Why I am Betting against TerraUSD

Stablecoins are cryptocurrencies whose market price is supposed to always be close to the price of a real-world currency, such as USD. In order to keep the price pegged, all stablecoins rely on arbitrage incentives that create demand (pushing up the price) when the price is below the peg and supply when the price is above the peg. Fiat-backed stablecoins, such as USDC or USDT, provide these incentives by promising to redeem issued coins one-to-one for real fiat USD. If a fiat-backed stablecoin trades for example at $0.99, arbitrageurs can make a profit by buying at $0.99 and redeeming at $1.00. In order to be able to keep their promise at all times, fiat-backed stablecoins (claim to) hold 1 USD in their reserves for every coin they issue. Due to this mechanism, the peg of a fiat-backed stablecoin stands and falls with the credibility of its redemption promise, that is, mainly with the perceived integrity of its reserves.

How TerraUSD intends to keep its peg

TerraUSD (UST) is a stablecoin pegged to USD, but not backed by USD. Nevertheless, there is a redemption promise similar to that of fiat-backed stablecoins. Namely, the Terra Protocol allows every 1 UST it issued to be redeemed for 1 USD worth of Terra’s other native token LUNA. So, if for example UST trades at $0.99, arbitrageurs can make a profit by

  1. buying 1 UST for 0.99 USD
  2. redeeming the bought 1 UST for 1 USD worth of LUNA (if LUNA were to trade for example at $100, that would be 0.01 LUNA)
  3. selling the redeemed LUNA for 1 USD

As I will discuss further below in section “Depegging scenarios”, it is the second step, the redemption, that will fail at some point. Initially because of the Terra protocol lowering the redemption ratio (by increasing the so-called spread fee) and in the end because of LUNA being worthless. There is no risk of running out of LUNA, though, since the redemption process is conducted by burning UST and minting new LUNA. As with fiat-backed stablecoins, if UST’s redemption process breaks down then so will its peg. Before regarding in more detail how such a depegging event might play out, let’s first understand the underlying reason for why Terra’s pegging mechanism is inherently fragile.

Fragility

For every 1 UST that wants to convert back to 1 USD there must be 1 USD (or any other non-Terra asset worth 1 USD) willing to either buy UST at a price of $1.00 or, due to Terra’s arbitrage mechanism, buy LUNA at whatever price. Otherwise, if there are more UST eager to leave Terra than there are USD willing to enter Terra in the way just described, UST can obviously no longer trade at parity. At the time of writing there are 18.5B UST while the market cap of LUNA is 28B USD. Naively, one might conclude from that that there should be more than enough USD available for any amount of UST that might want to leave. However, this conclusion would be incorrect. Market cap is defined as market price times circulating supply. So, one would have to sell the complete circulating supply of a token at the prevailing market price in order to generate proceeds to the tune of the token’s market cap. When selling a large amount of tokens, though, none but the first few of them will obtain the prevailing market price, because the price will quickly crash. For that reason, only a USD amount worth a fraction of a token’s market cap can be pulled out of the markets. Now, this line of reasoning implicitly assumes that one cannot sell more than the circulating supply, and for LUNA one can, given LUNA’s variable supply. Nevertheless, while the exact number of USD that can be extracted from LUNA markets is unknown, it is limited and the above reasoning might provide some clue about it. If net more UST than this unknown number of extractable USD want to convert to USD, then UST’s peg must break. (“Net” means that the number of USD that want to convert to UST is subtracted.) This is the reason for why UST supply contractions pose a permanent threat to the peg (assuming they are caused by UST leaving Terra and not by UST merely swapping to LUNA). Terra counters this threat by incentivizing UST supply expansion. However, its approach is not sustainable, as pointed out in the next section.

Terra’s ponzinomics

Terra incentivizes UST supply expansion by offering a staggering 19.5% interest rate on UST via its Anchor Protocol. This interest rate can be conveyed to USD by

  1. Convert 1 USD to 1 UST
  2. Deposit 1 UST into Anchor for some time and receive x UST interest
  3. Convert 1+x UST to 1+x USD

As noted in the last section, step 3 necessitates 1+x USD willing to buy either UST at a price of $1.00 or LUNA at whatever price. During UST supply expansion, there are sufficient USD willing to buy UST at parity, so that the principal (1 USD) and interest (x USD) received in step 3 can be sourced entirely from USD converting to UST. Most of these USD convert to UST as realization of step 1, that is, in order to profit from Terra’s 19.5% interest rate. So, to sum up, during UST supply expansion, principals and interests accrued pursuant to Terra’s 19.5% interest rate are paid by new money that enters Terra in order to enjoy this very interest rate. That, of course, is the hallmark of a Ponzi scheme and not sustainable. Sometime in the future, the inflow of new funds attracted by Terra’s exceptional interest rate will no longer be high enough to compensate for outflowing principals and interests. At that point, Terra’s resilience to UST supply contractions will be tested.

