In-depth Analysis of Algorithmic Stablecoins: Stability, Resilience, Reflexivity

The author of this article is Benjamin Simon, a researcher at Deribit, and it has been translated by Mars Finance.

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

In 2014, there were two academic papers on stablecoins worth our careful reading: one is Ferdinando Ametrano's "Hayek Money: The Cryptocurrency Price Stability Solution," and the other is Robert Sams' "A Study of Cryptocurrency Stability: Minting Shares." Ametrano argues that due to its deflationary nature, Bitcoin cannot fully perform the function of a unit of account required by money. Instead, he proposes a rules-based, elastic supply cryptocurrency that can complete a "rebase" (i.e., proportionally change the money supply of all token holders) based on demand.

In "Minting Shares," Sams proposes a similar model but with a significant difference. The Sams model does not use a rebase mechanism but consists of two tokens: a currency with elastic supply and network investment "shares." For the latter asset holders, Sams refers to them as "minting shares," which are the sole recipients of the inflation rewards from positive supply growth and the only bearers of the debt burden during declines in money demand and network contraction.

Astute crypto observers recognize that Ametrano's "Hayek Money" and Sams' "Minting Shares" are no longer academic abstractions. "Hayek Money" is almost identical to the Ampleforth protocol launched in 2019, which exploded in July 2020 with a market cap exceeding $1 billion. Recently, Sams' "Minting Shares" model has become the foundation for various algorithmic stablecoins, including Basis, Empty Set Dollar (ESD), Basis Cash, and Frax, to varying degrees.

Now that algorithmic stablecoins are thriving, the questions before us are no different from those faced by Ametrano and Sams six years ago. The questions listed at the beginning of the article have yet to reach conclusions, and it will take some time to achieve widespread consensus. However, this article attempts to explore some of these fundamental issues from first principles, combined with empirical data from recent months.

1. Background of Stablecoins

Algorithmic stablecoins are an independent world, but before delving deeper, it is essential to discuss stablecoins. (Readers already very familiar with stablecoins may skip or overlook this section).

Under the influence of institutional snowballing applications of Bitcoin, the DeFi boom, and Ethereum network upgrades, stablecoins have been reveling in the process, with a total market cap exceeding $25 billion. This exponential growth has attracted the attention of institutions outside the crypto circle, including many U.S. lawmakers.

Broadly, we can categorize stablecoins into three types: dollar-pegged stablecoins, multi-asset pool-backed over-collateralized stablecoins, and algorithmic stablecoins. Our focus in this article is on the last category, but it is also necessary to note the advantages and disadvantages of the other categories of stablecoins, as understanding these trade-offs will allow us to highlight the value proposition of algorithmic stablecoins.

The first type of stablecoins, including USDT and USDC, is dollar-pegged and can be exchanged one-to-one for dollars, including centralized exchange-based stablecoins like BUSD. These stablecoins have the advantage of capital efficiency (i.e., no excessive collateralization), but their permissioned centralized nature means users may be blacklisted.

The second type 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, these tokens can be minted without permission. Notably, centralized assets like USDC can serve as collateral. Additionally, the over-collateralized nature of these stablecoins means they are capital-intensive, highly volatile, and highly correlated, making them susceptible to crypto shocks in the past.

The third type is algorithmic stablecoins. Algorithmic stablecoins are tokens that adjust their supply in a deterministic manner (i.e., using algorithms) to move the token's price toward a price target. At the most basic level, algorithmic stablecoins expand their supply when above the price target and contract when below it.

Unlike the other two types of stablecoins, algorithmic stablecoins cannot be exchanged one-to-one for dollars and currently lack crypto asset collateral backing. Most importantly, algorithmic stablecoins often exhibit high reflexivity, meaning demand is largely determined by market sentiment, and the power of these demand-side forces is transferred to the token supply, which may ultimately create a feedback loop.

2. The Paradox of Reflexivity and Algorithmic Stability

For algorithmic stablecoins to exist long-term, they must achieve stability. Due to the inherent reflexivity of algorithmic stablecoins, this is particularly challenging for many of them. The purpose of algorithmic supply changes is to counteract cyclical movements; expanding supply will inevitably lower prices, and vice versa. However, in practice, supply changes reflexively amplify directional momentum, especially for those algorithmic models that do not follow the "minting shares" model, separating stablecoin tokens from valuation and debt financing tokens.

