Stability, Resilience and Reflexivity: In-Depth Analysis of Algorithmic Stablecoins

Algorithmic stablecoins are a world in their own right, but before delving too deep, it’s worth taking a step back and looking at the broader stablecoin landscape. (Readers who are already very familiar with stablecoins can skim or skip this section.)

In the shadow of Bitcoin’s snowballing institutional adoption, DeFi’s fiery summer, and Ethereum’s imminent network upgrade, stablecoins have been refreshing recently, with a combined market capitalization of more than $25 billion5. This parabolic growth has caught the attention of powerful people outside the cryptocurrency world, including most recently a cadre of U.S. lawmakers.

USDT is still the dominant stablecoin, but it is far from the only player. Broadly speaking, we can divide stablecoins into three categories: USD-backed, multi-asset pool over-collateralized, and Algorithm 7. This article focuses on the last category. However, it is important to be aware of the strengths and weaknesses of other classes of stablecoins, as understanding these tradeoffs will allow us to strengthen the value proposition of algorithmic stablecoins.

The first category of stablecoins (i.e. USDT and USDC, as well as exchange-based tokens like BUSD) are centrally managed, backed by the U.S. dollar, with a one-to-one exchange. These stablecoins have the advantages of a guaranteed peg and capital efficiency (i.e. no over-collateralization), but their delegated, centralized nature means that users can be blacklisted8 and the peg itself relies on central entities credible behavior.

The second category is multi-asset backed stablecoins, including MakerDAO’s DAI and Synthetix’s sUSD. Both stablecoins are overcollateralized by crypto assets and both rely on price oracles to maintain their peg to the U.S. dollar. Unlike centralized tokens such as USDT and USDC, these tokens can be minted without authorization, although it is worth noting that authorized centralized assets such as USDC are allowed to be used as collateral in DAI. Furthermore, the over-collateralized nature of these stablecoins means that they are extremely capital intensive, while the highly volatile and highly correlated nature of cryptoassets has made these stablecoins vulnerable to crypto-range shocks9 in the past.

All of this brings us to algorithmic stablecoins. An algorithmic stablecoin is a token that adjusts its supply deterministically (i.e. using an algorithm) in order to move the price of the token in the direction of a target price of 10. At the most basic level, algorithmic stablecoins expand their supply above a target price and contract their supply below it.

Unlike the other two stablecoins, algorithmic stablecoins are neither convertible one-to-one to dollars, nor are they currently backed by cryptoassets11. Finally, and perhaps most importantly, algorithmic stablecoins are often highly reflexive12: demand is largely (critics might say) driven by market sentiment and momentum. These demand-side forces are diverted into the token supply, which in turn creates further directional momentum, which could end up being an intense feedback loop.

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In order for algorithmic stablecoins to be viable in the long-term, they must achieve stability. This requirement is particularly difficult to achieve for many algorithmic stablecoins due to their inherent reflexive nature. Algorithmic supply changes are intended to be counter-cyclical; expanding supply should lower prices, and vice versa. In practice, however, supply changes often reflexively amplify directional momentum13, especially for algorithmic models that do not follow the “seigniorage share” model by separating stablecoin tokens from accretion and debt financing tokens.

For non-algorithmic stablecoins, network bootstrapping does not involve game-theoretic coordination; each stablecoin is (at least in theory) redeemable for an equivalent amount of dollars or other forms of collateral14. In contrast, the successful price stability of an algorithmic stablecoin is simply not guaranteed, as it is entirely determined by collective market psychology. Haseeb Qureshi aptly points this out15: “These schemes exploit a key idea: Stablecoins are ultimately Schelling points. If enough people believe the system can survive, this belief can lead to a virtuous cycle , to ensure its survival."

In fact, if we think more carefully about what is needed for algorithmic stablecoins to achieve long-term stability, we find an apparent paradox. To achieve price stability, algorithmic stablecoins must scale to a market cap large enough that buy and sell orders do not cause price volatility. 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 that it is not sustainable, and shrinkage is often just as reflexive. A paradox thus arises: the greater the network value of a stablecoin, the more resistant it is to large price shocks. However, only highly reflexive algorithmic stablecoins (i.e., those prone to extreme expansion/contraction cycles) are likely to achieve massive network valuations in the first place.

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Now, let’s move from abstract theory to the real world of algorithmic stablecoins, starting with the largest yet simplest protocol in existence, Ampleforth16.

As mentioned earlier, Ampleforth is almost identical to the "Hayekian currency" proposed by Ferdinando Ametrano. The supply of AMPL expands and contracts according to a determined rule based on the daily time-weighted average price (TWAP)17 of each AMPL: below the target price range (i.e. below $0.96), the supply shrinks, above the target price range (i.e. high at $1.06), supply expanded. Crucially, each wallet "participates" in proportion to each supply change. If Alice held 1000 AMPL before the rebase, and then the supply increased by 10%, Alice would now hold 1100 AMPL; if Bob owned 1 AMPL, he would now own 1.1 AMPL.

