Why the Terra / Luna protocol Will Almost Certainly Fail

1. The Point

TerraUST (ticker UST) is an “algorithmic stablecoin”. The Terra/Luna protocol uses a system of incentives to keep the UST price at its $1 “peg”. Over the last few months, the capitalization of UST has achieved a meteoric rise, from just under $3 Billion in November of last year, to around $16.6 Billion at time of writing (April 4, 2022).

UST is effectively “self-collateralized” by a support coin called Luna. As long as the market capitalization of Luna is greater than the nominal value UST, UST is over collateralized, and holders of UST are safe.

Currently Luna has more than twice the capitalization of UST, and so for the time being UST is able to stay close to its peg. The price of Luna will probably keep rising as long as the usage of UST increases. However, the demand for UST can’t continue to rise indefinitely. Once a steady state is reached it seems unlikely Luna will pay sufficient rewards to make it worthwhile to hold positions (see section 5 below). At this point, capitalization of Luna is likely to fall to below the outstanding nominal amount of UST. If this occurs UST will cease to be fully collateralized.

There seems to be a generally held belief that once a coin is widely enough used, full collateralization doesn’t really matter, and that therefore UST will be able to keep its peg just because everyone “believes it has value”. After all, the argument goes, national fiat currencies and gold only have value because the market believes in them. Actually, as discussed below (see Section 6) this is not correct: both fiat currencies and gold have much firmer foundations than just “the belief of the market”. Essentially, a currency will have stable value only if it is collateralized, or if prices are explicitly denominated in that currency. Neither of these apply to UST.

If the market capitalization of Luna falls below nominal value of UST, it is likely the market will lose confidence in the protocol, Luna will quickly fall to near zero, and UST will lose its peg. The same thing could happen at any time if the current enthusiasm becomes blunted and the market starts to doubt the validity of the protocol.

Algorithmic stable coins with protocols very similar to Terra/Luna have been tried and have failed. I think that there are very good reasons to expect that it is only a matter of time before Terra/Luna goes the same way.

2. What Makes a Stablecoin “Safe”

We can think about the safety of different (so called) stablecoins by considering the question: “What would happen in each case if the market lost confidence in the coin’s value?”.

If holders of the coin don’t suffer losses, even if people stop believing in it, then it seems like we are looking at something pretty solid.

Conversely, if a loss of confidence would result in a price crash — then the value of positions in the coin is sustained by no more than a nebulous cloud of the unfounded faith of the other market participants. If and when people realize this, they have an incentive to sell first, and loss of trust becomes a self-fulfilling prophecy¹

Centralized & Collateralized Stablecoins pass this test. Centralized collateralized stablecoins are issued and managed by central authority and backed by deposits of US dollars. Every stablecoin in circulation is matched by $1 of deposits in bank or trust accounts. Holders can redeem their coins at a rate of $1 per coin at any time by selling them back to the issuing authority.

The largest collateralized centralized and redeemable stablecoins are USDC, USDB, and PAX, having a combined capitalization of over $70 Billion.

Let’s consider what would happen in the case of a loss of confidence. For example, let’s assume that someone starts a false rumor that the coins are not truly backed by collateral. Holders would rush to redeem their coins and (assuming that the rumor is actually false) all holders would still get back the full value of their positions.²

Terra Luna does not pass the test. As is explained below, if people stop having faith in the protocol, it will almost certainly fail.

3. How Terra / Luna Protocol Works

The Terra/Luna protocol was built by Terra Form Labs in South Korea. The protocol is designed to support a number of stablecoins. The largest of these is TerraUST (ticker UST) which has a current market capitalization of $16.6 Billion. The next largest is TerraKRW pegged to the South Korean Won which currently has a capitalization of just over $30 Million.

The protocol aims to keep UST at its $1 price without the use of any external collateral.

Here is how it works:

The system has two coins. UST and Luna. Holders of UST can always swap $1 worth of Luna for 1 UST, or 1 UST for $1 worth of Luna.

If the price of UST rises above $1, anyone can give $1 worth of Luna to the protocol and get 1 UST in return. This creates an arbitrage opportunity. I buy $1 of Luna, swap it with the system for 1 UST, sell my UST for more than $1, and walk away with a profit.

Therefore, if the UST price exceeds $1, everyone will be buying Luna and selling UST. The additional supply of UST will drive its price back down to the $1 peg.

Conversely, if the price of UST falls below its peg, anyone can supply UST to the protocol and get $1 worth of Luna at the then current market price. The idea is that as holders know that they can always get $1 worth of Luna for each UST that they hold, the price can never fall below its $1 peg.

