Stability, Resilience, and Reflexivity: A Deep Dive into Algorithmic Stability
插兜小哪吒
2020-12-15 02:38
本文约8537字,阅读全文需要约34分钟
Which vision of an algorithmic stablecoin is more convincing: a simple rebasing model or a multi-token "control currency issuance" system?

Editor's Note: This article comes fromChatting with Xiaozha (ID: xiaonazha88), reprinted by Odaily with authorization.

By Benjamin Simon

Original link:https://insights.deribit.com/      

Editor's Note: This article comes from

Chatting with Xiaozha (ID: xiaonazha88)

Chatting with Xiaozha (ID: xiaonazha88)

, reprinted by Odaily with authorization.

By Benjamin Simon"Original link:"In 2014, the academy published two academic papers: one, "Hayek Money: The Cryptocurrency Price Stability Solution," by Ferdinando Ametrano. Stability Solution), and the other is A Note on Cryptocurrency Stabilization: Seanorage Shares by Robert Sams.

Crypto watchers will recognize that Ametrano's "Hayek Money" and Sams' "controlling the currency supply" are no longer academic abstractions. "Hayek Money" is nearly identical to Ampleforth, which launched in 2019 and rocketed to a fully diluted market cap of more than $1 billion in July 2020. More recently, Sams' "controlling the money supply" model has been the basis to varying degrees for basis, esd, basis cash, and Frax.

Stablecoin Background

The problems before us now are not dissimilar to those faced by readers of Amitrano and Sams' paper six years ago. Can algorithmic stablecoins truly achieve long-term survival? Will algorithmic stablecoins always suffer from inflation and deflation? Which vision of an algorithmic stablecoin is more convincing: a simple rebasing model or a multi-token

control currency supply

system (or something else entirely)?

For all of these questions, the jury is still out and it may be some time before broad consensus emerges. However, this paper attempts to explore these fundamental questions from first-principle reasoning and from some empirical data from recent months.

secondary title

Stablecoin Background

Algorithmic stablecoins are a world of their own, but before diving in, it's worth taking a step back and investigating the broader stablecoin landscape. (Readers who are already very familiar with stablecoins can skip or skip this section).

The first category of centralized stablecoins: USDT and USDC, as well as exchange-based tokens such as BUSD, are centrally managed, backed by U.S. dollars, and can be exchanged one-to-one for U.S. dollars. These stablecoins have the advantages of asset pegs and capital efficiency (i.e. no over-collateralization), but the centralized nature of their permissions means that users can be blacklisted, and the peg itself depends on the trusted behavior of a central entity.

The Paradox of Reflexivity and Algorithmic Stability

The second category of multi-asset collateralized stablecoins includes MakerDAO's DAI and Synthetix's sUSD. Both stablecoins are over-collateralized by crypto assets and both rely on oracles to maintain their peg to the U.S. dollar. Unlike centralized tokens like USDT and USDC, which can be minted permissionlessly, in DAI a permissioned centralized asset like USDC can be used as collateral. Additionally, the over-collateralized nature of these stablecoins means they are extremely capital intensive, and the highly volatile, highly correlated nature of cryptoassets has made these stablecoins vulnerable to crypto-wide shocks in the past."This all brings us to algorithmic stablecoins. An algorithmic stablecoin is a token that adjusts its supply in a deterministic manner (i.e. using an algorithm) in order to move the price of the token in the direction of a price target. At the most basic level, an algorithmic stablecoin expands its supply when it is above a price target and contracts when it falls below it."Unlike the other two types of stablecoins, algorithmic stablecoins are neither convertible one-to-one to U.S. dollars, nor are they currently backed by crypto asset collateral. Finally, and perhaps most importantly, algorithmic stablecoins are often highly reflexive: demand is largely, and entirely, driven by market sentiment and momentum. These demand-side forces are diverted into the token supply, which in turn generates further directional momentum in what could end up being a violent feedback loop.