Network-wide "rebasing" is what differentiates the Ampleforth algorithm model from the seigniorage share models adopted by other protocols. While the Ampleforth whitepaper18 does not provide a rationale for the design of a single-token rebase as opposed to a multi-token approach, there appear to be two main rationales for the design decision.

The first is simplicity. Regardless of how well it works in practice, Ampleforth's single-token model has an elegant simplicity unmatched by other algorithmic stablecoins. Second, Ampleforth's single-token design claims to be the fairest algorithmic stablecoin model. In contrast to fiat policy actions (which disproportionately favor those individuals who are “closest” to the source of money, the “Cantillon effect”19), Ampleforth is designed so that all token holders remain the same after each rebase network share. Ametrano makes this point in a 2014 paper in which he details the "gross inequity" of monetary policy actions and contrasts it with the relative fairness of "Hayek money."

This is the supposed rationale for the Ampleforth model, which has been replicated by other rebasing coins such as BASED20 and YAM21. But before turning to the flaws of the model, we can look at the data on Ampleforth's performance over the past year and a half. Since its inception in mid-2019 (over 500 days), more than three-quarters of Ampleforth's daily rebases have been positive or negative, in other words, over 75% of AMPL's time-weighted average price rebases since launch have exceeded target range. To be sure, the agreement is still in its infancy, so it's too soon to dismiss it on these grounds alone. However, we will shortly examine how a modified “seigniorage” stablecoin, the Empty Set Dollar, managed to more than double the stability of Ampleforth during its first few months of existence.

Defenders of Ampleforth often dismiss the lack of stability; many of them even take issue with the label “algorithmic stablecoin”22. Their argument was that it was enough for Ampleforth to be an "uncorrelated reserve asset" for portfolio diversification. However, this view is questionable. Take, for example, a cryptocurrency that rebases daily based on a random number generator. Like Ampleforth, the token will have a "significant volatility footprint," but it certainly won't be valuable for that reason alone.

Ampleforth's value proposition is built on its propensity towards equilibrium, a quality that would theoretically make AMPL a denomination currency.

But will it? Imagine if Ampleforth got rid of its current "sticky" nature and completely converted price fluctuations into supply fluctuations, so that the price of each AMPL would be basically stable. Is this "mature" Ampleforth really an ideal candidate for trading the base currency?

Here we find the crux of the matter and the core flaw in Ampleforth's design. Even if the price of AMPL reaches $1, the purchasing power of AMPL held by individuals will change in the process of reaching $1. Back in 2014, Robert Sams articulated this problem against Ametrano's Hayek money:

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Robert Sams’ vision of a “seigniorage share” never became a reality, but a new class of algorithmic stablecoin projects has recently emerged that shares many of its core ingredients.

Basis Cash23, a public attempt to revive Basis24 (an algorithmic stablecoin project that raised over $100 million in 2018 to much fanfare but never closed its offering), is just over a week old. Like Basis, Basis Cash is a multi-token protocol consisting of three tokens: BAC (algorithmic stablecoin), Basis Cash shares (holders can receive BAC inflation rewards as the network expands), and Basis Cash bonds (network Time contraction can be purchased at a discount, and BAC can be exchanged when the network exits the deflation phase). Basis Cash is still in the early stages of development and experiencing some early development difficulties; the protocol has yet to undergo a single successful supply change.

However, another seigniorage share-like protocol, Empty Set Dollar (ESD) 25, has been around since September and has gone through multiple cycles of expansion and contraction. In fact, nearly 60% of ESD's 200+ supply "periods" (one every 8 hours) so far occurred when ESD's time-weighted average price was in the $0.95 < x < $1.05 range - This means that ESD is more than twice as stable as Ampleforth, despite being around for a much shorter period of time26.

At first glance, ESD's mechanic design appears to be a mix of Basis and Ampleforth. Like Basis (and Basis Cash), ESD utilizes bonds ("coupons") to finance protocol debt, which must be purchased by burning ESD (thus contracting supply), and can be redeemed for ESD once the protocol enters expansion. However, unlike Basis, ESD does not have a third token that receives inflationary rewards as the network expands — after the network pays off its debts (i.e. after coupons are redeemed). In lieu of this third token, ESD holders can "bond" (i.e. stake) their ESD in the ESD Decentralized Autonomous Organization (DAO) for a proportional share of each expansion, similar to Ampleforth Rebase 27.

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Clearly, the multi-token design has more moving parts than Ampleforth's single-token rebase model. Still, this added complexity is a small price to pay for the potential stability it provides.

Simply put, ESD and Basis Cash employ designs that incorporate the inherent reflexivity of the system, while the "stablecoin" part of the system is (to some degree) insulated from market dynamics30. Speculators with a risk appetite can bootstrap the agreement during contractions to capture future gains from expansions. However, if a user simply wants to own a stablecoin with stable purchasing power, at least in theory, it is possible to hold BAC or ESD without buying bonds, coupons, shares, or binding their tokens to a DAO. This non-rebasing nature also brings an additional benefit: composability with other decentralized finance primitives. Unlike AMPL, BAC and (unbonded) ESD can be used as collateral or loaned without having to account for the complex dynamics of changing network-wide supply31.

