Editor's Note: This article comes fromChain News ChainNews (ID: chainnewscom), published with permission.

Chain News ChainNews (ID: chainnewscom)

Compiler: Perry Wang

Chain News ChainNews (ID: chainnewscom)

, published with permission.

Written by: Benjamin Simon, Researcher at Mechanism Capital

Compiler: Perry Wang

The English version of this article was published on Deribit Insights. The author and Deribit authorized Lianwen to translate and publish its Chinese version.

Two academic papers published in 2014 are notable: one by Ferdinando Ametrano, a professor at the Politecnico di Milano and a former program director at the Bitcoin Developers Conference, titled "Hayek Money: Solutions for Cryptocurrency Price Stability (Hayek Money: The Cryptocurrency Price Stability Solution); another, by Robert Sams, a cryptocurrency economist with 11 years of experience in hedge funds, entitled "Cryptocurrency Stability: Seignorage Shares" (A Note on Cryptocurrency Stabilization: Seigniorage Shares).

• Drawing on economist Friedrich Hayek's critique of the gold standard, Ametrano argues that, due to its deflationary nature, Bitcoin cannot adequately perform what we require of money to function as a unit of account. Instead, he proposes a rules-based, supply-elastic cryptocurrency that can “rebase” on demand, i.e. change the money supply proportionally to all token holders.

• In the paper "Seigniorage Shares", Sams proposed a similar model for similar reasons, but with an important adjustment: instead of readjusting the token supply, Sams' system proportionally changes the currency allocated in all wallets Instead, it consists of two tokens: the supply-elastic currency itself, and an investment "share" in the network. Owners of the latter asset, which Sams calls Seigniorage Shares, are the sole recipients of inflationary gains from increased supply, and sole bearers of debt when demand for money shrinks and the network shrinks.

• Astute cryptocurrency observers will immediately realize that Ametrano's "Hayek money" and Sams' "Seigniorage Shares" are no longer purely academic abstractions. "Hayek money" is almost identical to Ampleforth. Launched in 2019, Ampleforth skyrocketed in July 2020 with a fully diluted market cap of over $1 billion. And more recently, Sams' Seigniorage Shares model has served as the basis for Basis, Empty Set Dollar, Basis Cash, and Frax to varying degrees.

Can algorithmic stablecoins truly achieve long-term viability?

Stablecoin Background

Will algorithmic stablecoins be forever subject to extreme expansionary and contractionary cycles?

Which version of an algorithmic stablecoin is more compelling: a simple rebasing model, or a multi-token "Seigniorage Shares" system, or something else entirely?

On all of these issues, a popular jury is still out and it may take a while to reach a broad consensus. Nonetheless, this paper attempts to explore some fundamental questions from a first-principles approach, as well as some empirical data from recent months.

Stablecoin Background

Algorithmic stablecoins are a world of their own, but before delving too deep, it's worth taking a step back and exploring the broader stablecoin landscape

With Bitcoin being adopted by financial institutions like a snowball, the DeFi market of decentralized finance is booming, coupled with the upcoming network upgrade of Ethereum, stablecoins have also become popular recently, with a total market value of more than 25 billion US dollars. This parabolic growth has attracted the attention of big names outside the cryptography community, and recently even attracted the attention of a group of members of the US Congress.

USDT is still the stablecoin with the highest current market share, but it is by no means the only stablecoin. Broadly speaking, we can divide stablecoins into three categories: USD-collateralized stablecoins, multi-asset pool over-collateralized stablecoins, and algorithmic stablecoins. This article focuses on the last category. Still, it is important to be aware of the pros and cons of other classes of stablecoins, as understanding these trade-offs will allow us to enhance the value proposition of algorithmic stablecoins.

The first category of stablecoins (primarily USDT and USDC, but also exchange-issued stablecoins such as BUSD, HUSD, etc.) are centrally managed, backed by the U.S. dollar, and convertible at a 1:1 exchange rate. These stablecoins have the advantage of ensuring pegs and being capital efficient (i.e. no over-collateralization), but they are permissioned and centrally managed, and these properties mean that users can be blacklisted while the exchange rate is pegged 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 stablecoins are overcollateralized by cryptoassets and both rely on price oracles to maintain their peg to the U.S. dollar. Unlike centralized tokens like USDT and USDC, the second stablecoin can be minted without permission, though it’s worth noting that permissioned centralized assets like USDC can be used as collateral in the DAI use case. In addition, the over-collateralized nature of the second stablecoin means it is too capital intensive, and the highly volatile, highly correlated nature of crypto assets has made these stablecoins vulnerable to shocks that rippled through the entire crypto market in the past.

