An article that explains algorithmic stablecoins: origins, development, controversies, and future evolution

Written by: Benjamin Simon, Researcher at Mechanism Capital Translated by: Perry Wang

This article's English version was published on Deribit Insights, with the author and Deribit authorizing Chain News to translate and publish its Chinese version.

There are two academic papers published in 2014 that are particularly noteworthy: one written by Ferdinando Ametrano, a professor at the Politecnico di Milano who previously served as the project lead for the Bitcoin developer conference, titled "Hayek Money: The Cryptocurrency Price Stability Solution"; the other by cryptocurrency economist Robert Sams, who has 11 years of hedge fund experience, titled "A Note on Cryptocurrency Stabilisation: Seigniorage Shares."

Drawing on economist Friedrich Hayek's critique of the gold standard, Ametrano argues that Bitcoin, due to its deflationary nature, cannot adequately fulfill our requirements for money as a unit of account. Instead, he proposes a cryptocurrency based on rules with supply elasticity, which can undergo "rebase" to adjust the token supply according to demand, for example, proportionally changing the monetary supply of all token holders.

In the paper "Seigniorage Shares," Sams presents a similar model based on similar reasoning, but with an important adjustment: Sams's system consists of two tokens: the currency itself, which has supply elasticity, and investment "shares" in the network. The owners of the latter asset (which Sams calls Seigniorage Shares) are the sole recipients of the inflation gains from supply increases, while they are also the sole bearers of debt when monetary demand shrinks and the network contracts.

Astute cryptocurrency observers will quickly realize that Ametrano's "Hayek Money" and Sams's "Seigniorage Shares" are no longer purely abstract academic concepts. "Hayek Money" is almost identical to Ampleforth. Launched in 2019, Ampleforth skyrocketed in July 2020, with a fully diluted market cap exceeding $1 billion. Recently, Sams's Seigniorage Shares model has become the theoretical foundation for various projects like Basis, Empty Set Dollar, Basis Cash, and Frax to varying degrees.

Now, the questions before us are no different from those faced by the readers of Ametrano and Sams six years ago:

• Can algorithmic stablecoins truly achieve long-term viability?
• Will algorithmic stablecoins always be subject to extreme expansionary and contractionary cycles?
• Which version of algorithmic stablecoins is more compelling: a simple rebasing model, a multi-token "Seigniorage Shares" system, or something entirely different?

On all these questions, the public jury has yet to render a verdict, and it may take some time to reach a broad consensus. Nevertheless, this article attempts to explore some fundamental issues from a first principles reasoning approach, as well as some empirical data from recent months.

Background on Stablecoins

Algorithmic stablecoins exist as a distinct world, but before delving deeper, it is worth stepping back to examine the broader landscape of stablecoins.

With Bitcoin being adopted by financial institutions at an accelerating pace, the decentralized finance (DeFi) market booming, and Ethereum's upcoming network upgrade, stablecoins have recently gained immense popularity, with a total market cap exceeding $25 billion. This parabolic growth has attracted significant attention from big players outside the cryptography community, including a recent wave of interest from U.S. Congress members.

USDT remains the dominant stablecoin in terms of market share, but it is by no means the only stablecoin. Broadly speaking, we can categorize stablecoins into three types: dollar-collateralized stablecoins, multi-asset pool over-collateralized stablecoins, and algorithmic stablecoins. This article focuses on the last category. However, it is important to note the advantages and disadvantages of the other categories of stablecoins, as understanding these trade-offs will enable us to enhance the value proposition of algorithmic stablecoins.

The first category of stablecoins (primarily USDT and USDC, but also including exchange-issued stablecoins like BUSD, HUSD, etc.) is centrally managed, backed by dollars, and can be exchanged at a 1:1 rate. These stablecoins have the advantages of ensuring anchoring and high capital efficiency (i.e., no over-collateralization), but they are permissioned and centrally managed, which means users may be blacklisted, and the anchoring itself depends on the trustworthy behavior of centralized entities.

The second category is multi-asset collateralized stablecoins, including MakerDAO's DAI and Synthetix's sUSD. Both of these stablecoins are over-collateralized by crypto assets and rely on price oracles to maintain their peg to the dollar. Unlike centralized tokens like USDT and USDC, the second type of stablecoin can be minted without permission; however, it is worth noting that in the case of DAI, permissioned centralized assets like USDC can be used as collateral. Additionally, the over-collateralization mechanism of the second type of stablecoin means that capital is overly concentrated, and the highly volatile and correlated nature of crypto assets has made these stablecoins susceptible to shocks from the broader crypto market in the past.

