Reliability of Terra stablecoins under correlation with LUNA
Serhii Strutynskyi, Alex Kondratyuk.
Foreword. On April 27, 2022, an article «How the Anchor trouble can destroy the Terra economy and the cryptocurrency market» was published. At the same time we have prepared the material about reliability of Terra stablecoins, which is presented below.
Introduction
The purpose of stablecoins is to bind its value to a corresponding financial instrument. For the most common assets, its price corresponds to the US dollar. They have been issuing as ERC-20 tokens on the Ethereum blockchain. At the time of publication, stablecoins are issued on Tron, BNB Chain, Solana, and other EVM-compatible networks. Also, stablecoins can be issued as a cryptocurrency in a separate blockchain.
Various algorithms are used to issue tokens and support their stability. The most rational way is to use the corresponding amount of reserves in the currency to which they are linked. The funds are held in the bank accounts of the issuing organizations.
This algorithm is used by Tether Limited, which issued USDT tokens on the Tron, Ethereum, Solana, Omni, Avalanche and other networks. Initially issued stablecoins were fully backed by US dollars. However, at the time of writing, the tokens are also backed by securities and other financial instruments. The stability of USDT exchange rate can be ensured because token holders can exchange them for US dollars at any time. This will not affect the price of the stablecoin in any way, because it is unprofitable to sell USDT below $1. However, stablecoins are held by the company, which creates risks of unjustified blocking of assets.
A different algorithm for implementing of stablecoins is used in MakerDAO. The platform release the DAI token, which corresponds to a value of the US dollar. ETH or other cryptocurrency is used as collateral. High volatility of cryptocurrencies leads to the fact, that collateral cost should be higher than the stablecoin cost, equal $1. Significant coin prices variations require more than 145% backing for each issued DAI. Thus, 1 DAI account more than $1.45 in ETH, WBTC and other tokens. The MakerDAO platform manages a decentralized autonomous organization, which does not require a centralized holding of funds. Blocking of the collateral and DAI issuing is carried out using smart contracts. In the similar way, platform withdraw coins from circulation.
There is an algorithm for a fast withdrawal of DAI stablecoins, which engaged, when the value reduces below a certain level. In this case, an auction begins, during which users redeem collateral (for example, ETH) for DAI. Generated stablecoins are destroyed, which leads to a reduction of emission.
Features of Terra stablecoins
Terra stablecoins function in a similar way. The platform issues stablecoins backed by another asset. For all stablecoins of the project LUNA is used as collateral. The entire emission is used for this purpose. The most common token is UST, the value of which is pegged to the US dollar.
All operations are performed by users through a decentralized application. The issuance of UST results in the burning of the corresponding amount of LUNA. The user receives UST in return for the sent LUNA. When UST is withdrawn from circulation, the platform issues LUNA tokens of the corresponding value and sends them to the transaction initiator.
In some cases, the processes of issuing and burning can be considered similar to blocking an asset that acts as collateral. The statement is true if a LUNA price has not changed from the moment of issue to the withdrawal of stablecoins. If the value of LUNA has fallen over time, the platform need to issue more coins than was spent when issuing UST. On the contrary, if the LUNA rate increases, fewer tokens are issued.
A decrease of LUNA emission stimulates the growth of its value, and the reverse process, most likely, leads to a fall in its exchange rate. An increase in the capitalization of stablecoins in the past could have contributed to the growth in the value of LUNA cryptocurrency.
Such a relationship creates significant inflationary risks that arise when stablecoins are withdrawn from the Terra ecosystem.
The platform uses arbitrageurs to restore the balance between supply and demand for stablecoins. Exchanging of a significant amount of UST for LUNA reduces the capitalization of the stablecoin and leads to a drop in its price. The acquisition of a large amount of stablecoins triggers reverse process. Restoring the balance between supply and demand is provided by arbitrageurs through the purchase of UST. Transactions are beneficial for them, because they bring significant profits.
The absence of arbitrageurs would lead to a significant decrease in value of the stablecoin and an additional issuance of LUNA. If the transfer amount is a significant part of LUNA’s capitalization, one or more large transactions can trigger inflationary processes.
Action of arbitrageurs may hide some operations performed by market participants. An entity that withdraws stablecoins from circulation can pursue two goals:
● exchange UST for LUNA;
● exchange UST for LUNA for further conversion into another cryptocurrency.
