In-depth analysis of algorithmic stablecoins: stability, flexibility, and reflection

Can algorithmic stablecoins truly achieve long-term survival? Will algorithmic stablecoins always be affected by extreme expansion and contraction cycles? Which vision of algorithmic stablecoin is more convincing: a simple rebase model or a multi-token minting system or something else?

In 2014, there are two academic papers on stablecoins worth reading carefully, one is “Hayek Currency: Cryptocurrency Price Stability Solution” by Ferdinando Ametrano, and the other is Robert ·Sams’ “Study on the Stability of Cryptocurrency: Minting Shares.” Ametrano believes that due to the nature of deflation, Bitcoin cannot fully perform the function of a unit of account required by money. Instead, he proposed a rule-oriented, flexible supply of cryptocurrency that can be “rebase” based on demand (that is, to change the money supply of all token holders in proportion).

In “The Mint Share”, Sams proposed a similar model, but with one big difference. The Sams model does not use a rebase mechanism, but is composed of two tokens, namely, the elastic supply of money and the “share” of network investment. For the latter asset owners, Sams calls it “coin share”, which is the only recipient of inflationary rewards brought about by positive supply growth, and the only bearer of the debt burden when the demand for money falls and the network shrinks.

Keen crypto observers recognize that Ametrano’s “Hayek currency” and Sams’s “coin share” are no longer academic abstract terms. The “Hayek Currency” is almost exactly the same as the Ampleforth agreement launched in 2019. Ampleforth broke out in July 2020 and has a market value of more than $1 billion. Recently, Sams’s “coin share” model has become the basis of Basis, Empty Set Dollar (ESD), Basis Cash and Frax algorithm stablecoins to varying degrees.

Now that algorithmic stablecoins are popular, the problem before us is no different from the problem faced by Ametrano and Sams six years ago. The issues listed at the beginning of the article are still inconclusive, and it will take some time to reach a broad consensus. However, this article attempts to start from the first principles of reasoning, combined with the empirical data of the past few months, to discuss some of the basic issues in a simple way.

1. Stable currency background

Algorithmic stablecoins are an independent world, but before in-depth research, it is very necessary to talk about stablecoins. (Readers who are already familiar with stablecoins can skip or skip this section).

Under the influence of the snowballing application of Bitcoin by institutions, the DeFi boom and the upgrade of the Ethereum network, stablecoins have been carnival in this process, with a total market value of more than 25 billion US dollars. This exponential growth has attracted the attention of institutions outside the crypto circle, including many US lawmakers.

In general, we can divide stablecoins into three categories: USD-based stablecoins, multi-asset pools as over-collateralized stablecoins, and algorithmic stablecoins. Our focus in this article is on the last category, but we also need to pay attention to the advantages and disadvantages of other types of stablecoins, because understanding these trade-offs will allow us to highlight the value proposition of algorithmic stablecoins.

The first type of stable currency, including USDT and USDC, is based on U.S. dollars and can be exchanged for U.S. dollars one-to-one. It also includes stable tokens based on centralized exchanges such as BUSD. These stablecoins have the advantage of capital efficiency (that is, no over-collateralization), but the centralized nature of their permissions means that users may be blacklisted. ,

The second category is multi-asset collateralized stablecoins, including MakerDAO’s DAI and Synthetix’s sUSD. Both of these stablecoins are over-collateralized by encrypted assets, and both rely on price oracles to maintain a peg to the US dollar. Unlike centralized tokens such as USDT and USDC, these tokens can be minted without permission. It is worth noting that centralized assets such as USDC can be used as collateral. In addition, the over-collateralized nature of these stablecoins means that they are highly capital-intensive, highly volatile, and highly correlated, which makes these stablecoins vulnerable to crypto attacks in the past.

The third category is algorithmic stable coins. An algorithmic stablecoin is a token that adjusts its supply in a deterministic way (that is, using an algorithm) so that the price of the token moves in the direction of the price target. At the most basic level, algorithmic stablecoins expand their supply when they are above the price target, and shrink when they are below the price target.

Unlike the other two types of stablecoins, algorithmic stablecoins cannot be exchanged for US dollars one-to-one, and there is currently no collateral support for encrypted assets. Most importantly, algorithmic stablecoins are usually highly reflective, that is, demand is largely determined by market sentiment. These demand-side forces are transferred to the token supply, and the token supply may eventually become a feedback cycle.