All of this has led us to focus more on algorithmic stablecoins. Algorithmic stablecoins are tokens that adjust their supply based on deterministic mechanisms (i.e., algorithms) to move the token's price toward a target price.

In simple terms, algorithmic stablecoins expand their supply when the price is above the target and contract their supply when the price is below the target.

Unlike the other two types of stablecoins, algorithmic stablecoins cannot be exchanged at a 1:1 rate with the dollar, nor do they currently have crypto assets as collateral. Perhaps most importantly, algorithmic stablecoins typically exhibit high reflexivity: demand is largely driven by market sentiment and momentum (critics may disagree). The power of these demand-side forces is transferred to the token supply, generating further directional momentum that can ultimately create a severe feedback loop.

Each stablecoin model weighs its pros and cons differently. Investors who are less concerned about the effects of centralization may not see any issues with USDT and USDC. Others may feel that the capital inefficiency of over-collateralization is a price worth paying for permissionless, decentralized, hard-pegged currency. However, for those dissatisfied with both options, algorithmic stablecoins present an enticing alternative.

Reflexivity and the Paradox of Algorithmic Stability

For algorithmic stablecoins to achieve long-term viability, they must attain stability. For many algorithmic stablecoins, this is a particularly challenging task due to their inherent reflexivity. The supply changes based on algorithms are counter-cyclical policies; expanding supply aims to lower prices, while contracting supply aims to raise prices. However, in practice, supply changes often 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 tokens for accumulated value and debt financing are two distinct tokens.

For non-algorithmic stablecoins, network guidance does not involve game-theoretic coordination. Each stablecoin (at least theoretically) can be exchanged for an equivalent amount of dollars or other forms of collateral. In contrast, the successful price stability of algorithmic stablecoins is entirely uncertain, as it is wholly determined by collective market psychology.

Haseeb Qureshi, managing partner at Dragonfly Capital, aptly points this out: "These mechanisms leverage a key insight: stablecoins are ultimately a Schelling point. If enough people believe the system can survive, that belief creates a positive feedback loop that ensures its survival."

In fact, if we consider more closely what is required for algorithmic stablecoins to achieve long-term stability, we find an obvious paradox. To achieve price stability, algorithmic stablecoins must grow to a sufficiently large market cap so that buy and sell orders do not cause price fluctuations. However, the only way for pure algorithmic stablecoins to grow to a sufficiently large network scale is through speculative trading and reflexivity, and the problem with high reflexive growth is that it is unsustainable, with contractions also typically exhibiting reflexivity. Thus, the paradox arises: the greater the network value of the stablecoin, the greater its elasticity in the face of massive price shocks. However, only highly reflexive algorithmic stablecoins—those prone to extreme expansionary/contractionary cycles—are likely to achieve significant network valuations in the first place.

Bitcoin also faces a similar reflexivity paradox. For more and more people and organizations to use Bitcoin, it must possess increasing liquidity, stability, and acceptance. Over the years, these characteristics of Bitcoin have continually strengthened, expanding its user base from the initial dark web participants to later wealthy technologists and, more recently, traditional financial institutions. At this point, Bitcoin has gained resilience from being trapped in a reflexive cycle, a path that algorithmic stablecoins also need to follow.

Ampleforth: A Simple Yet Flawed Algorithmic Stablecoin

Now let us shift our focus from abstract theory to the real world of algorithmic stablecoins, starting with the largest and simplest existing protocol: Ampleforth.

As previously mentioned, Ampleforth is nearly identical to the "Hayek Money" proposed by Ferdinando Ametrano. The supply of AMPL expands and contracts based on a deterministic rule based on the daily time-weighted average price (TWAP): when below the price target range (e.g., below $0.96), the supply contracts, and when above the price target range (e.g., above $1.06), the supply increases. Crucially, each wallet "participates" proportionally in each supply change. If Alice holds 1,000 AMPL before a rebase and the supply increases by 10%, Alice now holds 1,100 AMPL; if Bob holds 1 AMPL, he now holds 1.1 AMPL.

The network-wide "rebase" is where Ampleforth's algorithmic model differs from the seigniorage share model adopted by other protocols. Although the Ampleforth whitepaper does not explain the fundamental principles behind adopting a single-token rebasing design instead of a multi-token approach, this design decision seems to be based on two main reasons.