Until then, step 1 above has for LUNA holders (in particular, founders and VCs) the pleasant side effect of pumping their bags. Why? The demand for UST lifts UST’s price above $1.00. This prompts arbitrageurs to buy and burn LUNA in order to mint and sell UST. As a result, the price of LUNA rises. It is this side effect that makes it difficult for those in charge of Terra to recognize the unsustainability of the scheme they are running.

Lastly, let’s have a look at Anchor and the 19.5% interest rate it offers on native UST. At the time of writing, there are 18.5B UST in total. 13.7B UST are deposited into Anchor receiving 6.7M UST in interest every day. Only around 1.5M UST of this daily paid-out interest come from borrowers which, besides, are subsidized by ANC tokens distributed to them. The remaining more than 5M UST stem from the so-called yield reserve. Whenever the yield reserve runs low, it is refilled by Terra, last time in February with 450M UST. Terra accomplishes these refills with funds it arbitrarily assigned to itself during its formation.

Death spiral

The eventual start of a UST supply contraction can trigger a fatal reinforcement of that very contraction due to the following undesired incentives and side effects.

Selling pressure on UST entails selling pressure on LUNA. There are two reasons for this cause-effect relationship. For one thing, as soon as the selling pressure pushes UST’s price below $1.00, arbitrage will set in. As described above, this arbitrage involves minting and selling LUNA. For another thing, UST is a central pillar of the Terra ecosystem. A lot of UST leaving this ecosystem may indicate a weakening interest in Terra and, by extension, prompt speculative LUNA holders to part with their tokens.

Selling pressure on LUNA entails selling pressure on UST. Luna plays a central role in UST’s redemption process. If the price of LUNA drops significantly or fast, then UST holders may worry about the future availability of these redemptions and, by extension, decide to sell their UST while they still get something for it.

These two cause-effect relationships constitute a positive feedback loop. Selling pressure on one token, say UST, causes selling pressure on the other token, LUNA, which in turn causes more selling pressure on UST, and so on. This vicious circle can send UST and LUNA on a death spiral that doesn’t stop before their respective prices hit $0. On top of that, the prospect of an approaching death spiral can unleash selling pressure on its own and thereby initiate that very death spiral as a self-fulfilling prophecy.

The two charts below show the death spiral that happened last year to Iron Finance, a project similar to Terra (UST was called IRON, and LUNA was called TITAN). Note that IRON was 75% backed by a USDC reserve. This reserve wasn’t consumed during the death spiral and therefore provided IRON with an intrinsic value of $0.75. Note also that a death spiral happening to Terra would proceed considerably slower due to some provisions built into Terra’s mechanics. Scenario 1 in the next section illustrates such a slow grinding to death.

TITAN price crashes to $0 in June 2021 (nomics.com)
IRON price crashes to ca. $0.75 in June 2021 (nomics.com)

Depegging scenarios

Terra states that “The Terra protocol’s market module enables users to always trade 1 USD worth of Luna for 1 UST, and vice versa, ..”. This statement, in particular the word “always”, is false. In reality, the Terra protocol offers less and less USD worth of LUNA for 1 UST the more UST per minute are traded. For example, with the current parameters (BasePool=50M SDR, PoolRecoveryPeriod=36 blocks), Terra protocol only pays

  • 0.95 USD for 1 UST, when 450k UST per minute are traded
  • 0.50 USD for 1 UST, when 7M UST per minute are traded

This provision throttles the arbitrage process. As a result, the peg will break, and has done so in the past, whenever a high arbitrage throughput would be needed in order to sustain the peg, that is, primarily during periods of stress. As an example, the chart below shows the depegging incident that happened in May last year. While, in this case, UST regained its peg after about a day, there is no guarantee of recovery, as we will see shortly.

UST price temporarily depegs in May 2021

Let’s assume that, within a certain timeframe, there are net 5B UST that want to convert to USD, but there are only 4B USD extractable from LUNA markets. As detailed further above in section “Fragility”, UST’s peg must break under this assumption. Nonetheless, depending on how UST holders behave, the possible outcomes can be quite diverse, as the following two examples illustrate.

Scenario 1 — Patient UST holders Let’s assume the holders of the 5B UST want to convert to USD as quickly as possible, but they are not willing to sell their UST below $0.95. With this assumption, the price of UST will fall to $0.95 and arbitrageurs will buy and burn UST in order to mint and sell LUNA. However, this arbitrage is only profitable as long as the arbitrageurs can mint more than 0.95 USD worth of LUNA for each burned 1 UST. Therefore, according to above, they have to limit their arbitrage throughput to 450k UST per minute. While the arbitrage goes on, 427.5k USD worth of newly minted LUNA is dumped to the markets every minute and constantly depresses the price of LUNA. Due to the decreasing price, more and more LUNA have to be minted for each newly burned 1 UST in order to create the required equivalent value of 0.95 USD. After about one week (!) of constant arbitraging, 4.21B UST will have been burned, an enormous amount of LUNA will have been minted, and 4B USD will have bought these LUNA. At this point, according to our assumption, no USD is willing to buy LUNA anymore and, therefore, LUNA’s price finally reaches $0. With LUNA being worthless, the arbitrage mechanism ceases to work and nothing prevents UST anymore from falling to $0 as well. Terra is dead. While the lucky first 4.21B UST got away with a 5% haircut, the remaining 790M UST (and, for that matter, all 13.5B UST that had no intention of converting to USD in the first place) leave empty-handed.

