Algorithmic stablecoins: origin, development, controversy and future evolution

There are two academic papers published in 2014 that are worthy of attention: one written by Ferdinando Ametrano  , a professor at the Politecnico di Milano, who was the project leader of the Bitcoin Developers Conference  . “(Hayek Money: The Cryptocurrency Price Stability Solution); another one, written by Robert Sams  , a cryptocurrency economist with 11 years of experience in hedge funds  , is titled “Cryptocurrency Stabilization: Seignorage Shares” (A Note on Cryptocurrency Stabilisation: Seigniorage Shares).


Drawing on economist Friedrich Hayek’s criticism of the gold standard, Ametrano believes that due to its deflationary nature, Bitcoin cannot fully perform our requirements for the function of currency as a unit of account. Instead, he proposed a rule built on,  the supply elasticity  of encryption currency, can be “on demand  token supply change  ” (rebase), for example, in proportion to changes in the money supply all tokens holders.

In the  paper ”  Seigniorage Shares “, Sams proposed a similar model based on similar reasons, but with one important adjustment: Sams’s system does not re-adjust the supply of tokens, that is, change the currency allocated in all wallets proportionally. The supply is composed of  two tokens  : the currency itself, which is flexible in supply, and the ” share  ” of investment in the network  . The owner of the latter asset (Sams called it Seigniorage Shares) is  the only recipient of the inflationary gains brought about by the increase in supply  , and  the only bearer of debt when the demand for money shrinks and the network shrinks  .

Smart cryptocurrency observers will immediately realize that Ametrano’s ”  Hayek Currency  ” and Sams’s “Seigniorage Shares” are no longer purely abstract academic concepts. “Hayek Currency” is  almost identical to  Ampleforth . Ampleforth was launched in 2019 and soared in July 2020. Its fully diluted market value has exceeded US$1 billion. Recently, Sams’ Seigniorage Shares model has become the theoretical basis of Basis, Empty Set Dollar , Basis Cash and Frax to varying degrees.

Now, the problem before us is no different from the problem faced by their readers when Ametrano and Sams published their paper 6 years ago:

  • Can algorithmic stablecoins truly achieve  long-term viability ?
  • Will algorithmic stablecoins be subject to extreme expansion and contraction cycles forever  ?
  • Which version of the algorithmic stablecoin is more compelling: a simple  rebasing  model, a multi-token ”  Seigniorage Shares  ” system, or something completely different?

On all these issues, the public jury has not yet reached a verdict, and it may take some time to reach a broad consensus. Nevertheless, this article attempts to  explore some basic questions from the  first-principles reasoning approach and some empirical data in recent months.

Stable currency background

Algorithmic stablecoin  itself is an independent world, but it is worth taking a step back and discussing the broader stablecoin landscape before delving into it

With Bitcoin’s snowball adoption by financial institutions, the hot market for decentralized financial DeFi, coupled with the upcoming network upgrade of Ethereum, stablecoins have also become popular recently, with a total market value of more than $25 billion. This parabolic growth has attracted the enthusiastic attention of bigwigs outside the cryptography circle, and even recently attracted the attention of a group of US congressmen.


USDT  is still the top stablecoin in the current market share, but it is by no means the only stablecoin. Broadly speaking, we can divide stablecoins into three categories: stablecoins secured by  US  dollars,  stablecoins over-collateralized  by multi-asset pools, and  algorithmic stablecoins  . The focus of this article is on the last category. However, it is important to pay attention to the advantages and disadvantages of other types of stablecoins, because understanding these trade-offs will allow us to enhance the value proposition of algorithmic stablecoins.

The first type of stablecoins (mainly USDT and USDC, but also stablecoins issued by exchanges, such as BUSD, HUSD, etc.) belong to  centralized management  , backed by U.S. dollars, and can be exchanged at a 1:1 exchange rate. These stablecoins have the advantages of ensuring anchoring and high capital efficiency (that is, no over-collateralization), but they require permission and are centrally managed. These properties mean that users may be blacklisted and exchange rate anchored It depends on  the trustworthy behavior of centralized entities  .

The second category is multi-asset mortgage stablecoins, including MakerDAO’s  DAI  and  Synthetix  ‘s  sUSD  . Both of these stablecoins are over-collateralized by  crypto assets  , and both rely on price oracles to maintain their anchor to the US dollar. Unlike centralized tokens such as USDT and USDC, the second stablecoin can be minted without permission. However, it is worth noting that in the DAI use case, licensed centralized assets such as USDC can be used as collateral. In addition, the nature of the over-collateralization mechanism of the second stablecoin means that the capital is too dense, and the highly volatile and highly relevant nature of crypto assets makes these stable currencies vulnerable to the impact of the entire crypto market in the past.