For non-algorithmic stablecoins, there is no game-theoretic coordination involved; each stablecoin (at least theoretically) can be exchanged for an equivalent amount of dollars or other forms of collateral. In contrast, the price stability of algorithmic stablecoins cannot be guaranteed at all, as it is entirely determined by market psychology. Haseeb Qureshi aptly states that stablecoins are ultimately a Schelling point (referring to people's tendency to choose when they cannot communicate); if enough people believe the system will survive, this belief will create a positive feedback loop ensuring its survival.

In fact, if we seriously consider how algorithmic stablecoins can achieve long-term stability, we will discover an obvious paradox. To achieve price stability, algorithmic stablecoins must expand to a sufficiently large market cap so that buy and sell orders do not cause price fluctuations. However, the only way for a purely algorithmic stablecoin to grow to a sufficiently large network size is through speculation and reflexivity, and the problem with highly reflexive growth is unsustainability, while contraction is often reflexive as well. Thus, a paradox emerges: the larger the network value of a stablecoin, the better it can withstand significant price shocks, and the more elastic it becomes. However, only highly reflexive algorithmic stablecoins (i.e., those prone to extreme expansion/contraction cycles) have the potential to achieve large network valuations from the outset.

Bitcoin also faces a similar reflexivity paradox; to gain wider acceptance, it must increase liquidity, stability, and acceptability. Bitcoin's growth over the years began with acceptance by dark web participants, then technical experts, and recently traditional financial institutions. At this point, Bitcoin has gained a resilience from being deeply entrenched in reflexive cycles, which is also the path that algorithmic stablecoins need to follow.

3. Ampleforth: A Simple Yet Flawed Algorithmic Stablecoin

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

As mentioned earlier, Ampleforth is almost identical to Ametrano's proposed "Hayek Money." AMPL expands and contracts based on a deterministic rule of AMPL's daily time-weighted average price (TWAP): when below the price target range (i.e., below $0.96), supply contracts; when above the target range (i.e., above $1.06), supply expands. Most critically, each wallet participates proportionally in the supply change. For example, if Zhang San holds 1,000 AMPL before the rebase and the supply expands by 10%, Zhang San now holds 1,100; if Li Si has 1 AMPL, he now holds 1.1 AMPL.

The "rebase" is where Ampleforth's algorithmic model differs from the "minting shares" model adopted by other protocols. Although the Ampleforth white paper does not provide reasons for the single-token rebase design versus a multi-token approach, this design decision seems to have two main reasons.

First is simplicity. Regardless of actual operational effectiveness, Ampleforth's single-token model possesses an elegance and simplicity unmatched by other algorithmic stablecoins. Second, Ampleforth's single-token design claims to be the fairest algorithmic stablecoin model. The design of Ampleforth allows all token holders to retain the same network share after each rebase. Ametrano pointed this out in his 2014 paper, where he elaborated on the "unfairness" of monetary policy actions and contrasted it with the relative fairness of "Hayek Money."

This is the reasoning behind the Ampleforth model, which has been replicated by other rebase tokens like BASED and YAM. However, before discussing the flaws of this model, let us first look at the data available for Ampleforth over the past year and a half. Since its establishment in mid-2019 (just over 500 days), over three-quarters of Ampleforth's rebases have been positive or negative; in other words, over 75% of AMPL's daily time-weighted average price TWAP has been outside the target range since its launch. It is certain that the protocol is still in its early stages, and it is too early to dismiss it based solely on these reasons.

Defenders of Ampleforth often deflect the issue of instability, with many even expressing dissatisfaction with the label of "algorithmic stablecoin." They argue that Ampleforth only needs to become an "uncorrelated reserve asset" in a diversified portfolio. However, this line of thinking is debatable. Take cryptocurrencies as an example; such currencies undergo rebase daily based on random number generators, just like Ampleforth, and these tokens will have "significant volatility footprints," which certainly does not make them valuable for that reason alone. The value proposition of Ampleforth lies in its tendency toward balance; theoretically, this characteristic would make AMPL a unit of account.