All of this leads us to focus more on algorithmic stablecoins. Algorithmic stablecoins are tokens whose supply is adjusted by a deterministic mechanism (i.e., using an algorithm), designed to move the price of the token toward a price target.

In simple terms, an algorithmic stablecoin expands its supply when it is above a target price, and shrinks its supply when it is below the target price.

Unlike the other two types of stablecoins, algorithmic stablecoins are neither exchangeable 1:1 with the U.S. dollar nor currently have crypto assets as collateral. Finally, and perhaps most importantly, algorithmic stablecoins are often highly reflexive: demand is largely driven by market sentiment and momentum (critics may dispute this). These demand-side forces are diverted into the token supply, which in turn creates further directional momentum, which can eventually create a violent feedback loop.

Each stablecoin model has its own trade-offs and trade-offs. Investors who don't care much about the impact of centralization will not think there is anything wrong with USDT and USDC. Others will feel that capital-inefficient over-collateralization is a price worth paying for a permissionless, decentralized, hard-pegged currency. But for those unsatisfied with either of these options, algorithmic stablecoins are an enticing alternative.

Reflexivity and the Algorithmic Stability Paradox

For algorithmic stablecoins to be viable in the long run, they must achieve stability. This is a particularly difficult task for many algorithmic stablecoins due to their inherent reflexive nature. Algorithmic changes in supply are counter-cyclical; increasing supply aims to lower prices, and decreasing supply aims to increase prices. But in practice, supply changes often amplify directional momentum through reflexivity, especially for algorithmic patterns that do not follow the pattern of "seigniorage shares". In the seigniorage shares model, the stablecoin token itself and the tokens that accumulate value and debt financing are two separate tokens.

For non-algorithmic stablecoins, network bootstrapping does not involve game-theoretic coordination. Each stablecoin is (at least in theory) redeemable for an equivalent dollar value or other form of collateral. In contrast, the successful price stability of an algorithmic stablecoin cannot be guaranteed at all, as it is entirely 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, then the This belief creates a virtuous circle that ensures its survival.”

In fact, if we consider more carefully what is needed for algorithmic stablecoins to achieve long-term stability, we find an apparent paradox. To achieve price stability, algorithmic stablecoins must grow 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 speculative trading and reflexivity, and the problem with highly reflexive growth is that it is unsustainable, and shrinkage is often also reflexive. Thus, a paradox arises: the greater a stablecoin's network value, the more resilient it is to large-scale price shocks. However, only highly reflexive algorithmic stablecoins, i.e. those prone to extreme expansion/contraction cycles, are likely to achieve extremely large network valuations in the first place.

Bitcoin has a similar reflexive paradox. In order for more and more people and organizations to use Bitcoin, it must become more and more liquid, stable and accepted. Over the years, these characteristics of Bitcoin have grown, taking Bitcoin users from initially darknet players, all the way to wealthy techies, and most recently, traditional financial institutions. At this point, Bitcoin has gained resistance from being caught in a deep reflexive cycle, a path that algorithmic stablecoins need to follow as well.

• Ampleforth: Simple but Flawed Algorithmic Stablecoin

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

As mentioned earlier, Ampleforth is almost identical to the "Hayek money" proposed by Ferdinando Ametrano. The supply of AMPL expands and contracts according to deterministic rules based on the daily time-weighted average price (TWAP): below the price target range (e.g., below $0.96) the supply contracts, above the price target range (e.g., high at $1.06) the supply increases. Crucially, 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, he now owns 1.1 AMPL.

The "rebase" covering the entire network is the difference between Ampleforth's algorithm mode and the seigniorage share mode adopted by other protocols. While the Ampleforth whitepaper does not explain the rationale for adopting a single-token rebasing design rather than a multi-token approach, there appear to be two main rationales for this design decision.

The first is simplicity. Regardless of how 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 stark contrast to the policy behavior of fiat currencies, which benefit most those individuals "closest" to the source of money (i.e., the "Cantillon effect"), Ampleforth is designed such that all token holders are It can keep its share of the network unchanged. Ametrano made this point in his 2014 paper, where he detailed the "gross inequity" of central bank monetary policy behavior and contrasted it with the relative fairness of "Hayek money."

This is the presumption of the Ampleforth model, which has been replicated by other algorithmic stablecoins that employ the rebase principle, such as BASED and YAM. But before exploring the flaws of the model, we might first look at the data we have on Ampleforth's year-and-a-half year performance.