All these make us pay more attention to algorithmic stablecoins. Algorithmic stablecoins are tokens  that use a  deterministic mechanism (that is, using algorithms) to adjust their supply, aiming to move the price of the token toward the price target.

In simple terms, algorithmic stablecoins will expand their supply when they are above the target price, and shrink when they are below the target price.

Unlike the other two types of stablecoins, algorithmic stablecoins can neither be exchanged with the US dollar at a 1:1 exchange rate, nor are there currently crypto assets as collateral. Finally, and perhaps most importantly, algorithmic stablecoins are usually  highly reflexive  : demand is largely driven by  market sentiment and momentum  (critics may object to this). These demand-side forces are transferred to the supply of tokens, thereby generating further directional momentum, which may eventually form a violent feedback loop.

Each stablecoin model weighs its pros and cons. Investors who don’t care much about the impact of centralization will not think there is something wrong with USDT and USDC. Others will feel that overcollateralization with inefficient capital is a price worth paying in exchange for unlicensed, decentralized, hard-anchored currency. But for those who are not satisfied with these two options, algorithmic stablecoins are an attractive choice.

The paradox of reflexivity and algorithm stability

For algorithmic stablecoins to achieve long-term viability, they must achieve  stability  . For many algorithmic stablecoins, this is a particularly difficult task due to its inherent reflexivity. The supply change based on the algorithm is a  countercyclical policy  ; expanding supply is aimed at lowering prices, and reducing supply is aimed at raising prices. But in actual operation, supply changes usually amplify directional momentum through reflexivity   , especially for algorithmic models that do not follow the “seigniorage shares” model. In the seigniorage shares model, the stablecoin token itself and the token that accumulates value and debt financing are two independent tokens.

For non-algorithmic stablecoins, network guidance does not involve game theory coordination. Each stablecoin (at least in theory) can be exchanged for equivalent dollars or other forms of collateral. In contrast, the successful price stability of algorithmic stablecoins cannot be guaranteed at all, because it is completely determined by  collective market psychology  .

Haseeb Qureshi,  managing partner of  Dragonfly Capital,  aptly pointed out this point: “These mechanisms use a key insight: the stablecoin is ultimately a Schelling point. If enough people believe that the system can survive, then this This belief will bring a virtuous circle to ensure its survival.”

In fact, if we consider more carefully what algorithmic stablecoins need to achieve long-term stability, we will find an  obvious paradox  . In order to achieve price stability, algorithmic stablecoins must grow to a large enough market value so that buying and selling orders will not cause price fluctuations. However, the only way for pure algorithmic stablecoins to grow to a large enough network is through  speculative trading and  reflexivity. The problem with high reflexivity growth is that it is unsustainable, and contraction is usually also reflexive. Therefore, a paradox arises: the greater the  network value of a stablecoin  , the greater its resilience to  large-scale price shocks  . However, only highly reflexive algorithmic stablecoins, that is, those coins that are prone to extreme expansion/contraction cycles, can first obtain a great network valuation.

Bitcoin has a similar paradox of reflexivity. In order for more and more people and organizations to use Bitcoin, Bitcoin must have increasingly stronger liquidity, stability and acceptance. Over the years, these characteristics of Bitcoin have been continuously enhanced, allowing Bitcoin users to  expand from the initial  dark web participants to the later  wealthy technical staff  , and more recently  traditional financial institutions  . At this point, Bitcoin has  gained resistance from a deep reflexive cycle  , which is a path that algorithmic stablecoins also need to follow.

Ampleforth: A simple but flawed algorithmic stablecoin

Let us now turn our attention from abstract theory to the real world of algorithmic stablecoins  . First, start with the largest but simplest protocol in existence:  Ampleforth .

As mentioned earlier, Ampleforth is  almost the same as the ” Hayek currency ” proposed by Ferdinando Ametrano  . AMPL’s supply is expanded and contracted according to the deterministic rule based on the daily time-weighted average price (TWAP): below the price target range (for example, less than $0.96), the supply shrinks, and above the price target range (for example, high At US$1.06) then the supply will increase. It is essential that each wallet “participates” in proportion to each supply change. If Alice held 1,000 AMPL before the rebase and the supply increased by 10%, Alice now holds 1,100 AMPL; if Bob owns 1 AMPL, then he now owns 1.1 AMPL.

