Stablecoins and Fiat Inflation: A Commentary

What if the Mighty USD does inflate?

What would happen to the value of stablecoins pegged to USD if the USD does inflate uncontrollably? This is still a hypothetical question, but still a good question to ask at this time.

There are several kinds of stablecoins, but I won’t even consider so-called algorithmic stablecoins because these remain unproven at this time. I would like to consider here only two types of stablecoins: fiat-backed (USD-backed) and crypto-backed using a DeFi dApp.

Let’s look at the most liquid and the one with the highest market cap: USDT. What would happen to USDT if USD inflates, say by 10%? It all depends on what Tether decides to do. This is what “centralized” really means: a small team of human managers have to decide what to do. The Tether management has basically three choices:

1. Keep the peg and allow USDT to devalue with USD;
2. Mint and redeem at a higher rate (say at 10% inflation, mint 1 USDT in exchange for $1.10 or redeem 1 USDT for $1.10);
3. Use the Quantity Theory of Money (QTM) and buy back and burn about 10% of USDT at $1.10 (at 10% inflation of USD).

Let’s consider these options one by one.

Visualizing monthly changes in CPI

Keep the Peg

If a stablecoin like USDT were to keep its peg with the USD, then it would have to go down in value also, by definition. Same goes with USD. Even DAI would go down in value along with USD, if it were to keep tracking the value of USD.

Let’s say the mighty USD inflates by 10% off its current purchasing power. What this means is that, on average, things that cost a dollar before would now cost $1.10. Most everything in the grocery goes up in price: bananas, rice, wheat, bread, most would go up in price, but not by the same percentage amount. What makes it difficult to detect inflation when it’s just starting is that, not all commodities go up in price at the same time. Some commodities would go up, but some won’t. As inflation continues, however, say by 20%, then 50%, then 80%, etc, all commodities would go up in price together. It is only at this point that inflation becomes unmistakable for anything else.

When inflation was just getting started in Venezuela, people accused groceries of “price gouging”. It was only when the value of the Venezuelan Bolivar (BEV) kept going down that people started seeing what was going on.

Stablecoins that inflate with USD will most certainly lose popularity. People don’t want to be holding a currency that loses value. Vendors also would rather accept a stablecoin that keeps its value than accept another that is going down in value. When people move to get rid of currency they don’t like, it can quickly spiral downwards. For this reason, I believe that keeping the peg to an inflating fiat can be dangerous to any stablecoin: it can inflate faster than even the fiat backing itself is inflating, simply because its network effect is not as strong as the fiat backing. Therefore, if and when USD starts to inflate, I believe most stablecoin managers would attempt to keep the value of their respective stablecoins. How would they do it? The other two options provide a way for stablecoins to keep the value.

Mint and Redeem at a Higher Exchange Rate

The second option is to mint at a new, higher exchange rate (say $1.10) and also redeem USDT for $1.10. Those who are holding USDT would favor this change. However, those who are just about to accept USDT won’t like it at least in the beginning, simply because it would feel like they’d be getting less USDT in exchange for a higher value ($1.10).

The market may or may not attain equilibrium at the new exchange rate, and it all depends on how Tether is going to mint and redeem at the new rate. Tether could simply use the existing backing to redeem at $1.10, or inject additional USD into the backing accounts in banks, which is equivalent to the third option (buying back using additional capital).

If Tether used the backing to redeem at $1.10, it would be obvious that if everybody redeemed (so called “bank run”), there won’t be enough backing. For this reason, big holders of USDT would redeem at $1.10 at the earliest opportunity. There would be more USDT redeemed than minted, thereby reducing the quantity of USDT in circulation. Normally this would further increase the value of USDT compared to USD, but it won’t because people know that Tether does not have enough USD to redeem all USDT at $1.10; in fact, the backing would be diminishing faster than USDT in circulation is diminishing in quantity. Unless Tether does something else, more and more people would want to redeem the USDT they have in hand, and Tether would be running the risk of running out of USD backing. The risk is real because the last people to redeem could end up holding USDT that could suddenly lose its value because all the backing would be gone. The fear of being last to redeem would cause people to rush to redemption, thereby exacerbating the situation.

Clearly, using the backing to redeem at $1.10 or any other inflating USD amount is not viable.

Use QTM: Buy Back and Burn Using Outside Capital

Tether can stop minting USDT (or mint at a higher exchange rate, say $1.15) and start buying back USDT at $1.10, using outside capital. The effect of this action would be to suddenly increase the backing by how much outside capital is injected; at the same time, the quantity of USDT in circulation would start to decrease.