Since mid-2019 (just over 500 days to date), three-quarters of Ampleforth's daily rebase has been positive or negative, in other words, more than 75% of AMPL's TWAP since launch was outside the rebase target range. To be sure, the agreement is still in its infancy so far, so it would be premature to dismiss it on these grounds alone. But we’ll soon be looking at how a modified seigniorage stablecoin, the Empty Set Dollar, managed to more than double the stability of Ampleforth in its first few months.

Die-hard Ampleforth fans often dismiss claims of the coin’s lack of stability; many of them would even hate the label “algorithmic stablecoin.” Their argument is that it is enough for Ampleforth to be a "reserve asset uncorrelated with traditional financial assets" in portfolio diversification.

However, this claim is questionable. For example, a cryptocurrency that rebases daily based on a random number generator, like Ampleforth, will have a "significant volatility footprint," but it doesn't hold value for that reason alone. Ampleforth's value proposition rests on its tendency toward equilibrium, which could theoretically make AMPL a pricing currency.

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

This brings us to the crux of the matter, 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 on the way to $1. Back in 2014, Robert Sams articulated this exact problem for Ametrano's Hayek concept of money:

Price stability is not only related to the stability of the unit of account, but also to the stability of the currency value store. Hayek money aims to address the former, not the latter. It simply swaps out fixed wallet balances and fluctuating currency prices for fixed currency prices and fluctuating wallet balances. The end result is that the purchasing power of Hayek wallets is as volatile as Bitcoin wallet balances.

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

The AMPL token is a speculative instrument 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 a stablecoin.

Multi-token "seigniorage" scheme

Robert Sams' "Seigniorage Shares" vision never became a reality, but a recent wave of new algorithmic stablecoin projects have collectively adopted many of its core ingredients.

Basis Cash, born just over a week ago, is a public attempt to revive Basis — the algorithmic stablecoin project that raised over $100 million in 2018 to much acclaim but never got off the ground. Like Basis, Basis Cash is a multi-token protocol consisting of three tokens: BAC (algorithmic stablecoin), Basis Cash Shares (whose holders can earn from BAC inflation as the network scales), and Basis Cash Bonds (can be purchased at a discount when the network is in a deflationary state, and can be redeemed for BAC when the network comes out of the deflationary phase). Basis Cash is still in the early stages of development and has encountered some early development hurdles; the protocol has not made a successful supply change to date.

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), and nearly 60% of the changes in ESD's TWAP are in the range of $0.95 < x < $1.05, which means that the price stability of ESD has More than double that of Ampleforth, although ESD has had a much shorter lifetime to date.

At first glance, ESD's mechanical design appears to be a hybrid of Basis and Ampleforth. Like Basis (and Basis Cash), ESD finances the agreement's debt with bonds (coupons), which must be purchased by burning ESD (thus reducing supply), and can be redeemed back to ESD after the agreement restores supply expansion. But unlike Basis, ESD does not have a third token that gets rewarded from inflation as the network pays off its debts into scaling. Instead, ESD holders can "bond" (such as pledge) their ESD in the ESD decentralized autonomous organization DAO, so as to distribute the benefits of inflation in proportion, similar to Ampleforth's rebase.

Crucially, unbonded ESDs from the DAO require a "staging" period, where ESD tokens are temporarily "stored" for 15 epochs (5 days), during which time they can neither be traded nor earned by their owners Inflation bonus. Therefore, the function of ESD's "temporary storage" mode is similar to Basis Cash Shares, because binding ESD to DAO and purchasing Basis Cash Shares both pre-assume risks (liquidity risk of ESD; price risk of BAS) in exchange for future inflation rewards potential. Indeed, although ESD uses a two-token model (ESD and coupons) instead of Basis Cash's three-token model, the end result of ESD's staging period is that ESD becomes a de facto three-token system, with bonded ESD similar to on Basis Cash Shares.

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

Clearly, the multi-token design contains more components of change than Ampleforth's single-token rebase model. This added complexity is a small price to pay for the potential stability it provides, though.

In short, the design patterns adopted by ESD and Bass Cash have the advantage of containing the inherent reflexivity of the system, while the "stablecoin" part of the system is (to some extent) insulated from market momentum. Risk-seeking speculators can bootstrap the protocol during money supply contractions in exchange for future distributions of gains from recovery expansions. But in theory, users who just want a stablecoin with stable purchasing power can hold BAC or ESD without buying bonds, coupons, stocks, or binding their tokens into a DAO. This rebase-free nature adds the added benefit of combining with other DeFi primitives. Unlike AMPL, BAC and (unbonded) ESD can be staked or loaned without having to account for the complex dynamics of token supply changes across the network.