• First is simplicity. Regardless of how it operates in practice, Ampleforth's single-token model possesses an elegant simplicity that other algorithmic stablecoins cannot match.
• Second, Ampleforth's single-token design claims to be the most equitable algorithmic stablecoin model.

In stark contrast to the policy behavior of fiat currencies, which benefits those individuals "closest" to the source of currency (i.e., the "Cantillon effect"), Ampleforth's design allows all token holders to maintain their share of the network unchanged after each rebase. Ametrano pointed this out in his 2014 paper, detailing the "serious unfairness" of central bank monetary policy behavior and contrasting it with the relative fairness of "Hayek Money."

This is the presumed principle of the Ampleforth model, which has been replicated by other algorithmic stablecoins that adopt the rebase principle (such as BASED and YAM). However, before discussing the flaws of this model, we may first want to look at the performance data of Ampleforth over the past year and a half.

Since mid-2019 (just over 500 days ago), three-quarters of Ampleforth's daily rebases have been positive or negative; in other words, over 75% of AMPL's TWAP has been outside the target range since launch. It is certain that the protocol is still in its infancy, so it is premature to dismiss it based solely on these reasons. However, we will soon examine the modified seigniorage stablecoin Empty Set Dollar, which maintained more than double the stability of Ampleforth in its first few months of existence.

Ampleforth's die-hard fans often scoff at claims of the token's lack of stability; many of them even dislike the label "algorithmic stablecoin." Their argument is that Ampleforth serves as a "non-correlated reserve asset" in portfolio diversification compared to traditional financial assets.

However, this claim is questionable. For example, a cryptocurrency that rebases daily based on a random number generator, like Ampleforth, would exhibit a "significant volatility footprint," but it would be unreasonable to claim it has value solely for that reason. Ampleforth's value proposition depends on its tendency toward equilibrium, theoretically allowing AMPL to become a pricing currency.

But will it? Imagine if Ampleforth shed its "difficult" characteristics and transferred its price volatility entirely into supply volatility, thereby keeping the price of each AMPL relatively stable. Would this "mature" Ampleforth truly be an ideal choice for a transactional base currency?

This brings us to the crux of the issue and the core flaw of Ampleforth's design: even if the price of AMPL reaches $1, the purchasing power of the AMPL held by individuals will continuously change as it approaches $1. As early as 2014, Robert Sams articulated this exact issue regarding Ametrano's Hayek Money concept:

Price stability relates not only to the stability of the unit of account but also to the stability of money as a store of value. Hayek Money aims to address the former, not the latter. It merely swaps fixed wallet balances with fluctuating currency prices for fixed currency prices with fluctuating wallet balances. The end result is that the purchasing power of a Hayek wallet is just as unstable as a Bitcoin wallet balance.

Ultimately, Ampleforth's simplicity (its straightforward single-token rebase model) has become a vulnerability rather than a feature.

The AMPL token is a speculative instrument that rewards its holders through inflation when demand is high, while forcing 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 required of a stablecoin.

Multi-Token "Seigniorage" Schemes

Robert Sams's "Seigniorage Shares" concept has never materialized, but a recent wave of newly emerging algorithmic stablecoin projects has adopted many of its core components.

Basis Cash, which was born just over a week ago, is a public attempt to revive Basis—a project that raised over $100 million in 2018 and was highly praised but never launched. Like Basis, Basis Cash is a multi-token protocol consisting of three tokens: BAC (the algorithmic stablecoin), Basis Cash Shares (which holders can benefit from BAC inflation as the network expands), and Basis Cash Bonds (which can be purchased at a discount when the network is in contraction and redeemed for BAC when the network exits the deflationary phase). Basis Cash is still in the early stages of development and has encountered some early development hurdles; the protocol has yet to successfully execute a supply change.

However, another project similar to Seigniorage Shares, Empty Set Dollar (ESD), has been active since September and has already undergone multiple expansion and contraction cycles. In fact, ESD has reached over 200 supply epochs (one every eight hours) so far, with nearly 60% of changes keeping ESD's TWAP within the range of $0.95 < x < $1.05, meaning ESD's price stability has been more than double that of Ampleforth, despite ESD's much shorter lifespan.