Every stablecoin model has its tradeoffs. Investors who don't care much about centralization will think there is no problem with USDT and USDC. Others will find that capital-inefficient over-collateralization is a price worth paying for a permissionless, hard-pegged decentralized currency. However, for those unsatisfied with either of these options, algorithmic stablecoins represent an enticing alternative."secondary title" 

The Paradox of Reflexivity and Algorithmic Stability

For algorithmic stablecoins to survive in the long run, they must achieve stability. This task is particularly difficult for many algorithmic stablecoins because of their inherent reflexivity. Algorithmic supply changes are designed to be counter-cyclical; expanding supply should lower prices, and vice versa. In practice, however, supply changes often reflexively amplify directional momentum, especially for those that do not follow

control currency supply

model, an algorithmic model that separates stablecoin tokens from pricing 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 equal amount of dollars or other forms of collateral. In contrast, the price stability of an algorithmic stablecoin cannot be guaranteed at all, as it is entirely determined by collective market psychology. Haseeb Qureshi makes this point aptly."These schemes exploit a key insight: stablecoins are ultimately a Schelling point. If enough people believe that the system will survive, that belief can lead to a virtuous cycle that ensures its survival."In fact, if we think more carefully about how an algorithmic stablecoin can achieve long-term stability, an apparent paradox emerges. To achieve price stability, an algorithmic stablecoin must scale to a market cap large enough that transactions do not cause price volatility. However, the only way a purely algorithmic stablecoin can grow to a sufficiently large network size is through speculation and reflexivity, and the problem with highly reflexive growth is that it is unsustainable, while shrinkage is often just as reflexive . A paradox thus arises: the greater the network value of a stablecoin, the more resilient it is to price shocks. However, only highly reflexive algorithmic stablecoins, those prone to extreme expansion/contraction cycles, are likely to achieve large network valuations in the first place.

A similar reflexive paradox exists with Bitcoin. In order for it to be viable for more and more people and organizations, it must have increasingly more fluidity, stability and acceptance. The growth of BTC in these characteristics over the years has made it accepted by darknet participants first, then by technical experts, and recently by traditional financial institutions. At this point, Bitcoin has acquired a kind of resilience from its deep reflexive cycle, which is the path that algorithmic stablecoins need to follow."rebase "Ampleforth: A simple but flawed algorithmic stablecoin.

Let’s now 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" proposal proposed by Ametrano. The supply of AMPL is inflated and deflated according to deterministic rules based on the daily time-weighted average price (TWAP) of each AMPL: below the target price range (i.e. below $0.96), deflation, above the target range (i.e. high at $1.06), inflation. The most important thing is that every wallet will be proportional"participate"Every supply changes. If Alice held 1000 AMPL before the repurchase and the supply expanded by 10%, Alice now holds 1100 AMPL; if Bob has 1 AMPL, he now holds 1.1 AMPL."whole network"It is the difference between Ampleforth's algorithm model and the control currency issuance model adopted by other protocols. While the Ampleforth white paper does not provide a rationale for the single-token rebase design versus the multi-token approach, there appear to be two main rationales for this design decision."The first is simplicity. Regardless of how it actually works, Ampleforth's single-token model has a simplicity unmatched by other algorithmic stablecoins. Second, Ampleforth's single-token design claims to be the fairest algorithmic stablecoin model. disproportionate to monetary policy actions that make those"Hayek Money"the closest

Cantillon effect"seigniorage"stable currency"ESD ") in stark contrast, Ampleforth is designed such that all token holders retain the same share of the network after each rebase. Ametrano makes exactly this point in his 2014 paper, where he elaborates on the rationale for monetary policy action.

, and combine it with"Algorithmic Stablecoins"The relative fairness was compared."This is the rationale for the Ampleforth model, which has been replicated by other reformulated tokens such as BASED and YAM. But before getting into the flaws of the model, let's look at Ampleforth's performance data over a year and a half. Since its inception in mid-2019 (just over 500 days), Ampleforth has been inflated or deflated more than three-quarters of the time, in other words, since launch, AMPL's TWAP has been out of the stable range for more than 75% of the time. To be sure, the protocol is still in its infancy, so it would be premature to dismiss it on these grounds alone. Nonetheless, we will be looking at the modified"stable currency"How it managed to remain more than twice as stable as Ampleforth during the first few months of its existence."Defenders of Ampleforth often dismiss the lack of stability; many of them even

dissatisfied with the label. Their argument is that Ampleforth only needs to be a"viscosity"Will suffice. However, this argument is debatable. Take, for example, a cryptocurrency that is recalculated daily based on a random number generator. Like Ampleforth, this token will have"Mature"Obvious 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 not yet

The essence of this method is to completely transfer price fluctuations to supply fluctuations, so that the price of each AMPL is basically stable. this kind

multi-token "Mature"Would Ampleforth really be an ideal candidate for a transactional base currency?