Ampleforth founder and CEO Evan Kuo criticized32 algorithmic stablecoin projects such as Basis Cash because they “rely on debt markets (i.e. bonds) to regulate supply.” Kuo urged people to stay away from these “zombie ideas,” arguing that these algorithmic stablecoins are flawed because, like traditional markets, they “always rely on the lender of last resort (i.e. bailout).”

However, Kuo's argument is questionable because it assumes, without any reason, that reliance on debt markets ("bailouts") is inherently dangerous. Indeed, debt financing in traditional markets is problematic due to moral hazard; too-big-to-fail corporate entities can risk impunity by socializing bailout costs. Algorithmic stablecoins like ESD and Basis Cash don’t have the luxury that Fannie and Freddie enjoyed33 during the 2008 financial crisis. In these agreements, there is no outside lender of last resort to whom bailout costs can be transferred. It is entirely possible for ESD or Basis Cash to enter a debt spiral: in the absence of a willing financier, debt accumulates and the protocol collapses34.

In fact, Ampleforth also needed debt financing to avoid a death spiral. The difference is that this debt financing is hidden in plain sight as it is simply spread among all network participants. Unlike ESD and Basis Cash, it is impossible to participate in the Ampleforth system without also acting as an investor in the protocol. Holding AMPL while the network shrinks is akin to taking on the network’s debt (in the words of Maple Leaf Capital35, “playing the role of a central bank”), as AMPL holders lose tokens for each negative supply rebase.

Starting from first-principles reasoning and empirical data, we can conclude that the multi-token “seigniorage share” incentive model has significantly more built-in stability than the single-token rebasing model. In fact, Ferdinando Ametrano recently updated36 his 2014 "first simplistic implementation" of Hayek's money, and given the issues listed above, he now supports a seigniorage-based multi-token model.

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The speculative nature of purely algorithmic stablecoins is inevitable. Recently, however, a number of new protocols have emerged that attempt to rein in the reflexive nature of algorithmic stablecoins by leveraging fractional asset backing (“fractional reserves”).

The insight here is simple. Haseeb Qureshi's observation is correct: "Essentially, you can say that the 'collateral' backing the share of seigniorage is the share of the future growth of the system." So, why not supplement these speculative "collaterals" with real collateral ", to make the system more robust?

ESD v237 and Frax38 do exactly that. ESD v2 is still in the research and discussion stage, after which it will be finally voted on by governance. If implemented, the upgrade would make some substantial changes to current ESD protocols. Chief among these is the introduction of a "reserve requirement".

Under the new system, the ESD protocol is targeting a 20-30% reserve ratio39, initially denominated in USDC. These reserves are partially funded by the protocol itself (the protocol sells ESD on the open market when the ESD is above a certain target price), but also by ESD holders who wish to unbond from the DAO (they have to pay a deposit into the reserve ). These USDC reserves are then used to stabilize the protocol by automatically purchasing ESD during contractions until the minimum reserve requirement is met.

The yet-to-be-launched Frax is a more elegant attempt at creating a partially-collateralized algorithmic stablecoin. 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 the other algorithmic stablecoins discussed so far, FRAX can always be minted and redeemed at $1, which means that arbitrageurs will play an active role in stabilizing the coin’s price.

This minting/exchanging mechanism is at the heart of the Frax network as it utilizes a dynamic fractional reserve system. In order to mint one FRAX, a user must deposit a combination of some 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 ratio of FXS to other collateral rises). Locking FXS to mint FRAX has a deflationary effect on FXS supply, as more FXS is needed to mint FRAX, the demand for FXS will naturally increase as the supply falls. Instead, as noted in Frax’s documentation note 40, during a contraction, “the protocol re-collateralizes the system, allowing Frax’s redeemers to receive more FXS and less collateral from the system. This increases collateral in the system As a percentage of FRAX supply, as support for FRAX grows, so does market confidence in it.”

In fact, dynamic guarantees serve as a stabilizing countercyclical mechanism, enabling the Frax protocol to weaken the harmful effects of extreme reflexivity when necessary. But it also allows the protocol to remain open and become fully unsecured in the future, if the market so chooses. In this sense, Frax's dynamic guarantee mechanism is "agnostic".

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Algorithmic stablecoins are a fascinating experiment in money, and their success is still unknown. While Charlie Munger's dictum is always true—"give me an incentive and I'll give you an outcome"—these agreements have game-theoretic complexities that are difficult to fully grasp with a priori reasoning alone. Furthermore, if past cryptocurrency market cycles are any indication, we should be prepared that these dynamics may behave in ways that do not match rational expectations.

However, it would be foolish to abandon algorithmic stablecoins at this early stage. It would also be a mistake to forget how high the stakes are. In his 1976 masterpiece, The Denationalization of Money, 41 Hayek wrote: "I believe that man can do better than historical gold. Government cannot do better. Free enterprise, for example, from a competitive process Institutions that come out on top, no doubt make good money, no doubt they will.” Although still in its infancy, algorithmic stablecoins could eventually serve as the blueprint for, and the basis for, Hayek’s vision of money markets.

Disclosure: The author may hold tokens mentioned in this article.