At first glance, ESD's mechanism design appears to be a hybrid of Basis and Ampleforth. Similar to Basis (and Basis Cash), ESD utilizes bonds (coupons) to fund protocol debt, which must be purchased by burning ESD (thereby reducing supply) and can be redeemed for ESD after the protocol resumes supply expansion. However, unlike Basis, ESD does not have a third token that rewards the network for paying off debt during expansion. Instead, ESD holders can "bind" (e.g., stake) their ESD in the ESD decentralized autonomous organization (DAO) to proportionally share in the inflationary gains, similar to Ampleforth's rebase.

Crucially, unbinding ESD from the DAO requires a "cooling-off" period, during which ESD tokens are temporarily "frozen" for 15 epochs (5 days), during which they cannot be traded by their owners or earn inflation rewards. Thus, ESD's "cooling-off" mechanism functions similarly to Basis Cash Shares, as binding ESD to the DAO and purchasing Basis Cash Shares both pre-suppose risks (liquidity risk for ESD; price risk for BAS) in exchange for the potential of future inflation rewards. Indeed, although ESD uses a two-token model (ESD and coupons) instead of Basis Cash's three-token model, the cooling-off period ultimately results in ESD becoming a de facto three-token system, with bound ESD resembling Basis Cash Shares.

Comparison of Single-Token and Multi-Token Algorithmic Stablecoin Models

Clearly, compared to Ampleforth's single-token rebase model, the multi-token design incorporates more variable components. However, this increase in complexity is a minor cost for the potential stability it offers.

In short, the design patterns adopted by ESD and Basis Cash have the advantage of mitigating the system's inherent reflexivity, while the "stablecoin" portion of the system achieves (to some extent) isolation from market momentum. Risk-preferring speculators can guide the protocol during periods of monetary supply contraction in exchange for future distribution of rewards from recovery expansion. However, theoretically, users who simply wish to hold a stablecoin with stable purchasing power can hold BAC or ESD without needing to purchase bonds, coupons, stocks, or bind their tokens to the DAO. This characteristic of not requiring a rebase adds additional benefits for combining with other DeFi primitives. Unlike AMPL, BAC and (non-bound) ESD can be collateralized or lent without considering the complex dynamics of token supply changes across the entire network.

Ampleforth founder and CEO Evan Kuo criticizes algorithmic stablecoin projects like Basis Cash for "relying on debt markets (e.g., bonds) to regulate token supply." Kuo advises people to steer clear of these "zombie ideas," as these algorithmic stablecoins are flawed like traditional markets, and they "will always rely on the last lender (e.g., bailouts)."

However, Kuo's argument is a red herring because it assumes that reliance on debt markets (bailouts) is inherently dangerous without any justification. In reality, due to moral hazard, debt financing in traditional markets is problematic. "Too big to fail" corporate entities can take on enormous risks without fear of punishment by socializing the costs of bailouts. Algorithmic stablecoins like ESD and Basis Cash do not enjoy this luxury that Fannie Mae and Freddie Mac had during the 2008 financial crisis. For these protocols, there is no last lender outside the system (i.e., no one to take on the costs of bailouts). ESD or Basis Cash could easily fall into a debt spiral, where debt accumulates without anyone willing to take on the debt, leading to the collapse of the relevant protocol.

In fact, Ampleforth also requires debt financing to avoid a death spiral. The difference is that this debt financing is hidden in plain sight, as it is merely distributed among all network participants. Unlike ESD and Basis Cash, one cannot join the Ampleforth system without acting as an investor in the protocol. Holding AMPL during network contraction is akin to bearing the debt of that network (as Maple Leaf Capital puts it, "acting as the central bank"), as AMPL holders will lose tokens during each negative supply rebase.

From both a first principles reasoning perspective and empirical data, we can conclude that compared to the "single-token rebase" scheme, the multi-token, "Seigniorage Shares"-inspired model has significantly higher built-in stability. In fact, Ferdinando Ametrano recently updated his personal 2014 proposal for Hayek Money to advocate for a multi-token, Seigniorage Share-based model, given the issues mentioned above.

However, even if multi-token algorithmic stablecoins outperform their single-token counterparts, there is no guarantee that any of these algorithmic stablecoins will sustain long-term development. In fact, the fundamental mechanism design of algorithmic stablecoins precludes any such guarantees, as mentioned earlier, the stability of algorithmic stablecoins ultimately hinges on the reflexive phenomenon of game-theoretic coordination. Even for protocols like ESD and Basis Cash that separate transactional, stable purchasing power tokens from value accumulation and debt financing tokens, the stability of the stablecoin can only be maintained if there are investors willing to guide the network when demand declines. When there are no longer enough speculators believing the network is resilient, the network will no longer be resilient.

