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How the UST peg works, and will it hold?

9 May 2022

UST peg risk
Matteo Bonato

Matteo Bonato

DeFi Risk Specialist

With recent volatility in Terra’s LUNA token, many TerraUSD investors have been wondering how this may impact the peg of UST.

In this article, we’ll explore the potential ramifications of LUNA volatility on UST stability, including examining how some other USD stablecoin pegs work, outlining how the UST peg works, and conditions for the UST peg to hold.

As always, remember to do your research on any investment you choose to make, keeping the risks front of mind.

How the DAI peg works

Dai is created when users borrow against locked collateral, and it is destroyed when loans are repaid. If you deposit Ether or other cryptocurrencies accepted as collateral, you will create a new Dai. When you pay back the borrowed Dai, the locked collateral will be recovered. 

As a stablecoin, Dai must be pegged to the US dollar (so 1 Dai = $1). To maintain its value, the Dai protocol changes its borrowing rate at the primary market level, aiming at a specific price of 1 dollar per DAI: this is called the Target Rate Feedback Mechanism (TRFM) in the DAI protocol. If the price is below $1, then TRFM increases the borrowing rate resulting in supply decreasing, as less people are ready to borrow, resulting in the price going back up (and vice versa if the price is above 1 dollar). 

This over collateralisation mechanism, however capital inefficient, is at the heart of the DAI robust peg.

The threat of final settlement in the primary market is, in the end, what keeps Dai’s value at a dollar. Simply knowing that the system can be settled at any time through liquidation and keepers, thus returning the proper dollar amount of corresponding collateral, is a powerful arbitrage incentive.

The DAI monetary mass is directly linked to the available collateral and that is why the market capitalisation of DAI is a direct function of the available collateral.

It is healthy to see the DAI market capitalisation decrease in a bearish market, as the collateral value decreases and also the appetence to DAI creation as farming opportunities and leveraged long positions tend to be less profitable.

How the USDC peg works

The USDC stablecoin was created by CENTRE, an organisation founded by crypto exchange Coinbase and financial technology (FinTech) firm Circle. 

Each USDC is redeemable for one dollar, and is backed by one dollar or a dollar-denominated asset with equivalent value held in accounts at regulated US financial institutions. Those accounts are audited by US accounting firm Grant Thornton LLP, which issues monthly attestations on the reserves backing USDC.

That simple 100% collateralisation approach with fiat world standard assets is the reason for its robust peg. This means that for every 1 USDC token in circulation there is USD $1 held in collateral. This guaranteed parity by Circle gives USDC its robustness. As soon as the price diverges enough than one dollar (plus/minus the creation/redemption cost), a primary market arbitrage will restore the parity.

How the UST peg works (and may not work)

Unlike other stablecoins (USDT and USDC), UST peg does not rely on the existence of ‘reserves’ to support the peg.

So how does 1 UST come into existence? 

A user can ‘mint’ (i.e. create) 1 UST by depositing 1 USD worth of LUNA tokens on the Terra Station (https://station.terra.money/swap, the primary market for UST). The LUNA tokens are ‘burnt’, i.e. they are destroyed. 

The UST peg to USD exists because (in theory) one can always exchange 1 UST for 1 USD worth of LUNA token in Terra Station. That is: 1 USD is ‘burnt’ (i.e. destroyed) and 1 USD worth of LUNA is ‘minted’ (i.e. created). 

So, if UST is trading, say, on Binance at 0.98 USD, one could: 

  • Buy UST cheap at 0.98USD
  • Go to Terra Station, swap it for 1USD worth of LUNA
  • Sell LUNA immediately and make a 0.02 cent profit for every dollar.

 

Importantly, this holds true only in theory!

If you tried this yourself and entered amounts of UST to be swapped for LUNA, you would see that only for small amounts is your UST worth 1 dollar. The larger the redemption, the larger the ‘price’ it costs you. This is called the ‘spread’, and is the difference between the bid (buy) and ask (sell) price of an asset. 

Why is there a ‘spread’ in the first place? Because it is paramount that the liquidity (i.e. the amount of UST that can be bought and sold) on the primary market be smaller than that on the secondary market (e.g. Binance or Curve). 