The ” rebase  ” that covers the entire network  is the difference between Ampleforth’s algorithm model and the seigniorage share model adopted by other protocols. Although the Ampleforth white paper does not explain the basic principles of the single-token rebasing design rather than the multi-token approach, the design decision seems to have two main basis.

  • The first is  simplicity  . No matter how it works in practice, 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 stablecoin model.

In stark contrast to the policy actions of fiat currency, the policy actions of fiat  currency benefit those individuals who are ”  closest ” to the source of the currency the most (the “Cantillon effect”). The design of Ampleforth allows all currency holders to rebase after each rebase. Can keep the network share held by it unchanged. Ametrano pointed out this in his 2014 paper. He detailed the “serious unfairness” of the central bank’s monetary policy behavior and compared it with the relative fairness of “Hayek currency”.

This is the presumption principle of the Ampleforth model, which has been replicated by other algorithmic stablecoins (such as BASED and YAM) that use the rebase principle. But before discussing the shortcomings of this model, we may first look at the data we have about Ampleforth’s performance for one and a half years.

Since mid-2019 (just over 500 days so far), three-quarters of Ampleforth’s daily rebases are positive or negative. In other words, more than 75% of AMPL’s TWAP since its launch has exceeded the rebase target range. To be sure, the agreement is still in its infancy so far, so it is too early to deny it for these reasons alone. However, we will soon study how the modified seigniorage stablecoin  Empty Set Dollar  can maintain the stability more than twice that of Ampleforth in the first few months of its birth.


Ampleforth’s diehard fans often dismiss the token’s lack of stability; many of them even hate the “algorithmic stablecoin” label. Their argument is that it is enough for Ampleforth to become a “reserve asset that has no correlation with traditional financial assets” in portfolio diversification.

But this statement is questionable. For example, a cryptocurrency is rebase based on a random number generator every day. Like Ampleforth, the token will have an “obvious volatility footprint”, but it is not valid to say that it has value for this reason alone. Ampleforth’s value proposition depends on its  tendency towards equilibrium  , which in theory can make AMPL a pricing currency.

But will it? Imagine if Ampleforth got rid of its “difficult” characteristics so far, and completely transferred its price fluctuations to supply fluctuations, so that the price of each AMPL would basically remain stable. Is this “mature” Ampleforth really an ideal choice for trading base currencies?

In this way, we have discussed the crux of the problem and the core flaw of Ampleforth’s design  :  even if the price of AMPL reaches $1, the purchasing power of AMPL held by individuals will continue to change as it reaches $1. As early as 2014, Robert Sams clarified this exact question regarding Ametrano’s Hayek currency concept:

Price stability is not only related to   the stability of the pricing unit , but also related to  the stability of currency value storage  . Hayek currency aims to solve the former, not the latter. It just replaces the fixed wallet balance and fluctuating currency price with a fixed currency price and fluctuating wallet balance. The end result is that the purchasing power of the Hayek wallet is as unstable as the Bitcoin wallet balance.

In the end, the simplicity of Ampleforth (its simple single-token rebase model) became a  loophole  rather than a feature.

AMPL token is a  speculative tool  that rewards its holders through inflation when demand is high, and forces its holders to become debt financiers when demand is low. Therefore, it is difficult to see how AMPL can achieve both speculative purposes and the stability necessary for stablecoins.

Multi-token “seigniorage” plan

Robert Sams’s “Seigniorage Shares” vision has never become a reality, but recently a batch of new algorithmic stablecoin projects have adopted many of its  core components  .

Basis Cash, which  was born just over a week  ago, is a public attempt to revive Basis. Basis is an algorithmic stablecoin project that raised more than $100 million in 2018 and was highly praised, but it has not been launched. Like Basis, Basis Cash is a  multi-token protocol  consisting of three tokens:  BAC  (algorithmic stablecoin),  Basis Cash Shares  (the holders of which can benefit from BAC inflation as the network expands) and  Basis Cash Bonds  (you can buy at a discount when the network is in contraction, and can be exchanged for BAC when the network is out of deflation). Basis Cash is still in the early stages of development and has encountered some early development obstacles; the agreement has not yet made a successful supply change.

But another project like Seigniorage Share  Empty Set Dollar  (ESD) has been active since September, and has gone through multiple cycles of expansion and contraction. In fact, ESD has so far reached more than 200 supply epochs (one every eight hours), of which nearly 60% of the changes, the TWAP of ESD is within the range of $0.95 <x <$1.05, which means that the price stability of ESD has been It is more than twice that of Ampleforth, although the life span of ESD is much shorter so far.


