# USC: Automated Stablecoin Backed by LSTs

Automated stablecoins are a class of stable assets that allow for scalability gains that are not typically found in CDP (Collateralized Debt Positions) stablecoins. The concept of a multi-token mechanism for automated stablecoins originated from the paper titled ["A Note on Cryptocurrency Stabilization: Seigniorage Shares."](https://blog.bitmex.com/wp-content/uploads/2018/06/A-Note-on-Cryptocurrency-Stabilisation-Seigniorage-Shares.pdf) Basis Cash and Empty Set Dollar were the first in implementing this concept, followed by Ampleforth, Fei Protocol, and Terra. Unfortunately, seigniorage shares has been misused, primarily due to i) absence of collateral assets, ii) solely price dependent mechanisms iii) specific limitations that made it hard to decentralize the underlying protocol.

The emergence of Liquid Staking Tokens (LSTs) make us to reconsider this approach. The main challenge of ensuring the stability of an automated stablecoin, especially during market downturns, can be effectively addressed by employing collateral assets (yield-generating) that consistently back the stablecoin supply, even in stressful conditions. This approach also compensates governance token holders with the rewards generated by the collateral, providing intrinsic value to the governance token based on the reserves' reference value. Full collateralization with LSTs not only guarantees security for all stablecoin users but also mitigates the risk of a stablecoin entering a death spiral.

This article discusses how a death spiral is mitigated and explains why LSTs are the suitable assets to achieve this goal.

# Overview
## What are Liquid Staking Tokens (LSTs) ?

LSTs mirror the value of a user's staked ETH position. They have gained significant attention in 2023 as they allow ETH holders to stake their Ethereum while retaining liquidity and accessing enhanced yield opportunities. To become an Ethereum validator, a minimum staking amount of 32 ETH is required, which can be quite costly for individual investors. To solve this issue, Ethereum staking pools were introduced with smaller-scale holders combining their holdings to reach the necessary 32 ETH threshold for validator qualification. Some of these pools then made a unique type of token known as Liquid Staking Derivatives (LSDs), also referred to as Liquid Staking Tokens (LSTs).

## How to optimize yields through LSTs in a stablecoin protocol?

Recently released overcollateralized stablecoin protocols have embraced Liquid Staking Tokens (LSTs) as part of their collateral assets, introducing in a novel category of stablecoins known as yield-bearing stablecoins.


*Note: This is a visual representation illustrating the process of the eUSD yield distribution mechanism within the [Lybra](https://lybra.finance/) system.*

This innovation extends the utility of stablecoins by allowing them to generate yields. However, it presents a challenge for governance token holders who don't benefit from expansion of the stablecoin market capitalization. Consequently, the protocol has no alternative but to impose fees on its users for utilizing the service.

For example, Lybra Finance imposes annual fixed service fees (1.5%) on the stablecoins in circulation, which can significantly diminish the initially promised yield of LSTs for stablecoin holders. This is not a desirable property for a system that wishes to optimize the distribution of yields across protocol's participants.

Within Chi Protocol, the distribution of ETH staking yield differs from the approach used by Lybra Finance. When CHI, the governance token of Chi Protocol, is staked, it entitles the holder to receive all of the LST yield generated by the stablecoin reserves. This not only provides governance token holders with the most rewards generated within the protocol but also establishes a reference value for the required CHI to be staked. Within this system, USC benefits from various sources of yields, including a unique yield mechanism paid in stablecoin and staked CHI incetives, which automatically earn ETH staking yield from the stablecoin reserves.


Since the goal of CHI is not to act as an LST its self, there can be periods where the market considers CHI to be a risky asset (market value of CHI staked < stETH reserves value), or periods where CHI is considered to be a safer asset (market value of CHI staked > stETH reserves value). In both scenario, the ETH staking yield behaviour is there to incetivize stakers and align the CHI staked value to the LST reserves value, such that an equilibrium level is reached.


# The Death Spiral Risk of Automated Stablecoins

## How did Terra work?

Terra-style stablecoins, falling under the category of seigniorage shares, operated using a dual-token system consisting of the native, volatile staking token (LUNA) and a stablecoin (UST). The primary objective of this system was to maintain stability through a simple mechanism:

- **If UST’s market price was above the target price of $1**, say at $1.10, arbitrageurs could buy $1.00 worth of LUNA and burn it in exchange for 1 newly issued UST, profiting from the difference between the UST market value and the target price of $1. This process would be repeated until the UST price returned to $1.
- **Conversely,if UST’s market price fell below the peg**, say to $0.90, the 1 UST could be first purchased and then burnt in exchange for $1.00 worth of newly minted LUNA and arbitrageurs would capitalize on the difference between the target price of $1 and the market value, repeating this until the peg was restored.

