This is one of my most in-depth analyses yet. You can find the interactive version of this article here: note this may take a minute or two to build, but it allows you to manipulate my code and see how I worked through the assumptions. Otherwise I will do my best to recreate it below:

Fei Protocol

The Fei protocol is the mechanism by which the Fei stablecoin is issued. It uses a mechanism called ‘Direct Incentives’ in order to maintain stability. TRIBE is the governance token that controls changes to the protocol. This token is issued to people who hold the Uniswap Liquidity Provider tokens for the FEI/TRIBE pair. The whitepaper is available here. ( Archive) ( My copy)

Direct Incentives

The direct incentives system is meant to provide a way for this undercollateralized stablecoin to maintain it’s peg. This mechanism differs from over-collateralized stablecoins like Dai or from pegged stablecoins like Tether.

Many Decentralized Finance (DeFi) applications rely on a concept known as Total Value Locked (TVL) and the users of the protocol will have some claim against those assets. Fei attempts to create a new idea around this called Protocol Controlled Value (PCV), which are funds controlled directly by the protocol that no one has a claim against. Note: they claim this is an entirely new innovation but Dai/MKR have a concept they refer to as the Maker Buffer which contains crypto assets (in this case Dai) that is value the protocol controls that no one else has a claim against.

The example they provide is one in which the Fei protocol controls 90% of the liquidity in the FEI/USDC pool on Uniswap (that’s a lot of liquidity to assume but we will get to that). They describe the current liquidity as containing 1100 Fei and 1000 USDC giving an implied value to the Fei stablecoin of $1.10 (assuming that USDC is still valued at $1).

In order for this model to have a chance to be successful, there needs to be a way to generally add to PCV so that these trades can continue to occur. Especially since this effectively serves as the backstop to restore the peg (at least in whichever pool it is active in). The Fei protocol relies on a concept called bonding curves to achieve this. A bonding curve is simply a curve that represents the price of a token as a function of its supply. The specific curve is described as a one-way curve bonded to Ether than does not allow selling. I am immediately skeptical of anything that is one-way, but let’s review the implementation before we jump to any conclusions.

The practical way this functions it that a user can deposit a certain amount of Ether into a smart contract and they receive in return a certain quantity of Fei. Unlike in Dai where you can return your stablecoin to the contract and get the collateral out, here you have no claim on that collateral, and the collateral is deployed as liquidity on Uniswap.

Trying to Mathematically Understand Bonding Curve

As expected we are incentivized to put our Ether into the bonding curve in order to get Fei at any period before it reaches the ‘Scale Target’

After reaching the supply target the exchange rate on the curve is now set at $1 (in Ether) plus a constant fee. These curves are one-way so you can always exchange Ether for Fei, but you can never exchange Fei for Ether using them.

Things get more complicated when we are forced to deal with the interaction between this bonding curve and the deposit of liqudity into Uniswap. The Ether that is sent to the bonding curve in order to receive Fei is then sent to another Minter contract that issues an amount of Fei proportional to the amount of Ether based on the Uniswap price and sends both (the minted Fei and Ether) to the FEI/ETH pool. This is what is contributing to PCV which helps backstop the peg. The importance of this is that the amount of Fei issued is actually TWICE (approximately) what you would initially believe based on the bonding curve. The effects of this on price/peg are minimized by the fact that the Fei sent to the pair does not circulate, but can be burnt to correct peg imbalances.

Trying to Understand Incentives to Maintain Peg

The Fei protocol will offer incentive contracts that attempt to maintain the peg. When Fei is below the peg then the contract will offer additional Fei to the next trader to purchase Fei. (This seems like it would further break the peg, I need to work through the example)

So based on the values given in the version of the whitepaper that I was seeing. ( My copy) I could not get my numbers to match theirs. A quick Twitter exchange:

with their cofounder showed me that their whitepaper was incorrect. Fixing that mistake, the numbers started to make more sense. Re-doing the math with the Fei liquidity corrected resulted in the appropriate value for additional Fei reward.

The effect of the quadratic on this equation is that it becomes incredibly expensive to trade your Fei for Ether when it is below the peg. If the peg breaks to $0.95, a very reasonable possibility considering the peg breaks in other historical algorithmic stablecoins, then you are paying an additional 25% in burnt fees to make the trade. This has a peculiar effect. Namely it makes it so that for those who are trading below the peg, you end up trading vastly below the peg. You are very strongly discouraged for selling your Fei for Ether in this pool. However, there could be other places where it could be possible for you to exchange that Fei. Combining this with the earlier minting mechanics results in this:

So as we can see the the quadratic again helps to ensure that generally this would be net deflationary, which would hopefully help provide a positive pressure to the peg.