At first glance, the mechanism design of ESD seems to be a mixture of Basis and Ampleforth   . Similar to Basis (and Basis Cash), ESD uses bonds (coupons) to fund agreement debts. Bonds must  be purchased by  burning ESD (therefore reducing supply), and can be exchanged for ESD after the agreement resumes supply expansion. But unlike Basis, ESD does not have a third token that is rewarded from inflation when the network pays off debts and enters expansion. Instead, ESD holders can ” bind  ” (such as pledge) their ESD in the ESD decentralized autonomous organization DAO  , thereby distributing the benefits of inflation proportionally, similar to Ampleforth’s rebase.

Crucially, the unbound ESD from the DAO requires a ”  temporary storage  ” period, in which ESD tokens are temporarily “temporarily stored” for 15 epochs (5 days), during which time they can neither be traded nor obtained by their owners Inflation rewards. Therefore, the “temporary storage” mode function of ESD is similar to  Basis Cash Shares  , because binding ESD to DAO and purchasing Basis Cash Shares presuppose risks (liquidity risk of ESD; price risk of BAS) in exchange for future inflation rewards potential. Indeed, although ESD uses two token models (ESD and coupons) instead of Basis Cash’s three-token model, the final result of the temporary storage period of ESD is that ESD becomes a de facto  three-token system  , and the bound ESD is similar At Basis Cash Shares.

Comparison of single-token and multi-token algorithm stablecoin models

Obviously, compared with Ampleforth’s single-token rebase model, the multi-token design contains more changing components. However, this increase in complexity is only a small price for the potential stability it provides.

In short, the design model adopted by ESD and Bass Cash has the advantage of  containing the inherent reflexivity of the  system, while the “stable coin” part of the system (to some extent) achieves isolation from market momentum. Speculators who prefer risk can guide the agreement during the contraction of the money supply in exchange for the future distribution of benefits from the recovery and expansion. But in theory, users who only hope to have stablecoins with stable purchasing power can hold BAC or ESD without buying bonds, coupons, stocks, or binding their tokens to DAO. This lack of rebase adds the additional benefit of combining with other DeFi primitives. Unlike AMPL, BAC and (unbound) ESD can be mortgaged or loaned without having to consider the complex kinetic energy of token supply changes in the entire network.

Evan Kuo  , founder and CEO of Ampleforth  , criticized algorithmic stablecoin projects like Basis Cash because they “rely on the debt market (such as bonds) to regulate the supply of tokens.” Kuo advises people to stay away from these “zombie ideas” because these algorithmic stablecoins are flawed like traditional markets. They “will always rely on the  last lender  (for example, bailout).”

But Kuo’s argument is an argumentation problem because it assumes that relying on the debt market (bailout) is inherently dangerous without any valid reason. In fact, due to moral hazard, debt financing in traditional markets is problematic. Business entities that are “too big to fail” can take huge risks without worrying about being punished by socializing the cost of assistance. Algorithmic stablecoins like ESD and Basis Cash do not enjoy the luxury treatment of Fannie Mae and Freddie Mac during the 2008 financial tsunami. For these agreements, there is no lender of last resort outside the system (that is, the last taker who takes over the rescue cost). ESD or Basis Cash  may fall into a debt spiral  . In this spiral, debt accumulates and no one is willing to take over the debt, and the relevant agreement collapses.

In fact, Ampleforth also requires debt financing to avoid a death spiral. The difference is that this debt financing is hidden in full view, because it is only distributed among all network participants. Unlike ESD and Basis Cash, if you do not act as an investor in the agreement, you cannot join the Ampleforth system. Holding AMPL when the network is in a contracting state is similar to taking on the debt of the network (“acting as a central bank” according to Maple Leaf Capital), because AMPL holders will lose tokens in each negative supply rebase.

From both first-principles inferences and empirical data, we can conclude that compared with the “single-token rebase” scheme, the multi-token, “Seigniorage Shares” inspired model has significantly higher built-in stability . In fact, Ferdinando Ametrano recently updated the Hayek currency “first simple realization concept” he personally proposed in 2014. In view of the above problems, he now supports the model based on multi-tokens and Seigniorage Share.