How much outside capital would need to be injected? In order to assure the market that USDT now has a higher value than USD, Tether can inject 10% of the current backing amount. So if the current backing is $63 billion, inject $6.3 billion. However, by starting a buy back and burn process, it appears that the requisite injected amount can be smaller. Let’s test this hypothesis.

Imagine a static world in which we are concerned only with two states (beginning and end of re-capitalization process), if x is the required minimum injected USD:

b + ∆b = (c - ∆c) * (r + ∆r)
and
x = ∆c * (r + ∆r)

where

b= current backing amount in USD
∆b = delta b: outside capital added to backing for raising exchange rate
x = outside capital for buying back ∆c at the new (r + ∆r) exchange rate
c = current quantity of USDT in circulation
∆c = delta c: USDT quantity in circulation bought back at (r + ∆r) and burned
r = rate of exchange prior to inflation (r = 1.0 and b = c initially)
∆r = delta r (change in rate of exchange)
and
x is used to buy ∆c at (r + ∆r), meaning x = ∆c * (r + ∆r)

Solving for minimum required outside capital x + ∆b for any change in exchange rate ∆r, we get:

b + x + ∆b = c*(r + ∆r) - ∆c*(r + ∆r) + ∆c*(r + ∆r)
b + x + ∆b= c*(r + ∆r)
x + ∆b = - b + c*(1.0 + ∆r)

but b = c ← initial condition, therefore

x + ∆b = c*∆r

The required minimum injected capital, in fiat (USD), is the inflation rate multiplied by current quantity of USDT or any fiat-backed stablecoin in circulation. This is a rough estimate, of course, because we did not take into account the fact that all the quantities involved are very dynamic in nature. We have simplified it quite a bit by freezing two points in time: the start of the re-capitalization process, when total stablecoin units in circulation is c, and the end of it, when total stablecoins in circulation is reduced to (c - ∆c).

This result makes sense: the minimum outside capital needed is proportional to how much the fiat backing has decreased in value. Tether needs as much outside USD to add to its backing for USDT as how much the USD has inflated. What the result doesn’t show is that, as a result of the buy back and burn program, how much of the additional outside USD capital would remain as backing (∆b) and how much would be used to buy back and burn USDT (x). Symmetry in the algebraic expressions suggests that x = ∆b.

As a concrete example, given the current circulation quantity of USDT at more than 63 billion, if the USD inflates by 10%, Tether should set a new exchange rate of 1 USDT = $1.1 and this would require a minimum outside capital of $6.3 billion. At an inflation of 20%, the minimum required outside capital is $12.6 billion. At 30% inflation, $18.9 billion.

The same algebraic calculations hold for any other fiat-backed stablecoin like USDC.

What About Crypto-Backed, Fiat Auto-Tracking Stablecoins?

Many dApps for keeping the value of a stablecoin fairly constant have been proposed and some have been implemented. Recently, a hybrid stablecoin has been introduced (FRAX) that combines backing with another, established stablecoin (USDC) and the classic idea of seignorage shares (algorithmic). FRAX works, but another one (FEI) failed miserably from the start. Here we consider the latest class of stablecoins exemplified by LUSD, the stablecoin issued by borrowing it under the Liquity Protocol.

Something to note with volatile crypto-backed stablecoins: We cannot assume that if the USD inflates, a volatile cryptocurrency used to back a stablecoin would also go up in price (with respect to USD). At any point in time, there may not be a direct correlation between USD inflation and volatile crypto exchange rate. There may be delays in effects, or pre-inflation effects: it’s all about how the market anticipates inflation.

The Liquity Protocol

LUSD is backed by ETH. It is issued to anybody who deposits ETH into the Liquity smart contract. The ETH deposited serves as a volatile crypto collateral to an LUSD “loan”. This loan is like a margin loan and there is no interest charged.

The beauty of the Liquity Protocol is that it does not directly manipulate the exchange rate of LUSD with USD. Rather, Liquity is an elaborate set of incentivized “levers” that reduce the quantity of LUSD in circulation if its value drops with respect to USD; and increase the quantity of LUSD in circulation if its value rises with respect to USD. Liquity is implemented in Ethereum.

A borrower in the Liquity system is motivated by the ability to use the value that’s in his ETH asset, while also participating in its appreciation. The advantages of the loan are apparent when the ETH asset appreciates; however, when ETH drops in market value, the debt position can get liquidated — and that is the risk. From the standpoint of managing the value of stablecoin LUSD, every LUSD borrowed this way increases the quantity of LUSD in circulation.