## The Collapse of UST

Besides lacking actual collateral, the speculative behavior surrounding the volatile coin was a significant factor that made the system vulnerable to a collapse. Assuming greater demand for stablecoins in the future, more LUNA tokens would have been burned to fully back the UST value. However, when future expected activity dropped to near-zero, the market capitalization of LUNA decreased to an extent where it was considerably smaller than that of the stablecoin. At this point, the system became highly fragile, as even a minor decrease in demand for the stablecoin could trigger the targeting mechanism to generate a large number of LUNA tokens, leading to hyperinflation of the volcoin and subsequent devaluation of the stablecoin.


The collapse of the system could have been highly anticipated, given that UST was supported by LUNA, but the value of LUNA was solely determined by market forces. Consequently, when the expectation of future activity, which formed the basis of LUNA's value, diminished, the market capitalization of the stablecoin decreased together with LUNA. This made the system even more vulnerable and increased the likelihood of the collapse occurring.

# Stopping Death Spirals

The primary risk associated with automated stablecoins is the ominous "death spiral." This peril became evident in the Terra network's experience, where it turned into a self-fulfilling prophecy. Death spirals primarily materialize due to stability mechanisms that are inadequately collateralized and rely solely on price movements. They can manifest in three distinct scenarios:

- A reduction in demand for volatile cryptocurrencies concurrent with an increase in demand for the stablecoin.
- A decrease in demand for volatile cryptocurrencies while the demand for the stablecoin diminishes at a slower pace.
- A decline in demand for volatile cryptocurrencies while the demand for the stablecoin remains constant.

In each of these situations, a mismatch arises between the equity and liabilities of the protocol, leaving it partially unbacked. Once the market becomes aware of this imbalance, it triggers a bank run, ultimately resulting in the collapse of both the stablecoin and the associated volatile token.

This situation has prompted us to propose a new automated stablecoin designed to minimize the risk of entering a death spiral during market crashes. This is achieved through full collateralization with LSTs and the implementation of a stability mechanism that relies not only on price fluctuations but also on solvency considerations. To provide an illustration, we will demonstrate the stopping time at which the stablecoin debt aligns with the backing reserves, creating a protective barrier against the potential dilution of governance token holders, effectively preventing a death spiral event.

## Stability Mechanism of Chi Protocol - A Fully Collateralized Model

The stability of the Chi Protocol is established through the implementation of an open-source[ Quadratic Automatic Market Maker (QAMM)](https://hackmd.io/@6jzKo0C7QCGkNGHQ9oU28g/ryQdB_5M6) built on top of Uniswap. The primary objective of this AMM is to autonomously engage with the USC/ETH liquidity pool with the aim of maintaining the USC price at $1, while simultaneously ensuring complete collateralization through LSTs.

This AMM operates as a three-token mechanism, relying on ETH, USC, and CHI. Whenever there are variations in the USC price from $1, adjustments are made to either the protocol's reserves or the stablecoin supply. This is done to maintain a balanced equilibrium between assets and debt within the system. It is worth mentioning that USC can only be minted with ETH/LST deposits. Upon minting, the arbitrage function is called to maintain asset and debt growth parity. In total, there are six distinct scenarios that have been coded to accommodate arbitrageurs:

## Market Active States
### Excess Reserves

- **Price of USC is above $1**
Issues the necessary amount of USC to bring the price down to $1 and executes a swap for CHI, subsequently burning the acquired CHI tokens.

- **Price of USC is below $1**
Acquires the required quantity of USC to raise the price back to $1 using the ETH reserves. The USC received in exchange is distributed to USC stakers to prevent burning.

## Deficit Reserves

- **Price of USC is above $1**
Mints required amount of USC to lower the price to $1 and initiates a swap for ETH. The ETH received is added to the reserves and subsequently swapped for stETH.

- **Price of USC is below $1**
Acquires the necessary quantity of USC to restore the price to $1 using CHI. The USC obtained is subsequently burned.