However, even if multi-token algorithmic stablecoins are better than their single-token counterparts, there is no guarantee that any of these algorithmic stablecoins will continue to develop in the long term. In fact, the basic mechanism design of algorithmic stablecoins excludes any such guarantees, because as mentioned above, the stability of algorithmic stablecoins is ultimately a  reflexive phenomenon coordinated based on  game theory . Even for agreements like ESD and Basis Cash that separate trading, purchasing power stability tokens from value accumulation and debt financing tokens, the stablecoins can remain stable only if 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 no longer be resilient  .

Partially reserve stablecoins: a new era of algorithmic stablecoins?

The speculative nature of pure algorithmic stablecoins is inevitable. However, some prototype agreements have recently appeared, trying to use partial asset mortgages (“partial reserves”) to control the reflexivity of algorithmic stablecoins.

The view on this issue is simple. Haseeb Qureshi’s observation is correct: “Fundamentally speaking, it can be said that the “mortgage” supporting Seignorage Share is a share in the future growth of the system.”

That’s why, why not use actual collateral to supplement this speculative “collateral” and make the system stronger?

ESD v2  and  Frax  did just that. ESD v2 is still in the research and discussion stage, after which it will finally decide its fate through governance voting. If implemented, this upgrade will make several substantial changes to the current ESD protocol. The most important of these is the introduction of ”  reserve requirements  .”

In the new system, the ESD agreement will consider a reserve ratio of 20% to 30%, initially priced in USDC. Part of these reserve funds comes from the agreement itself, which will sell ESD on the open market when the ESD is higher than a certain target price, and part comes from ESD holders who want to unbind with the DAO (they must deposit in the reserve). Then by automatically purchasing ESD until the minimum reserve requirement is reached, these USDC reserves can be used to stabilize the agreement during the network contraction.

Frax, which has not yet been released, is a more elegant attempt to create a partial mortgage algorithm stablecoin. Like Basis Cash, Frax contains three tokens:  FRAX  (stablecoin),  Frax Shares  (governance and value accumulation tokens) and  Frax Bonds  (debt financing tokens). However, unlike all other algorithmic stablecoins discussed above, FRAX can always be minted and redeemed at a price of 1 USD, which means that arbitrageurs will play an active role in stabilizing the price of the token.

This minting/exchange mechanism is the core of the Frax network because it utilizes a  dynamic partial reserve system  . To mint a FRAX token, users must deposit a certain combination of Frax Shares (FXS) and other collateral (USDC or USDT), which is worth one U.S. dollar. The ratio of FXS to other collaterals is determined by FRAX’s demand dynamics. As demand increases, the ratio of FXS to other collaterals will increase. Locking in FXS to cast FRAX has a deflationary effect on the supply of FXS. Therefore, as more FXS is needed to cast FRAX, the demand for FXS will naturally increase as the supply drops. On the contrary, as Frax’s document points out, during the network contraction, “the agreement re-collateralized the system, allowing FRAX redeemers to get more FXS and less other collateral from the system. This increases The proportion of collateral in the system in the supply of FRAX has been improved. With the increase in support for FRAX, the market’s confidence in FRAX has also increased.”

Effective and dynamic mortgage acts as a stable countercyclical mechanism, allowing the Frax protocol to passivate the harmful effects of extreme reflexivity when needed   . But it also retains the possibility that the agreement will become completely unsecured in the future, as long as the market makes this choice. In this sense, Frax’s dynamic mortgage mechanism is “operable under any circumstances.”

Both Frax and ESD v2 are not yet online, so it remains to be seen whether they can succeed in practice. But at least in theory, these hybrid,  partial-reserve  agreements are   promising attempts to combine reflexivity  and  stability , while still being more capital efficient than over-collateralization schemes such as DAI and sUSD   .

to sum up

Algorithmic stablecoin is a very attractive currency experiment, and its success is inevitable. Although Charlie Munger’s motto is always indisputable: “Tell me the motivation, I tell you the result”, these agreements are  game-theoretic and  cannot be fully grasped by a priori reasoning alone. In addition, if the past crypto market cycle can be used as a reference, we should prepare for these dynamics and promote its success with rational expectations.

It would be foolish to kill algorithmic stablecoins at such an early embryonic stage. It is also wrong to forget how high the risk is. Economist Friedrich August von Hayek in his 1976 masterpiece ”  currency denationalization  wrote” (The Denationalisation of Money) in: “I believe that gold can be in human history than Do it better. The government cannot do better. Free enterprises, such as institutions that stand out from the competition, can undoubtedly provide good currency, and they undoubtedly will.”

Although the algorithmic stablecoin is still in its immature state, it may eventually become Hayek’s blueprint for the currency market’s vision and lay the foundation for it.

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