If there is less liquidity on the secondary market (e.g. Binance), one could manipulate the price of UST or LUNA easily, then enter the Terra Swap (where the prices of UST and LUNA arrive with a delay of 30 seconds) and buy/sell LUNA/TERRA at a different price and pocket the difference. 

So, if the secondary market is larger than the primary market, it means it will be more difficult to manipulate. The spread is indeed introduced to incentivise players to trade, if possible, on the secondary market as opposed to the primary one. 

Conditions for the UST peg to hold

For the peg to hold, these two conditions are essential, and, needless to say, not guaranteed:

1. There must be more USD worth of LUNA than UST in circulation:

Let’s assume I am the only UST holder. I hold 100 UST. These should be in principle worth (i.e. redeemable for) 100 USD of LUNA. 

If the total value of circulating LUNA (i.e. the market capitalisation of LUNA) is less than 100 USD, it is clear that my 100 UST are worth less than 100 USD since there is not enough LUNA to sustain the redemption. 

So, one key condition is that the market capitalisation of LUNA be larger than that of UST.

2. There must be an economic gain to defend the peg:

I know that I can buy UST on Binance at 0.98 USD, move to Terra Station and swap it for 1 USD worth of LUNA. Sell LUNA and cash 2 cents on each dollar. 

But as soon as I try to swap a large amount (anything above 1 UST million) the price I pay for the swap destroys the gain from arbitraging the fact that UST is trading at a discount. 

In addition, the redeemable UST amount in Terra Station is capped at some level (50 million USD). An en masse redemption would result in an even larger spread.

 

In practice, in some circumstances there would be no incentive for market participants to restore the peg.  

So, who will be defending it?

In practice one could observe the two conditions from above being met simultaneously. 

Consider the following scenarios. 

 

Scenario 1 (Patience): The market capitalisation of LUNA is above that of UST, but UST is facing an en mass liquidation in the secondary markets. Because there are more sellers than buyers, UST trades below par, let’s say at 0.95 USD. Sellers are patient and are not willing to sell it cheaper. 

Now arbitrageurs would kick in, but only if it is profitable for them. Assuming there is a huge amount of UST sold, the same huge amount would need to be redeemed in the Terra Station. Now, because the spreads are very large for large amounts (and there is a daily limit to redemptions of 50 million USD), the arbitrager will have to split redemptions in small orders over a long time horizon. This could take a week. 

The redemption of UST also implies the creation of new LUNA to be immediately sold on the market. Therefore, the LUNA price collapses, making the available value of LUNA (in USD) to decrease, possibly below the value of outstanding USTs. Under this scenario, some UST investors would have managed to get rid of their tokens at a 5% discount, while some others would be left empty handed (no more LUNA USD worth to support the redemption).  

Scenario 2 (Panic): As just seen, it can be dangerous to be patient. UST holders are therefore incentivised to accelerate the conversion to USD by accepting a lower price. Lower prices incentivise arbitrageurs to take higher spreads on the UST redemptions, which happens quicker than in Scenario 1. A lower UST price also implies less LUNA to be minted and sold, so in this scenario LUNA price does not crash. Eventually, the storm is over and UST can regain its peg.

At first glance, Scenario 2 appears as a temporary depegging caused by panicking UST holders stupid enough to give away their UST a discounted price. In reality, though, Terra recuperated at the expense of these UST holders and would have died, if they had been as patient as in Scenario 1. 

Interestingly, these two examples show that Terra can cope better with bank runs and panic than with slow bleedings.

Luna Foundation Guard response to the recent events

Luna Foundation Guard (LFG), a non-protit organisation that seeks to maintain UST stability, has responded the the recent UST de-peg by entering into an over-the-counter loan of 1.5 billion USD so allocated:

  • Loan 750 million USD worth of BTC to OTC trading firms to help protect the UST peg (buy UST if < 1USD)
  • Loan 750 million UST to accumulate BTC as market conditions normalise (buy BTC if UST > 1USD)

Our main concern is that these loans are likely to be collateralised by LUNA, therefore exposing UST further to the LUNA price volatility. 

Conclusions

The safety of a stablecoin is not necessarily related to the quality of its collateral. It is related to the cost/opportunity of initiating a redemption, which is the force behind the stabilisation offered by arbitrageurs. 

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