But Kuo's argument is nonsensical because it assumes, without any justification, 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 take huge risks without fear of punishment by socializing bailout costs. Algorithmic stablecoins like ESD and Basis Cash do not enjoy the luxury that Fannie and Freddie enjoyed during the 2008 financial tsunami. For these agreements, there is no lender of last resort (ie, the receiver of last resort for bailout costs) outside the system. It's entirely possible that ESD or Basis Cash could get caught in a debt spiral where debt piles up and no one wants to take over the debt, and the protocol collapses.

Fractional Reserve Stablecoins: A New Era for Algorithmic Stablecoins?

In fact, Ampleforth also required debt financing to avoid a death spiral. The difference is that this debt financing is hidden from view, as it is simply distributed among all network participants. Unlike ESD and Basis Cash, it is not possible to join the Ampleforth system without being an investor in the protocol. Holding AMPL while the network is in contraction is akin to taking on the network's debt ("acting as the central bank" in Maple Leaf Capital parlance), as AMPL holders lose tokens on every negative supply rebase.

From both first-principles inferences and empirical data, we can conclude that the multi-token, "Seigniorage Shares" inspired model has significantly higher built-in stability than the "single-token rebase" scheme . In fact, Ferdinando Ametrano recently updated his personal Hayek currency "first simple implementation concept" in 2014. In view of the above problems, he now favors a model based on multi-tokens and Seigniorage Shares.

But even if multi-token algorithmic stablecoins outperform their single-token counterparts, there is no guarantee that any of these algorithmic stablecoins will be sustainable in the long run. Indeed, the underlying mechanism design of algorithmic stablecoins precludes any such guarantees, since, as noted above, the stability of algorithmic stablecoins is ultimately based 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, their stablecoins will only remain stable if there are investors willing to bootstrap the network when demand falls. The network ceases to be resilient when there are no longer enough speculators to believe that the network is resilient.

Fractional Reserve Stablecoins: A New Era for Algorithmic Stablecoins?

The speculative nature of purely algorithmic stablecoins is unavoidable. But recently a number of prototype protocols have emerged that attempt to harness the reflexive nature of algorithmic stablecoins using fractional asset collateralization ("fractional reserves").

The insights into this issue are simple. Haseeb Qureshi's observation is correct: "Fundamentally, the 'mortgage' backing the Seignorage Share can be said to be a stake in the future growth of the system."

So why not supplement this speculative “collateral” with actual collateral to make the system stronger?

ESD v2 and Frax do just that. ESD v2 is still in the research and discussion phase, after which it will ultimately decide its fate through a governance vote. If implemented, this upgrade would introduce several substantial changes to current ESD protocols. Chief among these is the introduction of a “reserve requirement”.

The currently unreleased Frax is a more elegant attempt at creating a fractional collateral 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 above, FRAX can always be minted and redeemed at $1, meaning arbitrageurs will play an active role in stabilizing the token’s price.

Summarize

This minting/exchanging mechanism is at the heart of the Frax network as it utilizes a dynamic fractional reserve system. To mint one FRAX token, a user must deposit some combination of Frax Shares (FXS) and other collateral (USDC or USDT), worth a total of one dollar. The ratio of FXS to other collateral is dynamically determined by FRAX's demand, and as demand increases, the ratio of FXS to other collateral will increase. Locking up FXS to mint FRAX has a deflationary effect on the FXS supply, so as more FXS is needed to mint FRAX, the demand for FXS will naturally increase as the supply falls. Instead, as Frax’s documentation notes, during network contractions, “the protocol rehypothecates the system, allowing FRAX redeemers to take more FXS and less other collateral from the system. This increases The ratio of collateral in the system to the supply of FRAX has been determined, and with the strengthening of support for FRAX, the market’s confidence in FRAX has also increased.”

Effective, dynamic staking acts as a stabilizing countercyclical mechanism, allowing the Frax protocol to "blunt the deleterious effects of extreme reflexivity" when needed. But it also leaves open the possibility of the protocol becoming completely collateral-free in the future, as long as the market chooses to do so. In this sense, Frax's dynamic mortgage mechanism is "workable under any circumstances".

Neither Frax nor ESD v2 is live yet, so it remains to be seen whether they will be successful in practice. But at least in theory, these hybrid, fractional-reserve protocols are promising attempts to combine reflexivity with stability, while still being more capital efficient than over-collateralization schemes like DAI and sUSD.

Summarize