What could go wrong, right?

Unfortunately, this doesn’t really work. The system is still subject to failure in the case of a loss of confidence.

4. What Happens If The Market Loses Confidence Terra Luna?

If the market were to lose confidence in UST, but to still trust in the value of Luna (at least under current circumstances) all would be well. The current capitalization of Luna is just over $40 Billion. This is more than twice the value of UST in circulation. All holders of UST could therefore exchange their positions for Luna; sell the Luna at market price, and so close their positions without loss.

The problem will occur if the market loses confidence in the protocol as a whole. Currently there are $16.6 Billion UST in circulation. If people were to stop believing that the combined value of UST and Luna is worth less than the UST in circulation, then the system would fail. Under these circumstances the fact that holders “can always exchange UST for $1 worth of Luna” wouldn’t help. As holders of UST tried to get out of their positions, more and more Luna would have to be issued driving the price down.

The problem is that the system is “self-collateralized” by Luna. If the market value of the Luna collateral falls below the outstanding issuance of UST, no algorithm, regardless of how clever, can ensure that holders of UST can exit their positions without loss. The value is simply not there.

Ultimately, in the case of a loss of confidence in the protocol, the price of Luna would fall to close to zero and of course UST would be unable to hold its peg.

This is exactly what happened to the Iron Finance’s attempt at an algorithmic stablecoin in June of last year. The protocol worked in a very similar way to Terra. In this case the stablecoin was “Iron” and the “support coin” was “Titanium”. People lost confidence in the protocol and, as we would expect, the Titanium price fell to close to zero. However, as protocol was partially collateralized by USDC (a fully collateralized and redeemable stablecoin) the value of Iron fell only to a low of just under $0.75, which was approximately equal to the value of the underlying collateral. (see Cointelegraph June 2021)

5. Terra/Luna’s business plan

Luna is effectively the equity backing Terra. All of the income earned by the protocol either goes to holders of Luna or is re-invested in the protocol.

The Terra/Luna protocol aims to earn revenue by charging fees for transactions. The whitepaper states that the Terra will achieve wide-spread usage as they intend to charge much lower fees than the major credit card companies. The “base fee” for transaction, they say, will be 0.1%, and fees are capped at 1%.

So far it has been profitable to hold Luna. Terra is only issued in exchange for Luna. Therefore, as the demand for Terra grows, so does the demand for Luna. This has driven up the price from around $59 at the end of November 2021 to $110.37 today.

At a certain point, even if that’s far in the future, the demand for Terra will stop growing. Thereafter it will be attractive to hold Luna only if the protocol generates sufficient revenues.

If Terra is to be fully collateralized, then the market value of Luna needs to be at least as great as that of UST. Let’s assume (conservatively) that a minimum attractive return for holding Luna is 5%.
Even assuming this relatively low target return, and that 100% collateralization is sufficient, this would mean with fees at 0.1%, that the average holder of Terra would need to spend their entire balance at least 50 times per year.

This is because each time all the Terra in existence is spent it would generate a return of 0.1% to Luna (the transaction fee). Therefore, a turnover of 50 times per year would be necessary to get to our target return of 5%. Even if Terra/Luna decides to raise transaction fees to the maximum level of 1%, everyone would still have to spend all of their UST an average of 5 times per year for Luna to achieve a return of 5%.

If we assume that the required collateralization rate is above 100% the required rate of transactions is even greater.

The frequency with which money is spent over a given period is called the “velocity”. The St Louis Fed tells us that the current annual velocity of money is 1.12 — in other words money held in cash or in bank accounts is spent an average of 1.12 times per year.

It seems unlikely that holders of UST will spend their balances fast enough to generate sufficient revenues to support Luna once the demand for UST reaches a steady state.

This implies that if and when the demand for UST stops growing, it will become unattractive to hold Luna, and the Luna price will fall. At this point UST will become under-collateralized and I believe that the protocol will fail.

Maybe then, it’s not important that the protocol should be fully collateralized?

6. Okay Confidence is Important, but What’s the Problem?

So, I’m hoping that it’s clear that if people stopped believing in the value of the Terra Luna protocol, UST would have a hard time maintaining its peg.³

However, people have been happy to hold UST, and investors have enthusiastically supported the protocol based on the idea that this doesn’t matter. More specifically there is a widespread belief that this is exactly equivalent to the situation faced by national fiat currencies which are also uncollateralized. The fact that these currencies have successfully held value, so the argument goes, is only because “people believe in them”. If it’s works for the U.S. Dollar and the Euro, why not for Terra?