Scenario 2 — Panicking UST holders As just seen, it can be dangerous to be patient. UST holders are therefore incentivized to accelerate the conversion to USD by accepting a lower price. Let’s assume the holders of the 5B UST decide that it is better to get 0.50 USD per UST than nothing. With this assumption, the price of UST will fall to $0.50 and prompt arbitrageurs to convert up to 7M UST per minute to LUNA. After about 12 hours of constant arbitraging, 5B UST will have been burned and 2.5B USD will have bought all newly minted LUNA tokens. Every UST holder who wanted to leave Terra got out, albeit with a 50% haircut. At this point, 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 at half 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. These two examples show that Terra can cope better with bank runs and panic than with slow bleedings.

Terra’s Bitcoin reserve

Since recently, Terra tries to mitigate its weaknesses by partially backing UST with non-Terra assets, mainly with Bitcoin. In the last three months, Terra purchased 42.5k Bitcoin (currently worth $1.6B) and $0.3B worth of USDC and USDT. At the time of writing, these assets collateralize the existing 18.5B UST to the tune of 10%. In the future, Terra plans to alter its UST minting process so that its reserve grows in lockstep with the UST supply. In order to mint 1 UST, one would have to add maybe 0.40 USD worth of Bitcoin to Terra’s reserve and burn 0.60 USD worth of LUNA (the exact ratio is yet to be determined). Conversely, it is planned that UST can be redeemed for Bitcoin in addition to LUNA. For the remainder of this article I will assume that these plans have already been realized.

While the Bitcoin reserve does make Terra more robust, the fundamental weaknesses still persist. The pegging mechanism is still inherently fragile, since a sufficiently large UST supply contraction can easily consume the reserve and then still break the peg as before. In addition, the risk of a death spiral persists because of the following positive feedback loop between selling pressure on UST and a weakening reserve.

Selling pressure on UST weakens Terra’s reserve. Selling pressure on UST prompts arbitrageurs to buy and burn UST in order to take Bitcoin out of the reserve and sell them. The selling of these Bitcoin depresses Bitcoin’s price. So, all in all, Terra’s reserve shrinks and its remaining Bitcoins lose value.

A weakening reserve entails selling pressure on UST. Terra’s Bitcoin reserve and LUNA guarantee that 1 UST can be redeemed for an equivalent value of 1 USD. A weakening of this guarantee may prompt UST holders to sell their UST while they still get something for it. What makes it worse is that crypto markets are highly correlated. If the reserve weakens due to a slumping Bitcoin price, chances are that LUNA struggles as well.

Salvation through Bitcoin appreciation

Now, if the Bitcoin reserve would collateralize UST sufficiently strongly that, theoretically, all UST (or at least all UST not controlled by Terra) could be redeemed at parity, then the risk of a collapse would no longer exist. As it happens, the price of Bitcoin more than doubled each year on average during the last 10 years. If this appreciation continues, then UST’s partial collateralization could soon turn into overcollateralization. This is the scenario that Terra is betting on.

However, even if, thanks to a rising Bitcoin price, UST becomes overcollateralized at some point in the future, there is no guarantee that it stays overcollateralized. For one thing, newly minted UST, which each only add about 0.40 USD worth of Bitcoin to the reserve, will lower the collateralization ratio in periods of UST supply expansion. For another thing, if Bitcoin’s price reverses its direction for some reason, then the reserve loses value which, again, effects a lower collateralization ratio. Due to the risk of UST becoming undercollateralized again, Terra will remain fragile in the long run no matter what. The longer it takes for Terra to bust, the bigger Terra will be when it happens, and the bigger the repercussions will be across the DeFi and crypto space and possibly beyond.

Conclusion

Terra’s mechanism for pegging UST to USD is vulnerable to large UST supply contractions. Additionally, it has stress-amplifying properties that allow even not so large contractions to trigger a death spiral. In order to prevent these weaknesses from surfacing, Terra incentivizes UST supply expansion. It does so by offering an artificial 19.5% interest rate on UST and relying on Ponzi’s method for converting principals and interests back to USD. This approach is obviously not sustainable. When the outflow of principals and interests eventually exceeds the inflow of newly attracted money, then the induced expansion will turn into an all the more pronounced contraction. To escape its collapse, Terra recently started acquiring Bitcoin in the hope that a rising Bitcoin price will bring salvation. When this hope is disappointed, UST holders who mistakenly believe they are holding a safe asset are in for a rude awakening.

If you think this article is nothing but FUD, then note that I am happy to put my money where my mouth is. I am offering two bets on UST’s demise, one for charity and one for profit. Up to now, nobody accepted. In particular, Do Kwon, one of Terra’s founders and presumably its most vocal proponent, stayed silent.

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Crypto trader, effective altruist, vegan, occasionally enjoys poker, physics and climbing

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Hjalmar Peters

Hjalmar Peters

Crypto trader, effective altruist, vegan, occasionally enjoys poker, physics and climbing

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