At some point, when there is too much LUSD borrowed, it can inflate and start to lose market value. The Liquity Protocol has an incentivized mechanism for getting the quantity of LUSD in circulation reduced and thereby increase in market value. LUSD is always redeemable for ETH at the target exchange rate (normally 1 LUSD = 1 USD). So if / when the market rate of LUSD is $0.95, anybody who already holds LUSD can redeem those for ETH at $1.00, meaning that the redeemer gains more ETH, precisely $0.05 in ETH per LUSD redeemed. In short, people are incentivized to redeem LUSD for ETH whenever it drifts lower, which then tends to reduce the quantity in circulation and increase its value.

Note that in the Liquity scheme, the collateral can be another volatile asset. Right now only ETH is supported, but the scheme is extensible to other crypto assets. The more types of crypto assets that can be used as collateral, the better for the stability of LUSD.

So, What Happens to LUSD if USD Inflates?

Unfortunately, the target exchange rate for LUSD in the Liquity Protocol will always be 1.0; it is not modifiable. Lacking governance, the Liquity Protocol as it is, is unable to deal with USD inflation. LUSD would keep tracking USD value downwards, if USD inflates.

A Feature Missing in All Current Stablecoins

It’s not just LUSD that can’t adjust its target exchange rate (TER). In fact, this simple feature is missing in all stablecoins today. We therefore propose adjustable TER as a required feature for any new stablecoin. Let’s consider what an adjustable TER means to stablecoin users.

First of all, who should decide when and by how much to adjust the TER? I propose that these can be decided by owners of the reward token. The feature itself is not difficult to add to the Liquity Protocol.

Any upcoming target exchange rate (TER) adjustment has to be pre-announced in order to give a chance for borrowers to improve their collateralization level. Raising the TER (to, say $1.10 per LUSD) could cause some debt positions to be liquidated. It would also cause redemptions to spike because more LUSD holders would want to redeem at the new target exchange rate, for profit. As expected, these incentives would cause a reduction in the quantity of LUSD in circulation, in proportion to the increase in TER.

TER Adjustment Details

Let’s look into the TER adjustment details by way of a particular example. What would happen during the process of a TER adjustment?

Recall that, in the case of fiat-backed stablecoins, the stablecoin managers have to come up with additional injected capital in the form of fiat, in order to 1) increase the backing and 2) to buy back and burn a large amount of stablecoins. In the case of the Liquity Protocol, the injected capital comes from users themselves, in the form of either increased collaterals and also liquidations.

Let’s say a new, higher TER is announced and you have a “trove” (collateralized debt position) with 10 ETH, your collateral is worth 130% of your loan (minimum is 110%), and the current price of ETH is $3000. Your collateral value is then $30,000 and your loan must be ($30,000 / 1.3) = 23,077 LUSD. If the TER is suddely raised to 1.5 (so that now 1 LUSD = $1.50), then your loan value goes up to 23,077 * 1.5 = $34,615, which is now even higher than the $30,000 collateral. Your trove is immediately liquidated because you did not adjust your trove according to the new TER. Even if your trove is liquidated, however, you should not feel bad because, using your previously borrowed LUSD (all those LUSD are now yours, if you haven’t spent those), you can now buy more ETH than you started with. However, you would probably not open another trove even if you have more ETH to do so, because you now would need more ETH for less LUSD.

In case you decide to do something about the announcement (of a new, higher TER), how much extra ETH would you need to shore up your trove so it doesn’t get liquidated? Using the same situation as in the example above, you would know that, after the TER upgrade, you loan value would increase to $34,615. Therefore, in order to keep the same collateral to loan ratio of 130%, you would have to come up with $15,000 worth of ETH (5 ETH), which is a 50% increase corresponding to the 50% increase in the TER (from 1.0 to 1.5). If you haven’t spent what you originally borrowed, you could use the LUSD you borrowed to buy more ETH; however, you would have to do this prior to the TER raise, which means that you would have to use more than half of your borrowed LUSD (23,077 borrowed versus 15,000 needed) to buy ETH. You would be left with 8,077 LUSD and 15 ETH in the trove. From the standpoint of the trove, however, you would still be 23,077 LUSD behind. Your remaining LUSD are now worth 8,077 * 1.5 = $12,115.50.

If you haven’t spent your LUSD, would you have been better off letting your trove be liquidated than shoring it up? If you chose to be liquidated, you would have 23,077 LUSD net in your hands, now worth 1.5 times in USD. If you chose to shore up, your resulting net worth in LUSD is as follows:

15 ETH = $45,000 = 30,000 LUSD
plus 8,077 LUSD remaining in your hands
minus 23,077 LUSD still to be paid to close the trove
— — — — — — — — — — — — —
Net worth = 15,000 LUSD

Clearly, you would have been better off if you let your trove be liquidated, in case of a TER raise to 1.5.