In the second case, the subject can exchange Terra USD for another stablecoin, such as DAI. A detailed review of market processes shows that the withdrawal of a significant amount of UST from circulation does not affect the value of stablecoins due to arbitrageurs, but the operation stimulates a decrease in the price of LUNA.
The transfer of a significant amount of funds in this direction upsets the balance between supply and demand for the LUNA cryptocurrency. In the context of a downtrend and negative news, a significant drop in the value of LUNA may occur.
Correlation on the cryptocurrency market
Buying or selling a significant amount of cryptocurrency significantly affects its value. To demonstrate the relationship, consider the situation on February 8, 2021, when Tesla investing in Bitcoin. Company acquired $1.5 billion, and the purchase of the cryptocurrency was officially confirmed. From a technical point of view, this operation is equivalent to depositing funds into a Bitcoin ecosystem. As a result of the transaction, there was a significant increase in the value of the first cryptocurrency.
At the same time, the increase in a market capitalization of Bitcoin, caused by an increase in its price, many times exceeded the funds invested by Tesla. In a short period of time after the event, capitalization growth amounted to more than $59 billion, according to CoinGecko data.
Market data indicates that there is a relationship between investments in cryptocurrency and its capitalization growth. From a mathematical point of view, the relationship of these quantities can be denoted using the correlation coefficient. In this case, a correlation coefficient is 39.
As a result of the withdrawal of funds from the ecosystem, a significant drop in value of a cryptocurrency can occur. However, in order to provoke a significant decrease in capitalization, it is necessary to conduct a transaction in a falling market.
Modeling a drop of LUNA capitalization under correlation with UST
A significant drop of LUNA capitalizationcan may occur when a large amount of UST are withdrawn from the ecosystem, since the operation is carried out using LUNA cryptocurrency. A similar incident could occur as a result of exchanging UST for another stablecoin or cryptocurrency. In other words, there is a correlation between the capitalizations of Terra (mainly UST) and LUNA.
The considered processes force us to rethink the backing of Terra stablecoins with LUNA cryptocurrency. Comparing UST with DAI stablecoin, we can note that for DAI this dependence is practically absent. The reason is that the capitalization of ETH at the time of writing is more than 33 times exceeds the capitalization of DAI. The exchange of a full amount of DAI emission for another stablecoin in case of insufficient liquidity on trading platforms can be done by withdrawing DAI from circulation and releasing blocked funds in ETH. In this case, less than 3.3% of total ETH emission will be sold. Cryptocurrency sales can significantly affect its value when the market falls.
A significant decrease of LUNA`s cost could lead to its capitalization approaching the cost of all Terra stablebloins. The publication presents simulation results that determine the conditions under which the capitalization of LUNA and Terra stablecoins will equalize.
Initial parameters for modeling:
● initial capitalization of LUNA: $43.19 billion;
● initial capitalization of Terra stablecoins: $12.23 billion;
● correlation coefficient: k=10.
The correlation coefficient shows the ratio between the decline in LUNA’s capitalization and the amount of UST withdrawn from circulation.
The simulation results are illustrated by two dependencies:
● The LUNA_Market_Cap chart shows the dependence of LUNA’s capitalization (in $ billion) on the amount in UST withdrawn from the ecosystem (UST_trnsfer, $ billion);
● The TERRA_Market_Cap chart shows the dependence of Terra stablecoins capitalization (in $ billion) on the amount in UST withdrawn from the ecosystem (UST_transfer, $ billion).
The second dependence is used for clarity. It allows to demonstrate that with decreasing in the capitalization of UST to $3.44 billion, the LUNA`s capitalization will decrease to $8.75 billion and become equal to the capitalization of all Terra stablecoins.
The proposed model does not take into account the dependence of the correlation coefficient on the number of transfers, the volume of one transfer and other factors. The largest impact has the total amount of Terra stablecoins withdrawal from the ecosystem in a short period of time.
Let us consider detailed negative scenario in conditions of a significant correlation between the capitalization of TERRA stablecoins and LUNA cryptocurrency. Negative news, panic in the market, or a FUD attack can initiate stablecoins withdrawal from the ecosystem. Under the influence of these factors, UST holders may resort to exchange asset for other stablecoins (USDC, USDT or DAI). Liquidity on trading platforms is limited, which will require LUNA usage as an intermediary in exchange operation. Conducting transactions will leads to additional LUNA emission.
