stablecoin ecosystem is that the ecosystem itself will always recognise the stablecoin as 1 dollar which is very important because this is how arbitrage happens. Arbitrage is when the same asset has two different values in different places. You can buy from a place where it is cheaper and sell it at a place where it is more expensive.

>$1

When it is more than 1 dollar then users will want to mint $FRAX and sell it in the secondary market.

<$1

When it is less than 1 dollar people will buy from the secondary market and sell it in the primary market. Selling means burning and redeeming it for the underlying collateral. This helps to balance the system back to 1 dollar because supply is reduced which helps to bring the prices up.

C-Ratio Update

The other important thing is the C ratio update. $FRAX itself wants to update the C ratio quite dynamically. The C ratio as mentioned is a system-wide matrix-like Alchemix, but it allows you to change which is similar to Maker because they have a different kind of C ratio within the system.

PID Controller

The C ratio is maintained using the PID controller which is something that was updated in Q1 of this year. It updates the C ratio based on the growth rate which is a relative matrix, to understand the price of $FRAX as well as the circulating supply of $FXS. When the price of $FRAX increases or decreases it affects the total supply of $FRAX shares available.

When it is more than 1 dollar people mint more $FRAX and when it is less than 1 dollar people will burn and redeem it for the underlying $FXS. This increases or decreases the supply and affects the prices. There is a relationship between the $FXS and the $FRAX which is important in maintaining the stability of the system.

They calculate a simple ratio to understand the relationship between the circulating supply of $FXS as well as the total supply of $FRAX available. Using this ratio they will update the collateral amount or the collateral ratio by the entire system. It’s like a small controller where you can change the knobs of the entire system. You can increase or decrease the C ratio based on the relationship of $FRAX versus the $FXS.

Token Design

Dynamic C Ration Change

It is good to have a dynamic C ratio change with the growth factors because these are important relationships that we want to balance in the system. When we talk about the economics of a system it is not just the demand and supply, but the interacting dynamic relationship between a lot of different supporting factors. In the FRAX protocol, there is $FXS as well as $FRAX, so the C ratio changes dynamically based on the growth rate.

Number Of Days Unpegged

I did an analysis of about 100 days with a band of +/- 5% in Q1 and based on that, 0% of the days were unpegged. This means that 100% of them were pegged within a +/- 5% range, which is pretty stable.

The Proportion Of Days Above And Below $1

If you look at the analysis it was 62% above $1 and 38% below $1. It is much easier when the token is above $1 because then you are looking at expansionary policies. When it is below $1 then you are looking at contractionary policies that can create doom loop cycles, which is not very healthy for the ecosystem.

The Flexibility Between Algo And Reserve Stablecoins

Reserve means it is backed by $USDC, whereas Algo is backed by another asset which is the $FXS and it captures value in different ways.

Financial Incentives

  1. It generates revenue through the collateral in V2. This helps to support the value of $FXS itself which helps to support the value of $FRAX in general.

  2. The secondary token ($FXS) is used to absorb the volatility linked to $FRAX and this is very important because the growth rate also links $FRAX with $FXS.

  3. It is backed by $USDC at least to some percentage so that means that if the $FXS goes to zero at least a good amount of it is still backed by $USDC. If we say it is 75%, that means that for every 1 dollar 75 cents is backed by some underlying asset so you can have faith that there is still some value in these assets. In this situation, the prices will not go lower than 75 cents because 75 cents is definitely backed by $USDC.

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TLDR:

Frax, the project has a different approach than all other algorithmic stablecoins with a model of 2 tokens that complement each other. When $FRAX becomes stable, the supply of FXS decreases, and when $FRAX decreases in value, the supply of $FXS increases.

Ps: Order the textbook “Economics and Math of Token Engineering and DeFi” today!