2. The paradox between reflectivity and algorithm stability

For algorithmic stablecoins to survive for a long time, they must be stable. Due to the internal reflection of algorithmic stablecoins, this is especially difficult for many algorithmic stablecoins. The purpose of algorithmic supply changes is to counter-cyclically, expanding supply will inevitably lower prices, and vice versa. However, in practice, supply changes reflexively magnify directional power, especially for those algorithmic models that do not follow the “coin share” model and separate stablecoin tokens from valuation and debt financing tokens.

For non-algorithmic stablecoins, game theory coordination is not involved, and each stablecoin (at least in theory) can be exchanged for an equivalent amount of US dollars or other forms of collateral. In contrast, the price stability of algorithmic stablecoins cannot be guaranteed at all, because it is completely determined by market psychology. Haseeb Qureshi put it right. In the final analysis, a stable coin is a Schelling point (referring to people’s tendency to choose when there is no communication). If enough people believe that the system will survive, this belief will form a virtuous circle. To ensure its survival.

In fact, if we carefully consider how algorithmic stablecoins can achieve long-term stability, we will find an obvious paradox. In order to achieve price stability, algorithmic stablecoins must expand to a sufficiently large market value so that buy and sell orders will not cause price fluctuations. However, the only way for a purely algorithmic stablecoin to grow to a large enough network is through speculation and reflexivity. The problem with highly reflective growth lies in unsustainability, and contraction is often also reflective. Therefore, there is a paradox: the greater the network value of a stablecoin, the greater its resilience and the greater its ability to withstand huge price shocks. However, only highly reflective algorithmic stablecoins (that is, stablecoins that are prone to extreme expansion/contraction cycles) can reach the large network valuation at the beginning.

Bitcoin also has a similar reflective paradox. In order to be accepted by more and more people, it must increase liquidity, stability and acceptance. The growth of Bitcoin over the years has first been accepted by dark web participants, then by technical experts, and recently by traditional financial institutions. At this point, Bitcoin has gained a kind of tenacity from the deep reflection cycle, which is also the path that algorithmic stablecoins need to follow.

3. Ampleforth: a concise but flawed algorithmic stablecoin

Now let’s move from abstract theory to the real world of algorithmic stablecoins, starting with the largest and simplest Ampleforth protocol.

As mentioned earlier, Ampleforth is almost the same as the “Hayek currency” proposed by Ametrano. AMPL expands and contracts based on the deterministic rule of AMPL Daily Time Weighted Average Price (TWAP): below the price target range (that is, below US$0.96), supply shrinks; above the target range (that is, above US$1.06), supply expansion. The most important thing is that each wallet will participate proportionally in supply changes. For example, if Zhang San held 1,000 AMPL before rebase and the supply increased by 10%, Zhang San now holds 1,100; if Li Si has 1 AMPL, he now holds 1.1 AMPL.

“Rebase” is the difference between Ampleforth’s algorithm model and the “coin share” model adopted by other protocols. Although the Ampleforth white paper did not provide the reasons for the single-token rebase design and the multi-token method, there seem to be two main reasons for this design decision.

The first is simplicity. Regardless of the actual operation effect, Ampleforth’s single-token model has the elegance and simplicity that other algorithmic stablecoins cannot match. Secondly, Ampleforth’s single-token design claims to be the fairest algorithmic stable currency model. Ampleforth is designed so that all token holders can retain the same network share after each restart. Ametrano pointed out this point in his 2014 paper. He elaborated on the “unfairness” of monetary policy actions and compared it with the relative fairness of “Hayek currency”.

This is the reasoning behind the Ampleforth model, which has been copied by other rebase tokens such as BASED and YAM. But before talking about the shortcomings of this model, let’s take a look at Ampleforth’s data for one and a half years. Since its establishment in mid-2019 (only over 500 days), more than three-quarters of Ampleforth’s rebase has been positive or negative. In other words, since its launch, AMPL’s daily time-weighted average price TWAP has exceeded 75% Rebase is outside the target range. To be sure, the agreement is still in its infancy, and it is too early to deny it for these reasons alone.

The defenders of Ampleforth often shirk the problem of lack of stability, and many of them are even dissatisfied with the label of “algorithmic stablecoin”. They believe that Ampleforth only needs to be an “unrelated reserve asset” in a diversified portfolio. However, this idea is very debatable. Take cryptocurrency as an example. This currency is rebase based on a random number generator every day. Just like Ampleforth, this token will have a “significant volatility footprint” and it will certainly not be valuable for this reason alone. Ampleforth’s value proposition lies in its tendency to balance, and in theory this feature will make AMPL a denominated currency.

Imagine if Ampleforth got rid of its not yet “sticky” characteristics and completely transferred price fluctuations to supply fluctuations, so that the price of each AMPL would be basically stable. Will this “mature” Ampleforth really become an ideal choice for transactional base currencies?