Imagine if Ampleforth could shed its yet-to-be "sticky" characteristics and completely transfer price volatility into supply volatility, making the price of each AMPL essentially stable. Would this "mature" Ampleforth truly become an ideal choice for a transactional base currency?

We encounter the crux of the problem—also 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 change on the way to reaching $1.

Price stability requires not only stable account units but also stable value storage of money. Hayek aimed to address the former, not the latter. It merely exchanges a floating coin price for a fixed coin price and a floating wallet balance. The end result is that the purchasing power of a Hayek Money wallet is as unstable as that of a Bitcoin wallet balance.

Ultimately, Ampleforth's simplicity, its single-token rebase, is a bug. The AMPL token is a speculative tool that rewards holders with inflation during high demand and forces holders to become debt financiers during low demand. Therefore, it is hard to see how AMPL can achieve both speculative purposes and stability, while stability is a necessary condition for stablecoins.

4. Multi-Token "Minting Shares"

Robert Sams' vision of "Minting Shares" has never been realized, but a new class of algorithmic stablecoin projects has recently emerged, incorporating many core components.

Basis Cash raised over $100 million in a grand manner in 2018 but ultimately did not launch. Like Basis, Basis Cash is also a multi-token protocol consisting of three tokens: BAC (algorithmic stablecoin), Basis Cash Shares (which holders can claim BAC inflation when the network expands), and Basis Cash Bonds (which can be purchased at a discount during network contraction and redeemed with BAC when the network exits the inflation phase). Basis Cash is still in the early stages of development and has encountered some early developmental hurdles; the protocol has yet to experience successful supply transformations.

However, another Seigniorage Shares-style protocol—Empty Set Dollar (ESD)—has undergone multiple expansion and contraction cycles since its launch in September. In fact, to date, nearly 60% of ESD's 200+ supply "periods" (one every 8 hours) have occurred when ESD's TWAP is within the range of $0.95 < x < $1.05, indicating that ESD's stability is more than twice that of Ampleforth.

At first glance, ESD's mechanism design seems to be a hybrid of Basis and Ampleforth. Like Basis (and Basis Cash), ESD uses bonds to finance protocol debt, which must be purchased by burning ESD (thereby contracting supply), and once the protocol enters expansion, ESD can be redeemed. However, unlike Basis, ESD does not have a third token; when the debt is repaid (i.e., the coupon is redeemed), ESD can receive inflation rewards during expansion.

Most critically, separating ESD from the DAO requires a period (5 days) during which it cannot be traded by its owners or earn accumulated inflation rewards. Therefore, ESD's segmented model functions similarly to the role of Basis Cash Shares, tying ESD to the DAO and purchasing Basis Cash Shares, which both preset risks (ESD's liquidity risk; BAS's price risk) and the potential for inflation rewards.

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

Clearly, multi-token designs are more complex than Ampleforth's single-token model, but they incur only a small cost for the potential stability they offer.

In simple terms, the designs adopted by ESD and Basis Cash incorporate inherent reflexivity within the system, while the "stablecoin" portion of the system is (to some extent) insulated from market dynamics. Risk-seeking speculators can guide the protocol during contraction to exchange for future expansion benefits. However, for those who simply want a stablecoin with stable purchasing power, at least theoretically, they can hold BAC or ESD without needing to purchase bonds, coupons, or stocks, nor do they need to bind their tokens to the DAO. This non-rebase characteristic also has the advantage of being combinable with other DeFi projects. Unlike AMPL, BAC and ESD can be used as collateral or lent without considering the complex dynamics of continuous supply changes across the entire network.

Evan Kuo, the founder and CEO of Ampleforth, has criticized algorithmic stablecoin projects like Basis Cash for relying on debt market platforms to regulate supply. Advising people to steer clear of these "zombie ideas," Kuo believes these algorithmic stablecoins are flawed because, like traditional markets, they always depend on the last lender.