Similarly, the argument is made for gold that it “only has value because everyone thinks that it does”.

In both cases this is incorrect. Fiat currencies and gold have much firmer foundations than just shared belief in their value. To understand why, we first need to look at what we mean by “Loss of Confidence”.

6.1 What do we Mean by “Loss of Confidence” ?

So far I have only talked in general terms about “loss of market confidence”. To understand the difference between cryptos and fiat currencies, we need to be a bit more precise.

Currencies have worth because they can be exchanged for goods and services. No one cares per se about the number of monetary units that they hold; they care about the stuff that those units will enable them to buy.

Therefore, for this paper, I will define “market confidence” in a currency or a crypto to specifically mean the confidence that the bundle of goods and services for which that asset can be exchanged will not decline precipitously over time.

In other words, by “market confidence” in an asset, I mean the confidence that this asset will maintain its “purchasing power”.

I stated above that holders of fully a collateralized stablecoins will be protected from loss, even if the market loses confidence in that currency. Given my definition of “market confidence” this could be restated more precisely as:

“Holders of fully collateralized stablecoins will be protected from loss, even if the market ceases to have confidence in the purchasing power of those coins.”

Similarly, my concerns about Terra Luna could be restated more precisely as:

“Holders of Terra will not be protected from loss if the market ceases to have confidence in the combined purchasing power of Terra and Luna”

6.2 Why Fiat Currencies Can Maintain Value Without Collateral

We have said that potential “loss of confidence” is a problem for cryptos. This is equally a problem for fiat currencies. However, if we use definition of “confidence” given above, the difference between fiat currencies and non-stable cryptocurrencies becomes clear.

The question then becomes: Are we confident that the asset will not lose large amounts of its purchasing power?

Although most national currencies are not explicitly backed by an asset, they have intrinsic value and stability because there is a “universal agreement” to use them as the denominator for prices and wages.

Wages and prices are “sticky” and don’t change by large amounts on a moment-to-moment basis. This means that if we own currency, we know what we can buy. We know what our currency is “worth”.

This is not however true for non-stable cryptos.

To say that an asset is “collateralized” means that we know that as a last resort it can be exchanged for the collateral. This implies that as long as the collateral has value, the asset value is protected.

Effectively therefore, as long as the “universal agreement” holds, national currencies are “collateralized” by all of the goods and services that are available for sale.

I can hear the screams of dissent. But please consider:

- We value currency for the goods and services it allows us to buy

- As long as the “universal agreement” holds we are guaranteed to be able to exchange our currency for known amounts of goods and services

- This is the definition of collateralization: the currency can be exchanged for something of known value.

Of course, fiat currencies can fail if the universal agreement breaks down. This can happen with hyperinflation or government failure. But then no collateral is 100% secure.

However, this means that we can be “confident” in the value of fiat currencies (that is, confident that they will not lose most of their purchasing power) unless we expect hyperinflation or government collapse.

6.3 Why Crypto Currencies are Different from Fiat Currencies

No non-stablecoin cryptocurrency is used as a denominator for prices and wages. You can buy cars, real-estate, or just about anything else using Bitcoins. However, in all cases the underlying price is really in U.S. Dollars, or some other national currency, and the Bitcoin price is determined using the Bitcoin/USD exchange rate at the time of the sale.

Therefore, a position in Bitcoins, or any other non-stable crypto, does not have a defined value in goods and services. Price is simply determined by demand, which is in turn driven almost exclusively by future expectations of price. This means that there is no “fair value”, and this causes the price volatility that we see in the crypto markets to far exceed the exchange rate volatility of fiat currencies. For example, US Dollar/Yen exchange rate over the last year had an annualized volatility of 5.96%, whereas the Bitcoin price (equivalent to the US Dollar/Bitcoin exchange rate) had an annualized volatility of 73.85% (Source: Yahoo finance)

Let’s consider what would happen if everyone came to believe with a high degree of confidence, that in one year from now Bitcoins would be worth less than they are today. The vast majority of Bitcoin balances are held as “an investment”, so almost everyone would sell, and the price would collapse. A small proportion of Bitcoins are held as transaction balances (mainly by drug dealers and cyber-criminals) so the price would find a floor, but at far below the current level.

This is a slight over-simplification as some cryptos, including Luna, pay fees or dividends. In some cases, again including Luna, holdings of the crypto are required to engage in mining or other profitable activities. So, in these cases we can only expect a collapse in price if the total return on holding the crypto, including any fees and dividends, is expected to be negative.