We have encountered the key to the problem-the core flaw in the design of Ampleforth. Even if the price of AMPL reaches $1, the purchasing power of AMPL held by individuals will change on the road to $1.

Price stability must not only stabilize the account unit, but also stabilize the value store of the currency. Hayek aims to solve the former, not the latter. It just uses floating currency prices to exchange fixed currency prices and floating wallet balances. The end result is that the purchasing power of the Hayek currency wallet is as volatile as the Bitcoin wallet balance.

Ultimately, the simplicity of Ampleforth, its single-token rebase is a bug. AMPL tokens are a speculative tool that rewards holders with inflation when demand is high, and forces holders to become debt financiers when demand is low. Therefore, it is difficult to see how AMPL can achieve both speculation and stability, which is a necessary condition for stablecoins.

4. Multi-token “coin”

Robert Sams’ vision of “coin share” has never been realized, but a new class of algorithmic stablecoin projects have recently emerged, which have many core components.

Basis Cash raised more than $100 million in funding in 2018 with great fanfare, but it was not launched in the end. Like Basis, Basis Cash is also a multi-token agreement consisting of three tokens, namely BAC (algorithm stablecoin), Basis Cash Shares (when the network expands, its holders can request BAC inflation) and Basis Cash Bonds (when the network is in contraction, it can be purchased at a discount, and when the network exits the inflation phase, it can be redeemed with BAC). Basis Cash is still in the early stages of development and has encountered some early development obstacles. The agreement has not yet undergone a successful supply change.

However, another Seigniorage Shares agreement, Empty Set Dollar (ESD), has gone through multiple cycles of expansion and contraction since its launch in September. In fact, so far, of the more than 200 supply “periods” of ESD (one every 8 hours), nearly 60% of the time TWAP occurs in ESD within the range of US$0.95<x<$1.05, which means ESD The stability is more than twice that of Ampleforth.

At first glance, the mechanism design of ESD seems to be a mixture of Basis and Ampleforth. Like Basis (and Basis Cash), ESD uses bonds to finance agreement debts. These debts must be purchased by burning ESD (thus shrinking supply). Once the agreement expands, it can be exchanged for ESD. But unlike Basis, ESD does not have a third token. When the debt is paid off (that is, after the coupon is redeemed) for expansion, ESD can receive inflation rewards.

The most important thing is that it takes a period of time (5 days) to separate ESD from DAO. During this period, neither can it be traded by its owner, nor can it be rewarded for accumulated inflation. Therefore, the segmented mode of ESD is similar to the function of Basis Cash Shares. Both binding ESD to DAO and purchasing Basis Cash Shares have preset risks (liquidity risk of ESD; price risk of BAS), which may be rewarded for inflation. .

5. Comparison of single-token and multi-token algorithm stable currency models

Obviously, the multi-token design is more complicated than Ampleforth’s single-token model, but it actually only pays a small price for the potential stability it provides.

Simply put, the design adopted by ESD and Basis Cash includes the inherent reflectivity in the system, and the “stable coin” part of the system is (to a certain extent) insulated from market dynamics. Speculators with a risk appetite can guide the agreement during the contraction period in exchange for the benefits of future expansion. However, for those users who only want to have a stable currency with stable purchasing power, at least theoretically, they can hold BAC or ESD, without buying bonds, coupons, stocks, or tying their tokens with DAO. set. Another advantage of this non-rebase feature is that it can be combined with other DeFi projects. Unlike AMPL, BAC and ESD can be used as collateral or loan without having to consider the complex dynamics of continuous supply changes throughout the network.

Evan Kuo, founder and CEO of Ampleforth, criticized algorithmic stablecoin projects such as Basis Cash because they rely on debt market platforms to regulate supply. Advising people to stay away from these “zombie ideas”, Kuo believes that these algorithmic stablecoins are flawed because, like traditional markets, they always rely on the lender of last resort.

However, Evan Kuo’s argument is problematic. Without any reason, it is dangerous to assume dependence on the debt market itself. In fact, due to moral hazard, debt financing in the traditional market is problematic, and corporate entities that are “big to fail” can bear the risk of impunity through socialized assistance costs. ESD or Basis Cash is entirely possible to enter the debt spiral. In this case, if there is no person willing to provide funds, debt will accumulate and the agreement will collapse.