However, Evan Kuo's argument is problematic; assuming that reliance on debt markets is inherently dangerous without any justification is risky. In reality, due to moral hazard, traditional market debt financing has issues; "too big to fail" corporate entities can bear risks without punishment through socialized rescue costs. ESD or Basis Cash could very well enter a debt spiral, where, in the absence of willing funders, debt accumulates, and the protocol collapses.

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

From both first principles reasoning and empirical data, we can conclude that multi-token, "minting shares"-inspired models exhibit significantly greater inherent stability than single-token rebase schemes. In fact, Ametrano has recently updated his theory of Hayek Money, which he began in 2014. In light of the aforementioned issues, he now leans more toward multi-token, "minting shares"-based models.

However, even if multi-token algorithmic stablecoins are superior to single-token models, it does not guarantee that any of these algorithmic stablecoins can sustain long-term viability. In fact, the underlying mechanism design of algorithmic stablecoins precludes such guarantees. As mentioned above, the stability of algorithmic stablecoins ultimately is a reflexive phenomenon based on 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, stablecoin tokens will only remain stable when there are investors willing to guide the network during demand declines. When there are no longer enough speculators believing the network is resilient, the network will indeed cease to be resilient.

6. Fragmented Reserve Stablecoins: A New Era for Algorithmic Stablecoins?

The speculative nature of pure algorithmic stablecoins is unavoidable. However, several emerging protocols are attempting to control the reflexivity of algorithmic stablecoins by utilizing partial asset collateral. Fundamentally, one could argue that the collateral supporting "minting shares" is a share of the system's future growth. So why not supplement this speculative "collateral" with actual collateral to make the system more robust?

ESD v2 and Frax are doing just that. ESD v2 is currently in the research and discussion phase and will ultimately be voted on by the governance layer. If implemented, the upgrade will make some substantial changes to the current ESD protocol. The most significant change is the introduction of "reserve requirements."

Under the new system, the ESD protocol will initially be priced in dollars, targeting a reserve ratio of 20-30%. Part of these reserves will come from the protocol itself; when ESD is above a certain price target, the protocol will sell ESD on the open market. Then, USDC reserves will stabilize the protocol during contractions by automatically purchasing ESD until the minimum reserve requirement is met.

The yet-to-be-launched Frax is a more elegant attempt aimed at creating an algorithmic stablecoin with fragmented collateral. Like Basis Cash, Frax consists of three tokens: FRAX (stablecoin), Frax Shares (governance and value accumulation token), and 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.

The minting/redeeming mechanism is at the core of the Frax network, utilizing a dynamic partial reserve system. To mint one FRAX, 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 determined dynamically by demand for FRAX (as demand increases, the ratio of FXS to other collateral also increases). By locking FXS to mint FRAX, it has a deflationary effect on the supply of FXS; as more FXS is required to mint FRAX, the supply decreases, naturally increasing demand for FXS. Conversely, as noted in Frax's documentation, during contractions, the protocol will re-collateralize the system, allowing FRAX redeeming users to receive more FXS and less collateral from the system, thereby increasing the proportion of collateral in the FRAX supply and boosting market confidence in FRAX as the support ratio rises.

In practice, dynamic collateralization serves as a stable counter-cyclical mechanism, enabling the Frax protocol to mitigate the negative impacts of extreme reflexivity when necessary. But it allows the protocol to remain open to potentially becoming a fully uncollateralized protocol in the future. In this sense, Frax's dynamic collateralization mechanism carries a significant degree of unpredictability.

Neither Frax nor ESD v2 has launched yet, so whether either can succeed in practice remains to be seen. However, at least theoretically, these hybrid partial reserve protocols hold great promise, combining reflexivity with stability while maintaining higher capital efficiency than over-collateralized alternatives like DAI and sUSD.

Conclusion

Algorithmic stablecoins are remarkable monetary experiments. Despite the game-theoretic complexities of these protocols, it is challenging to fully capture them through reasoning alone. Moreover, if past crypto market cycles are any indication, we should be prepared for these dynamics to operate in ways that believe in rational expectations.

Nevertheless, it is foolish to dismiss algorithmic stablecoins at this early stage, but it is also a mistake to forget how significant the risks are. Although algorithmic stablecoins are still in their infancy, they may ultimately become the blueprint for Hayek's vision of a thriving monetary market.