After each operation additional emission of LUNA will occur and its price will drop rapidly. At a certain stage, it will be impossible to exchange UST for another stablecoin until a significant decrease in the value of LUNA. As a result, the user will lose money when exchanging Terra USD for another stablecoin.
As soon as the likelihood of a further drop in the value of stablecoins becomes high enough, arbitrageurs will refuse to maintain the price peg and may resort to withdrawing funds from the ecosystem. With further deterioration of the situation, the owners of Terra stablecoins will get rid of assets massively. As soon as the UST depreciates significantly, the price peg will be completely lost.
Events can occur in the following sequence:
1. The arbitrageurs absence leads to price decrease of stablecoins.
2. The fall in the value of UST provokes its exchange for other stablecoins.
3. The price of Terra stablecoins rapidly falls on the trading platforms. The exchange of UST for other stablecoins through Luna leads to a sharp decrease of this cryptocurrency.
Loss of a price peg may occur with a smaller fall of LUNA’s capitalization due to limited liquidity on exchanges. Significant parts of coins are blocked, so part of assets cannot be used to restore the balance between supply and demand.
In January 2022, the non-profit organization Luna Foundation Guard (LFG) was created. Their main task is to increase the reliability of Terra stablecoins. For this purpose were created reserves that allow maintaining a target value of stablecoins. Funds are held in USDT and BTC. Assets can be used in emergency situations, such as a sharp drop of LUNA price caused by decrease in demand.
However, the volume of reserves was significantly lower than the capitalization of stablecoins, which did not eliminate described problems. The funds are held under an organization control, so UST is not an algorithmic stablecoin. This approach brings Terra stablecoins closer to the tokens issued by Tether Limited, which have a centralized issuer.
Conclusions
A significant decline in LUNA’s capitalization has low probability. Such an incident is possible in downtrend conditions; panic in the market or as a result of targeted action. In the simulation, the correlation coefficient was chosen to be 10 for demonstrative purposes. Determination of its value is the task of further research, because coefficient depends on various factors.
However, obtained results allow us to offer practical recommendations to increase the resilience of ecosystems like Terra and improve the stablecoins peg to the target value:
1. It is necessary to limit the maximum emission of stablecoins, which should depend on the capitalization of the collateral cryptocurrency.
2. It is required to add market levers that allow adjusting the number of stablecoins in circulation depending on the current capitalization of the collateral cryptocurrency.
Fees can serve as a lever that allows you to smoothly regulate the number of stablecoins in circulation. Positive results can be obtained by dynamically changing of fees. Commissions should depend on the direction of exchange of stablecoins for collateral cryptocurrency (forward or reverse).
Fees should be reduced to zero when exchanging stablecoins for collateral cryptocurrency in the case of high capitalization of stablecoins. Comissions for transfers in the opposite direction should be doubled. The income of validators will be stable with the same volume of transactions in both directions. However, this will encourage users to exchange stablecoins for collateral cryptocurrency. When total market capitalization of stablecoins decreases, commissions for transfers in both directions will be equalized. It is also necessary to pay commission fees to validators in collateral cryptocurrency.
The platform can regulate an emission of stablecoins by information impact. This requires three zones, which limit a ratio between the capitalization of the collateral cryptocurrency and stablecoins:
● the green zone — low capitalization of stablecoins;
● the yellow zone — optimal capitalization of stablecoins;
● the red zone — high capitalization of stablecoins.
Platform needs to inform users that it is risky to store savings in stablecoins when the ecosystem is in the red zone. This factor will lead to decrease of the issuance of stablecoins. In the yellow zone, a price drop of stablecoin is unlikely, but there are no incentives for further growth of its issuance. When the capitalization of stablecoins is below a certain value, the ecosystem is in the green zone and risks are minimal. In this case platform can stimulate an additional issue of stablecoins.
The platform should use economically justified threshold ratios between the capitalization of stablecoins and collateral cryptocurrency. These parameters separate red, yellow and green zones. The platform can use an experience of the MakerDAO, which uses collateral that is more than 1.45 times the value of DAI.