Let’s ask the same question for U.S. Dollars. What would happen if everyone came to believe with a high degree of confidence, that in one year from now the U.S. Dollar will be worth less than today? Well, this is of course exactly the situation that we face. The current inflation rate is around 8% (U.S Bureau of Labor Statistics) which means that in a year’s time we can expect our holdings of Dollars to buy less goods and services than they do today. However, unlike what we would expect with cryptos, people are not rushing to sell their Dollars for Yen, Euros or Bitcoins.

This is because, despite the expected fall in value, the universal agreement to denominate prices in U.S. Dollars means that the best way we can protect our purchasing power is to hold U.S. Dollars, or dollar denominated assets.

This is a vast difference. For the market to “lose confidence” in a fiat currency there has to be a generalized expectation of hyperinflation or government failure. For the market to “lose confidence” in a cryptocurrency, there just has to be a generalized expectation that holding the currency will result in a negative return.

6.4 A Stable (Non-Stablecoin) Cryptocurrency IS Possible

In order for a cryptocurrency to have a relatively stable price, it needs to have relatively consistent purchasing power. In order to achieve this, prices need to be denominated in that currency and be relatively stable over time.

Hypothetically we can imagine a market for real estate, cars or other goods and services were sellers posted prices in Bitcoins, and guaranteed to transact at these prices for a period of at least a month.

If the market were large enough, it would mean that a value in Bitcoins would, as fiat currencies do, represent the right to a specific amount of goods and services, and the Bitcoin price would stabilize.

Stability could also be achieved by creating an asset that could be exchanged for a specific amount of a commodity such as kilowatt hours of energy, or agricultural commodities.

The point is that to achieve price stability a cryptocurrency needs to represent a consistent value in goods and service.

6.5 How About Gold?

It is often argued that cryptocurrencies are the “new gold” and are therefore a rational investment as a store of value or a hedge against inflation. Once again, the argument is that gold only has value, because everyone believes that it does.

The misses the point that gold does have intrinsic value. There are several industrial applications, but these make up a relatively small proportion of total demand. The main value of gold is the subjective consensus that gold is beautiful. Gold has been valued for its beauty across multiple continents and cultures for at least five thousand years.

This is reflected in the fact that 46.3% of the world’s gold exists in the form of jewelry, far exceeding the amounts held for private investment or in national reserves (Gold.org Feb 2021 estimate).

Holding gold, or investment funds linked to gold, may or may not yield good long term returns. This depends on what happens to supply, and the demand for its various uses. However, given that it has been valued for its beauty for thousands of years, and that there is no expectation of a large new source of supply, it is likely that it will continue to be a highly valued commodity

(For a fuller explanation see Bitcoins Are Not Digital Gold)

7. The Problem for Terra Luna

I have tried to show that for a currency or cryptocurrency to stable in long term, people need to be confident in the amount of goods and services for which it can be exchanged.

This can be achieved either if the currency is backed by collateral, or if there is a large market for goods and services with stable prices denominated in that currency.

UST can’t be expected to maintain its value just because “the market believes in it”. If people start to suspect that the value of their holdings is subject to the whims of others, there will be an incentive to sell. This is particularly true as there are fully collateralized stablecoins which do not have the same risks.

This means that UST can be expected to hold its peg only as long as it is at least 100% collateralized by Luna.

The price of Luna will keep rising as long as the demand for UST is increasing. However, once demand reaches a steady state, it is difficult to see how the protocol will generate sufficient revenues to make it attractive to continue holding Luna. At this point the price of Luna will fall. When this happens, UST will cease to be fully collateralized, and we can expect a loss of confidence in the protocol which will probably result in a complete failure of both Luna and UST.

[1] This is a classic “Prisoner’s Dilemma”. All holders would be better off if no one liquidates their positions. However, if others liquidate, anyone left holding UST will lose. As each holder is acting independently and cannot control the actions of others, everyone has an incentive to liquidate so as avoid loss.

[2] The stablecoin with the greatest outstanding value is Tether, issued by the company Tether Limited. Tether has a current market capitalization of close to $82 Billion. Tether also claims to be fully collateralized. However many have expressed doubts as to whether this is actually the case (see Bloomberg October 7th 2021). Tether is also not redeemable. We can’t be certain therefore, what would happen if the market lost faith in the value of Tether.

[3]If anyone is still not convinced, imagine that I replicate all elements of the protocol exactly, with two coins called Doomed Stablecoin (DmUSD) and Worthless Supportcoin (WTS). I’m pretty sure that WTS would never gain any traction and that DmUSD would not keep its peg. The only difference between my hypothetical failed attempt and Terra/Luna is the confidence of the market