USDE Price Stability

On Price Stability of ERD

Various implicit and explicit mechanisms ensure that USDE will closely follow the price of USD. We call mechanisms that are based on direct arbitrage opportunities “hard peg mechanisms” and call less direct processes “soft peg mechanisms”. In the following, we go through the different mechanisms one by one.

How does USDE closely follow the price of USD?

The ability to redeem USDE for collateral behind at face value (i.e. 1 USDE for $1 of collateral) and the minimum collateral ratio of 110% create a price floor and price ceiling (respectively) through arbitrage opportunities. We call these "hard peg mechanisms" since they are based on direct processes.

USDE also benefits from less direct mechanisms for USD parity — called "soft peg mechanisms". One of these mechanisms is parity as a Schelling point. Since ERD treats USDE as being equal to USD, parity between the two is an implied equilibrium state of the protocol. Another of these mechanisms is the borrowing fee on new debts. As redemptions increase (implying USDE is below $1), so too does the baseRate — making borrowing less attractive which keeps new USDE from hitting the market and driving the price below $1.

Hard peg mechanisms

Price floor at USD 1 (minus the applicable redemption fee)

One of the core innovations of ERD is that its native stablecoin is redeemable against the underlying collateral held by the borrowers. That means, every USDE holder can exchange their coins for Ether at face value, i.e. for 100 USDE they would get USD 100 worth of Ether. When redeemed, the system uses the USDE to repay the riskiest Trove(s) with the currently lowest collateral ratio, and transfers the respective amount of Ether from the affected positions to the redeemer. In other words, the Ether is drawn from the Troves’ collateral, starting from the position with the lowest collateral ratio.

To enhance user experience for low-collateral borrowers whose loans (Troves) may be vulnerable to redemptions, the system charges a one-off fee on every redemption, called the redemption fee. Being variable, this fee starts at 0%* and increases with every redemption, while decaying to 0% if no redemptions occur over time. The fee makes sure that redemptions will not be more frequent than necessary from a price stability perspective.

As a result of the redemption mechanism, speculators can make instant arbitrage gains whenever the Ether they get in return is worth more than the current value of the redeemed stablecoins. In other words, when the price of 1 USDE is below 1 USD minus the redemption fee applied to 1 USDE, they can immediately sell the redeemed Ether at a higher price than what they paid for USDE in the first place.

Since the redeemed USDE is burned by the protocol, the stablecoin supply (monetary base) will shrink upon every redemption, which usually has a positive effect on the price. As redemptions can be triggered automatically by bots whenever there is an arbitrage opportunity, we expect the exchange rate to quickly recover if it drops below the line.

It is important though to have the right formula for the redemption fee. If the fee is too high, redemptions may become prohibitively expensive even if the price of 1 USDE is significantly below USD 1. In other words, if the redemption fee spikes due to a large redemption without an equivalent immediate reaction of the USDE price, further redemptions may not be profitable until the fee comes down to a sufficiently low level again. On the other hand, if the fee is too low, there will be more or larger redemptions, increasing the risk for low-collateral borrowers of being hit by a redemption.

In our white paper, we propose to determine the redemption fee based on the following base rate formula:

b(t) := b(t-1) + 𝛼 * m/n

where b(t) is the base rate at time t, m the amount of redeemed USDE, n the current supply of USDE, and 𝛼 is a constant parameter. By modulating the fee resulting from a redemption, 𝛼 has an impact on the “hardness” of the price floor. To find the sweet spot, we have to make two assumptions:

• Arbitrageurs redeem their USDE as soon as the peg falls below USD 1, and attempt to maximize their profit

• The Quantitative Theory of Money (QTM) holds: if the price of USDE is below parity by k%, it takes a redemption of k% of the total USDE supply to restore the peg

These assumptions allow us to derive the optimal value for 𝛼. It turns out that by setting 𝛼 to 0.5, profit-maximizing arbitrageurs will redeem just as much USDE as is needed to restore the peg based on the QTM.

Of course, this formula based on classical monetary theory does not guarantee that the exchange rate will always immediately return to parity. However, given the soft peg mechanisms described below, it is unlikely that such a situation will persist for longer periods of time.

If we just look at the hard price ceiling, the recovery speed will mainly depend on how fast the underlying base rate decays to 0%. The exact formula as well as the decay factor are still subject to research and will be determined based on extensive economic modelling.

Price ceiling at USD 1.10

Interestingly, the minimum collateral ratio of 110% creates a natural price ceiling at USD 1.10. When the USDE:USD exchange rate exceeds that level, borrowers can make an instant profit by borrowing the maximum amount against their collateral and selling the USDE on the market for more than USD 1.10. If 1 USDE trades at USD 1.11 for example, you can lock up USD 110 worth of Ether, take out a loan of 100 USDE and sell it for USD 111. No matter if your loans gets liquidated or not, you have made an arbitrage gain of 1 USD.