## Market Inactive States
- **Price of USC is at approximately $1 and reserves are in excess**
Purchases CHI using the surplus ETH to eliminate the excess, and burns the acquired CHI.


- **Price of USC is at approximately $1 and reserves are in deificit**
Buys ETH with CHI, swaps ETH for stETH and adds the acquired stETH in the reserves to eliminate the deficit.


In the first four scenarios, the system responds to changes in USC price by making necessary adjustments to reserves or USC supply. Meanwhile, in the fifth and sixth cases, the system reacts solely to fluctuations in the underlying collateral's price without requiring market activity for the stablecoin. In all instances, the system maintains stability while preserving solvency.

## Experimenting Stability

Let's denote the value of LST reserves as $V(t)$ and the outstanding stablecoins in the market as $D(t)$.

Our objective is to test the stability of USC under the most challenging market conditions. This scenario could occur due to a sudden drop in the prices of volatile cryptocurrencies, leading to a situation where USC is only partially backed by the USD value of LST reserves. In this context, we are interested in exploring two specific cases:

- When the stablecoin's value moves in the same direction as the market for volatile cryptocurrencies, possibly due to the market's reaction to the sudden price drop.
- When the demand for USC remains unchanged despite the market turbulence.

This will allow us to assess the stability of USC in the face of extreme market stress.

### Thought experiment 1: What happens if the price of ETH declines and the stablecoin trades below peg?

In a scenario where the price of ETH declines, causing selling pressure on USC (resulting in its price falling below $1), the arbitrage contract automatically steps in by purchasing USC using CHI tokens and subsequently burning the USC acquired. During this process, the staked ETH reserves remain untouched, serving as a protective barrier against the dilution of CHI token holders.

The intervention continues until the circulating supply of USC reaches the predetermined barrier set by the reserves. This can be thought of as a predictable stopping time, denoted as $τ = \inf \{t ≥ 0:V(t) \ge D(t) - \Delta K\}$, which limits the CHI dilution. The mechanism effectively prevents a scenario similar to the death spiral that occurred with LUNA and UST, where there was no predefined rule to halt the issuance of LUNA for UST buybacks.


*Note: In this particular scenario, $\Delta$ represents the specific amount of USC that needs to be purchased to increase its price back to $1. The symbol $K$ is simply the target price, which is set at 1 USD.*

When we reach the stopping time, the stablecoin is entirely backed by LSTs. This means that the arbitrage contract can once again perform USC buybacks with ETH using the available reserves. From this point onward, the stability mechanism keeps working, but at a lower equilibrium level.

### Thought experiment 2: What happens if the price of ETH falls and there is no market activity on USC?

In a scenario where the price of ETH decreases significantly, and there is minimal trading activity on USC (with its price close to $1), the arbitrage contract steps in by performing a swap of CHI for ETH, ETH for stETH and adds the acquired stETH to the reserves to eliminate the deficit. This mechanism effectively solves the demand issues of automated stablecoins by allowing the system to respond to market fluctuations without relying on stablecoin's transactional activity.

To describe how the reserves behave in this particular scenario, we can implement a step function. It operates as follows: if the USC debt exceeds the reserves, and the price is approximately $1, the new reserves value at the next time step becomes the current value plus the deficit. In mathematical terms: $V(t+1) = V(t) +\mathbf{1}_{P(t) \approx K, \space D(t)>V(t)}[D(t) -V(t)]$.


Once stETH is added to the reserves, a new equilibrium level is established at a higher point. At this stage, the stability mechanism can continue with full LST collateralization.

## Conclusion

In 2023, the decentralized stablecoin sector remains relatively underrated. CDP-based stablecoins are the most commonly utilized, but they struggle to meet scalability demands. LSTs possess properties that are highly beneficial for a cryptocurrency-native stablecoin, including yield potential and exposure to ETH.

Chi Protocol is focused on addressing critical questions. How to get the most value out of LST deposits? How do we ensure the system's safety and maintain full collateralization during adverse market conditions? We have demonstrated that these challenges can be effectively addressed through an automated stablecoin system built on a three-token mechanism.

Chi Protocol has the potential to bring about significant changes in the DeFi landscape, which would otherwise be dominated by a handful of centralized stablecoin issuers. The fact that 90% of the $130 billion market cap is controlled by entities like Tether, Circle, and Binance underscores the opportunity to explore new stablecoin designs that makes use of the potential given by LSTs and DeFi.