Above the peg there is a buffer of relatively free trade. When the peg is between 1 and the value of the buffer embedded in the curve, there is no additional fee to exchange your Fei for Ether. This hopefully provides an incentive for people to make that trade and keep it near the target price. If the price rises above the buffer, you can still trade without the extra ‘burn’ fee, but there is also an added incentive for people to go directly to the bonding curve contract and mint new Fei, and immediately exchange them for Ether here. This does seem like a clever way to keep the value within the window between 1 and (1 + the buffer).

Governance and TRIBE

In order to govern this protocol, set various parameters, and decide which wallets and accounts are excluded from the incentives above there is an additional token involved in this system TRIBE. This token is being distributed to early adopters through a 2 year staking pool, given to those who participate in the very first bonding curve transaction (remember that one is already getting a huge discount on Fei), and sold on Uniswap over the next four years. The remainder is held by the development team and investors. It is unclear to me how much is held by investors.

So is this really stable?

Well, maybe? The incentives combine together such that the most liquid market for Fei will generally be in the Fei protocol incentivized FEI/Ether pool (remember whatever you get from the bonding curve also goes into this pool). This helps ensure that in that pool at least the protocol can maintain the peg. However, this would not necessarily be true across all pools or liquidity venues. In order to model the likelihood of breaking peg the Fei team was using a concept they referred to as the liquidity ratio of the protocol in order to determine what the likely behavior would be under difference situations.

This liquidity ratio is defined as the portfolio controlled value dividided by the user controlled Fei in circulation. This is somewhat analgaous to a measure of protocol collateralization, except that this is not collateral, no one has a claim to it, and it’s deployed in an active liquidity pool. The PCV in this ratio is important because that is what is used to re-balance anytime the burn and mint incentives are inadequate.

When the price is above the buffer then there is a pressure for people to go to the bonding curve and mint new Fei. This increases the user controlled Fei, but also similarly increases portfolio controlled value, this provides a pressure to move this liquidity ratio towards 1.

When above the peg but below the buffer we are in the ‘free zone’ where there is little active incentives and so the liquidity ratio is unlikely to change much.

When the price is below the peg things get more interesting. The minting and burning mechanics we discussed earlier are generally net deflationary, which results in a decrease in user controlled Fei which should generally increase the liquidity ratio. However, if a reweight is needed, generally the portfolio controlled value is going to decrease which will decrease the liquidity ratio. If the liquidity ratio is below 1 when a reweight begins then it is possible that the peg will not recover. This can be compounded by significant external liquidity in the pool that needs to be paid to correct the peg. The burn mechanisms below the peg will also make it seem like the peg is even more broken for holders of Fei since they will effectively need to burn part of their Fei holdings in order to get Ether.

Overall, this is a fascinating protocol. Significant downward pressure on the peg can make things funky and expensive below the peg, but the re-weights provide a clever mechanism to get back to parity. I do think there is an implied assumption built into this stablecoin that Ether will either hold it’s value or increase. Otherwise the actual protocol controlled value can rapidly decrease and can quickly end up in low liquidity ratio scenarios. In cases like this it is still somewhat possible to retrieve a quantity of Ether proportional to your control of Fei (minus the burn fees), but that Ether will be worth much less than your Fei was. I think it is very important for governance members to make sure they try to maintain a liquidity ratio significantly greater than 1 to help handle the regular flunctuations of Ether.

I am worried about the governance of this token. Control of liquidity like this with a mandate that allows for finding ways to earn yield on that liquidity may result in hidden risks to the overall capitalization of the protocol, and if not done carefully can significantly reduce the resiliency. Furthermore, without knowing how much will be allocated to each category there is definitely risk of a small number of people controlling governance for this token. There are three categories where the public can initially get it:

  1. 1. Staking FEI/TRIBE Uniswap LP tokens
  2. 2. Be part of the first group to purchase Fei from the bonding curve
  3. 3. Buy on Uniswap

The remainder is reserved for:

Without knowing how much is reserved for each group and with large whales potentially able to get large amounts of Fei in the initial genesis group, it is possible that the token distribution of TRIBE will be overly concentrated.

Originally published at on March 29, 2021.

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