If you’ve already spent the LUSD you originally borrowed, is it worth investing additional USD cash in order to save your ETH in the trove? As already calculated above, you would need $15,000 to buy 5 ETH to add to your collateral in the trove. It all depends on whether you think ETH would climb instead of crash. If it did climb, you could be ahead; otherwise, if it goes down to a level that would cause your trove to be liquidated anyway, that additional $15,000 you invested would have been a waste. (Note that your trove could be redeemed against rather than liquidated, and in this case your $15,000 wouldn’t be a complete waste.)

Independent Measure of Consumer Price Index (CPI)

Unit fiat value is managed by a central bank, by generally controlling the quantity in circulation. There are several ways by which a central bank manages fiat value, but it all revolves around QTM.

For example, the interest rate can indirectly control the quantity of fiat in circulation by raising the cost of borrowing (creating new units of fiat) or lowering that cost. Raising the interest rate discourages borrowing and encourages banks to keep their cash deposited with the central bank, thereby decreasing fiat quantity in circulation. Lowering the interest rate has the opposite effect, more people borrow money from banks and at larger amounts, thereby introducing new units of fiat into the economy.

Another example of central bank action that can increase or decrease the quantity in circulation is for the central bank to buy or sell assets like T-Bills (Federal government debt, in the case of the U.S.) or even corporate stocks, as the Fed is now doing. When there is too much fiat already in circulation, the central bank would have to mop up excess fiat by selling what it bought during fiat deflation. (Note: controlling quantity of money in circulation has become more complicated since 2008. The above two examples are no longer good example of central bank control — especially the U.S. Fed.)

How do well-managed central banks determine the inflation rate of the fiat currency they manage? By measuring the currency’s purchasing power. Well-managed central banks monitor a fiat currency’s purchasing power using a measure called the Consumer Price Index (CPI). In other words, when oil goes up in price at the gas pump, this price increase does not constitute inflation unless several other commodities go up in price also, commodities that are tracked in the CPI measure.

Now stablecoins can track their respective CPI also, but for any stablecoin currently in existence this is impractical and cannot be measured accurately because none of the existing stablecoins are used widely enough outside of crypto exchanges. For this reason, the only way to control the purchasing power of any stablecoin is to peg it to a fiat currency, usually USD.

A stablecoin pegged to USD is basically taking advantage of the CPI measured for USD. Pegging to a fiat also begins the Value Trust Transference process which quickly builds trust in addition to taking advantage of USD CPI. The Value Trust Transference process recognizes that any existing stablecoin cannot be used to put a price on any commodity other than crypto assets; because nobody buys bananas using USDT, for example.

Pegging to a very widely-used fiat like USD is only necessary until a stablecoin becomes widely used to buy all kinds of commodities. We haven’t witnessed any stablecoin having its own CPI measure, but it will become necessary once (and if) fiat value degrades or inflates by more than 50% and the stablecoin in question achieves wide, multi-national usage.

There will be oracles for a stablecoin CPI, as soon as that stablecoin gains wide enough usage to warrant its own CPI measure. If and when this happens, the TER would become irrelevant for such stablecoin; instead the Liquity-like protocol would track its own purchasing power using a CPI oracle measure. The true measure of stability then becomes disconnected from fiat, but would mean a CPI that is fairly constant over long periods of time.

Epilogue

This whole idea about TER adjustments was presented to the Liquity team, and Robert himself has commented. Robert suggested that pegging to a sort of CPI-adjusted USD could be better than introducing the TER parameter. There are several advantages:

1. Governance would remain unnecessary, as in the original Liquity Protocol, because no TER need be adjusted;
2. Adjustments would come in small monthly updates to the CPI (also looking at the Produce Price Index or PPI as another possible measure), instead of an occasional, abrupt adjustment to the TER.
3. We can still add a hook for when a stablecoin-based (rather than USD-based) CPI becomes a viable measure. The hook would remain dormant until our stablecoin becomes usable for everybody in our daily lives.

I am testing the CPI-adjusted USD idea in BSC. If it gains enough traction in BSC, or more precisely, if it can catch up with Fluity, even though it’s a later entry in the DeFi race, then we know that it is indeed a good idea.

Another useful email comment came from Prof. Lawrence White of George Mason University: there is really no need to buy back USDT in order to increase its value relative to USD. All that is needed is to add outside capital to the backing. The point remains that outside capital is needed to shore up the value of USDT relative to USD.

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