We expect that this arbitrage opportunity will steer USDE away from reaching USD 1.10 and if it ever hits the ceiling, it will rebound very quickly. This should mitigate a mass influx of risky loans taken out at the minimum collateral ratio in such breakout situations.

Soft peg mechanisms

Parity as a Schelling point

Similarly to other collateralized debt platforms like MakerDAO, ERD treats its stablecoin as being equal to USD when determining the collateral ratio of its Troves. Even though the borrower’s debt is denominated in USDE, the current value of the Ether held as collateral is expressed in USD. Thus, the collateral ratio is defined as the collateral in USD divided by the debt in USDE.

With this enshrined formula, parity between USDE and the USD is fundamentally anchored in the system as its intended natural equilibrium state. Given the redemption mechanism, hard price floor and clear branding as a dollar-based stablecoin, we expect users to view the 1:1 dollar peg as a Schelling Point to which the system tends to return after temporary deviations.

As long as most people foster that belief, it will have a self-reinforcement effect: a USDE price above $1 makes borrowing more attractive (as you can expect to repay at a rate of $1 or lower), whereas a price below $1 incentivizes repaying existing debts (as this state is likely to be short-lived). When more USDE is borrowed than repaid over time, the total USDE supply will grow, which should make the tokens cheaper with regard to the USD and other currencies. Conversely, if the repaid amounts are higher than the new debts, the money supply will shrink, such that USDE will appreciate.

Generally, the long-term outlook of a 1:1 exchange rate between USDE and USD will stabilize the price in the short run too since users will factor in future price changes in their current decisions (buy/sell/borrow/repay etc.). Given that this mechanism crucially depends on assumptions about the future, it only acts a soft peg and does not provide hard guarantees for price stability.

Dampened speculation against the price ceiling

As shown above, the floating range of USDE is confined between USD 1 (minus fees) and USD 1.10. Speculating against those hard borders is difficult and hardly profitable. We posit that this will make USDE less prone to adversarial speculation in general. Let’s assume that USDE trades at USD 1.09 for example. It is clear that the upside for holders is realistically only 1 cent, while the downside is 9 cents. The closer the price gets to the price ceiling, the less interesting it becomes to speculate on further price increases.

Stability Pool as a ERD reserve

A certain fraction of the entire USDE supply will be inside the Stability Pool and thus outside regular circulation. However, the pooled fraction of USDE may depend on the current USDE:USD exchange rate. The higher the price of USDE in USD, the lower will be the (expected) collateral surplus gains in case of liquidations, since the conversion is based on the nominal value of USDE being equal to USD.

As the price of USDE approaches USD 1.10, the risk of a potential loss for depositors increases accordingly, and stability deposits become less attractive. Eventually, owners may withdraw their stability deposits if the loss risk becomes too high. With more ERD being injected into the money markets by former stability depositors, the USDE price should depreciate.

As a result, the Stability Pool will also act as a ERD reserve and help to mitigate the ERD crisis that might occur in case of black swan events affecting the Ether price. With that, the Stability Pool will serve both system stability (solvency) and price stability.

We think that this is a useful tradeoff despite the fact that it reduces the primary buffer for liquidations. Thankfully, the redistribution fallback mechanism and the Recovery Mode are designed to cope with mass liquidations even if the Stability Pool is emptied. While the redistribution of defaulted loans does not directly change the total collateral ratio of the system, it does reduce the individual collateral ratios of the borrowers who receive the debt and collateral shares, potentially below their respective comfort levels. Those borrowers may then either top up their collateral or reduce their debts in order to improve their collateral ratios, which in aggregate increases the total collateral ratio.

As an ultima ratio, the Recovery Mode changes the incentive structure for both borrowers and stability depositors. Only loans with a collateral ratio of 110% or higher at the time of liquidation are offset against the Stability Pool during Recovery Mode, while loans below 110% are directly redistributed to the other borrowers. This not only allows for higher collateral gains, but makes stability deposits practically risk free, assuming that the price of USDE never exceeds USD 1.10.

Economic Modelling

We already mentioned that we are planning to do extensive modelling of our system. One of the questions we would like to answer is how price stability depends on the base rate, and what the optima parameters for the redemption and issuance fee formulas should be. We have already been talking to a few candidates that are experts in macroeconomic modelling and monetary economics.

It turns out that it probably makes sense to pursue our macroeconomic modelling separately from our agent-based simulations and stress testing. The latter are micro-focused, and explore how the behaviors of specific actors like arbitrageurs and speculators drive the system dynamics.

*Note that in the live version of ERD borrow and redemption fees have been capped at a minimum of 0.25%