Here, we discover the crux of the problem, a core flaw in AMPL's design. Even if the price of AMPL reaches $1, the purchasing power of AMPL held by individuals will change on the way to $1. Back in 2014, Robert Sams addressed this exact issue for Ametrano's Hayek Money."Seigniorage Shares ""Price stability requires not only stabilizing the unit of account, but also stabilizing the value store of the currency. Hayek money is to solve the former, not the latter. It just exchanges a fixed wallet balance and a fluctuating currency price for a fixed currency price and a fluctuating wallet balance. The net effect is that the buying power of Hayek money wallets fluctuates just as much as bitcoin wallet balances.”

Ultimately, the simplicity of Ampleforth, with its straightforward single-token model, is a bug, not a feature. The AMPL token is a speculative vehicle that rewards holders with inflation during times of high demand and forces holders to become debt financiers when demand is low. Therefore, it is difficult to see how AMPL can achieve this speculative purpose while also achieving the stability that is a necessary condition for stablecoins.

secondary title"token storage"alternative plan

Robert Sams's"The vision never became a reality, but a new class of algorithmic stablecoin projects has recently emerged that shares many of its core ingredients."However, another protocol similar to Seigniorage Shares - Empty Set Dollar (ESD) has gone through multiple expansion and contraction cycles since its launch in September. In fact, to date, more than 200 supply"bond"period of time

(one every 8 hours), nearly 60% of the time occurs in ESD TWAP at $0.95"At first glance, ESD's mechanical design appears to be a hybrid of Basis and Ampleforth. Like Basis (and Basis Cash), ESD utilizes bonds ("coupon") to finance protocol debt, which must be purchased by burning ESD (thus contracting supply), which can be redeemed for ESD once the protocol enters expansion. But unlike Basis, ESD does not have a third token that ESD can claim for inflationary rewards when the network expands after debt is paid off (i.e. after coupons are redeemed). As an alternative to third tokens, ESD holders can stake their ESD in an ESD Decentralized Autonomous Organization (DAO)"(i.e. equity) to get a prorated share of each expansion, similar to Ampleforth.

Crucially, unbanning ESD from the DAO requires a

installments

installments"stable currency"For 15 epochs (5 days), it can neither be traded by its owner nor accrue inflationary rewards. Therefore, the staging mode of ESD is similar to the function of basis cash share, because binding ESD to DAO and purchasing basis cash share both preset risks (liquidity risk of ESD; price risk of BAS), and it is possible to obtain future currency Swell rewards. In fact, even though ESD uses a two-token model (ESD and coupon) rather than the three-token model of basis cash, the net effect of ESD's installment period is that ESD becomes a de facto three-token system.

secondary title"Comparison of single-token and multi-token algorithm stablecoin models"Clearly, the multi-token design involves more moving parts than Ampleforth's single-token regression model. However, this added complexity is a small price to pay for the potential stability it provides."In short, the result of the design employed by ESD and Basis Cash is that the reflexivity inherent in the system is contained, while the"stable currency"Some are (to an extent) insulated from market dynamics. Speculators with a risk appetite can bootstrap the protocol during contractions in exchange for the benefit of future expansions. However, users who just want to own a stablecoin with stable purchasing power can, at least in theory, hold BAC or ESD without buying bonds, coupons, stocks, or binding their tokens to a DAO . This non-repetitive quality also has the benefit of being synthesizable with other DeFi primitives. Unlike AMPL, BAC and (non-bond) ESD can be used as collateral or lent without having to account for the complex dynamics of constant network-wide supply changes."。 

Ampleforth founder and CEO Evan Kuo criticized algorithmic stablecoin projects like Basis Cash because they"Rely on the bond market (ie: bonds) to regulate supply)"zombie idea"too big to fail", Kuo argues, these algorithmic stablecoins are flawed because, like traditional markets, they