In fact, Ampleforth also needs debt financing to avoid falling into a death spiral. The difference is that this kind of debt financing is hidden in full view, and it is just apportioned to all network participants. Unlike ESD and Basis Cash, it is impossible to participate in the Ampleforth system without becoming an investor in the agreement at the same time. When the network is in a state of contraction, holding AMPL is similar to assuming the debt of the network (in Maple Leaf Capital’s term “acting as a central bank”), because AMPL holders lose tokens every time a negative supply is rebase.

From the perspective of first-principle reasoning and empirical data, we can conclude that the model inspired by multi-token and “coin share” has obvious inherent stability than the single-token rebase scheme. In fact, Ametrano recently updated his Hayek currency theory that he started in 2014. In view of the above problems, he is now more inclined to multi-pass, based on the “coin share” model.

However, even if the multi-token algorithmic stablecoin is better than the single-token model, there is no guarantee that any of these algorithmic stablecoins can last for a long time. In fact, the underlying mechanism design of algorithmic stablecoins excludes such guarantees. As mentioned above, the stability of algorithmic stablecoins is ultimately a reflexive phenomenon based on game theory coordination. Even for agreements such as ESD and Basis Cash that separate transactional and stable purchasing power tokens from value accumulation and debt financing tokens, stablecoin tokens will remain stable only when investors are willing to guide the network when demand drops. When there are no longer enough speculators to believe that the network is resilient, the network will really no longer be resilient.

6. Fragmentary reserve stablecoin: a new era of algorithmic stablecoin?

The speculative nature of pure algorithmic stablecoins is inevitable. However, several nascent agreements have recently emerged that try to control the reflexivity of algorithmic stablecoins by using partial asset mortgages. Fundamentally speaking, you can say that the collateral supporting the “coin share” is the share of the system’s future growth. So, why not add this speculative “collateral” to the actual collateral to make the system more robust?

ESD v2 and Frax do exactly this. ESD v2 is currently still in the research and discussion stage, after which the governance layer will finally vote. If implemented, the upgrade will make some substantial changes to the current ESD protocol. The most important of these is the introduction of “reserve requirements.”

Under the new system, the ESD agreement was initially priced in U.S. dollars, and the target was a reserve ratio of 20-30%. Part of the funds for these reserves comes from the agreement itself. When ESD is higher than a certain price target, the agreement sells ESD on the open market. The USDC reserve will then stabilize the agreement by automatically purchasing ESD during the contraction period until the minimum reserve requirement is reached.

Frax, which has not yet been launched, is a more elegant attempt to create an algorithmic stablecoin with fragmented mortgages. Like Basis Cash, Frax consists of three tokens. FRAX (stable currency), Frax Shares (governance and value accumulation token), Frax Bonds (debt financing token). However, unlike all other algorithmic stablecoins discussed so far, FRAX can always be minted and redeemed at a price of 1 USD.

The minting/redemption mechanism is the core of the Frax network, and it uses a dynamic partial reserve system. To mint a FRAX, users must deposit a certain combination of Frax stock (FXS) worth one dollar and other collateral (USDC or USDT). The ratio of FXS to other collateral is determined by the dynamics of demand for FRAX (as demand increases, the ratio of FXS to other collateral will also increase). Casting FRAX by locking FXS will have a deflationary effect on the supply of FXS. When more FXS is needed to cast FRAX, the supply will decrease and the demand for FXS will naturally increase. On the contrary, as the Frax document pointed out, during the contraction period, the agreement re-collateralized the system, allowing FRAX redeemers to obtain more FXS and less collateral from the system, which increases the collateral in the system The proportion of products in the supply of FRAX, as the support rate of FRAX increases, has increased the market’s confidence in FRAX.

In fact, dynamic mortgage as a stable countercyclical mechanism enables the Frax protocol to weaken the negative effects of extreme reflexes when necessary. But it allows the agreement to remain open in order to become a completely unsecured agreement in the future. In this sense, Frax’s dynamic mortgage mechanism is very unpredictable.

Neither Frax nor ESD v2 are online, so it remains to be seen whether the two can be successful in practice. But at least in theory, these hybrid partial reserve agreements are promising. They combine reflexivity with stability while still maintaining higher capital efficiency than over-collateralized alternatives such as DAI and sUSD.

in conclusion

Algorithmic stablecoin is a great currency attempt. Although these agreements have the complexity of game theory, it is difficult to fully capture them from reasoning alone. In addition, if there are any signs of past crypto market cycles, we should be prepared for these dynamics to work in ways that believe in rational expectations.

Nevertheless, it is foolish to deny algorithmic stablecoins at this early stage, but it is also a mistake to forget how risky it is. Although the algorithmic stablecoin is still in its infancy, it may eventually become Hayek’s blueprint for the vigorous development of the currency market.