Partially Collateralized Stablecoins: A New Era for Algorithmic Stablecoins?

The speculative nature of pure algorithmic stablecoins is inevitable. However, some nascent protocols have recently emerged that attempt to leverage partial asset collateralization ("partial reserves") to control the reflexivity of algorithmic stablecoins.

The insight into this issue is straightforward. Haseeb Qureshi's observation is correct: "Fundamentally, one could argue that the 'collateral' supporting Seignorage Shares is a stake in the system's future growth."

So why not supplement this speculative "collateral" with actual collateral to strengthen the system?

ESDv2 and Frax are doing just that. ESDv2 is still in the research and discussion phase, and its fate will ultimately be determined by governance votes. If implemented, this upgrade will make several substantive changes to the current ESD protocol. The most significant of these is the introduction of a "reserve requirement."

In the new system, the ESD protocol will consider a reserve ratio of 20% to 30%, initially denominated in USDC. These reserve funds will partly come from the protocol itself, which will sell ESD on the open market when ESD is above a certain target price, and partly from ESD holders wishing to unbind from the DAO (who must deposit into the reserves). These USDC reserves can then be used to stabilize the protocol during network contractions by automatically purchasing ESD until the minimum reserve requirement is met.

The yet-to-be-released Frax represents a more elegant attempt to create a partially collateralized algorithmic stablecoin. Like Basis Cash, Frax includes three tokens: FRAX (the stablecoin), Frax Shares (the governance and value accumulation token), and Frax Bonds (the debt financing token). However, unlike all the other algorithmic stablecoins discussed earlier, FRAX can always be minted and redeemed at a price of $1, meaning arbitrageurs will play an active role in stabilizing the price of the stablecoin.

This minting/redemption mechanism is at the core of the Frax network, as it utilizes a dynamic partial reserve system. To mint one FRAX token, users must deposit a combination of Frax Shares (FXS) and other collateral (USDC or USDT) worth one dollar. The ratio of FXS to other collateral is dynamically determined by the demand for FRAX; as demand increases, the proportion of FXS relative to other collateral will rise. Locking FXS to mint FRAX creates a deflationary effect on FXS supply, so as more FXS is needed to mint FRAX, the demand for FXS will naturally increase as supply decreases. Conversely, as Frax's documentation points out, during network contractions, "the protocol re-collateralizes the system, allowing FRAX redeemers to receive more FXS and less of the other collateral. This increases the proportion of collateral in the system relative to FRAX supply, enhancing support for FRAX and simultaneously boosting market confidence in FRAX."

Effectively, dynamic collateralization serves as a stable counter-cyclical mechanism, allowing the Frax protocol to mitigate the harmful effects of extreme reflexivity when needed. Yet it retains the possibility for the protocol to become completely uncollateralized in the future, should the market choose to do so. In this sense, Frax's dynamic collateralization mechanism is "operational under any circumstances."

Both Frax and ESDv2 have yet to go live, so whether they can succeed in practice remains to be seen. However, at least theoretically, these hybrid protocols requiring partial reserves represent a promising attempt to combine reflexivity with stability, while still being more capital efficient than over-collateralized solutions like DAI and sUSD.

Conclusion

Algorithmic stablecoins are a highly attractive monetary experiment, and their success is inevitable. While Charlie Munger's adage remains unassailable: "Show me the incentive, and I'll show you the outcome," these protocols possess game-theoretic complexities that cannot be fully grasped through a priori reasoning alone. Additionally, if past cryptocurrency market cycles can serve as a guide, we should prepare for these dynamics and drive their success with rational expectations.

It would be foolish to dismiss algorithmic stablecoins at such an early stage of development. It is also erroneous to forget just how high the risks are. Economist Friedrich August von Hayek wrote in his 1976 masterpiece, The Denationalisation of Money: "I believe that mankind can do better than the gold of history. Governments cannot do better. Free enterprise, such as institutions that emerge from the competitive process, can undoubtedly provide good money, and will do so."

Although algorithmic stablecoins are still in their infancy, they may ultimately serve as the blueprint for Hayek's vision of a monetary market and lay the groundwork for it.

Interests: The author of this article may hold positions in the tokens mentioned.