Will always rely on lender of last resort (ie: bailout)"However, Kuo's argument is problematic because it assumes, without any justification, that reliance on debt markets ("Rescue

) are inherently dangerous. In fact, debt financing is problematic in traditional markets because of moral hazard;"too big to fail"of commercial entities can take non-punitive risks by socializing bailout costs. Algorithmic stablecoins like ESD and Basis Cash are not as extravagant as Fannie and Freddie were during the 2008 financial crisis. For these agreements, there is no single lender of last resort outside the system to whom the bailout costs can be shifted. It is entirely possible for ESD or Basis Cash to enter a debt spiral, in which case there is no one willing to provide funds, debt will accumulate and the protocol will collapse."In fact, Ampleforth also needs to raise debt to avoid falling into a death spiral. The difference is that this debt financing is hidden from view because it is simply spread across all network participants. Unlike ESD and Basis Cash, it is impossible to participate in the Ampleforth system without also being an investor in the protocol. When the network is in a state of deflation, holding AMPL is similar to taking on the debt of the network (in the words of Maple Leaf Capital, it is"act as a central bank

From first-principle reasoning and empirical data, we can conclude that multi-token,

control currency supply

The inspired model is significantly more intrinsically stable than single-token schemes. In fact, Ferdinando Ametrano recently updated his Hayek Money from 2014"The first simplistic implementation", in view of the above problems, he is now more inclined to multi-token, control currency circulation model.

Still, even if multi-token algorithmic stablecoins outperform their single-token counterparts, there is no guarantee that these algorithmic stablecoins will last in the long run. In fact, the underlying mechanism design of algorithmic stablecoins precludes any such guarantees because, as noted above, the stability of algorithmic stablecoins is ultimately 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 if there are investors willing to bootstrap the network when demand falls . When there are no longer enough speculators to believe that the network is resilient, the network will no longer be resilient."secondary title"Fractional Reserve Stablecoins: A New Era for Algorithmic Stablecoins?"The speculative nature of purely algorithmic stablecoins is inevitable. Recently, however, several nascent protocols have emerged that attempt to leverage fractional asset collateralization ("partial reserve

) to control the reflexivity of algorithmic stablecoins."The insight here is simple. Haseeb Qureshi's observation is correct,"。

Fundamentally, you could say that the 'collateral' backing Seignorage Shares is a stake in the future growth of the system

. So why not make this speculative

collateral"What about adding to the actual collateral to make the system more robust?"

ESD v2 and Frax do exactly that. ESD v2 is currently still in the research and discussion stage, after which it will eventually be voted on by the governance layer. If implemented, the upgrade would make some substantial changes to current ESD protocols. The most important of these is the introduction of"reserve requirement"。

This minting/redeeming mechanism is at the heart of the Frax network as it utilizes a dynamic fractional reserve system. To mint a single FRAX, a user must deposit some combination of $1 worth of Frax shares (FXS) and other collateral (USDC or USDT). The ratio of FXS to other collateral is dynamically determined by the demand for FRAX (as demand increases, so does the ratio of FXS to other collateral). Locking FXS to mint FRAX will have a deflationary effect on the supply of FXS, so when more FXS is needed to mint FRAX, the demand for FXS will naturally increase as the supply decreases. Instead, as Frax's paper points out, during contractions,

conclusion

The protocol re-hypothecates the system, enabling FRAX redeemers to obtain more FXS and less collateral from the system. This increases the proportion of collateral in the FRAX supply in the system, and as the support rate of FRAX increases, it increases the market's confidence in FRAX."In effect, dynamic staking serves as a stabilizing countercyclical mechanism, enabling the Frax protocol to mitigate the harmful effects of extreme reflexivity when necessary. But it also allows the protocol to remain open to become fully collateral-free in the future, if the market so chooses. In this sense, Frax's dynamic mortgage mechanism is"unknowable

Neither Frax nor ESD v2 is live yet, so it remains to be seen whether either 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 remaining more capital efficient than over-collateralized alternatives like DAI and sUSD."secondary title"conclusion

插兜小哪吒
作者文库