The purpose of this article is to show that there is no algorithm that can maintain the peg.
Author: SparkDAO
Cover: Photo by Sebastian Svenson on Unsplash
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A "stablecoin" is an attempt to create a synthetic asset that is "more stable" than its base currency . In this paper, we demonstrate that the only viable stablecoins consist of simple (weighted) averages of assets, often referred to as "basket currencies" or simply "portfolio diversification".
While stablecoins are the holy grail for crypto enthusiasts and are backed by Tether, it's not a new idea. There are currently 66 countries whose currencies are pegged to the U.S. dollar and 25 countries whose currencies are pegged to the euro. The motivation is understandable, small countries with their own currencies will naturally have higher volatility than larger markets, to the detriment of their own importers and exporters. By linking their currencies to the larger market through responsible fiscal policy, they achieve stability for their country's importers and exporters and a more favorable trade balance.
The dollar currency peg works by buying and selling U.S. Treasury bonds, also known as Treasury bills. However, if large market volatility causes the pegged currency government to run out of bonds, they will not be able to maintain the peg. When this happens, the only way the government can repay its debt is to print more money, causing hyperinflation.
In other words, in this case, the pegged currency is not fully collateralized. While governments typically operate currency pegs manually, crypto stablecoin enthusiasts often come up with algorithmic solutions. The fact that the algorithm is anchored doesn't matter because any bond buying/selling strategy with human intervention can be turned into an automated algorithm.
**The purpose of this article is to show that there is no algorithm that can maintain the peg. **Argentina, Mexico, Greece and Thailand are all countries that have learned this lesson the hard way. That said, the potential for large price swings in stablecoins is much greater than is generally believed. While the probabilities are finite and can be calculated, the size of the expected movement is infinite, so the assumption that the price will remain within any given trading range is false.
We can model financial markets in terms of probability distributions between two different time intervals. That is, if the price at the current time t is p, the probability distribution gives the price at the next time interval t+1, where 1 can be 1 hour, 1 day, or whatever time interval you want. This is called the 1-point correlation function.
The Alpha -stable Lévy distribution for multiple values of its variance parameter α. When α =2, the distribution is Gaussian (normal); when α =1, it is Cauchy. In mathematical terms, the second and higher moments of the price probability distribution are infinite. The famous Vifred Pareto used the above Alpha -stable Lévy distribution with 1 < α < 2 as a better model for stock and commodity prices than the Gaussian distribution.
For example, the use of the Gaussian assumption in the Black-Sholes model of option pricing is well known for underpriced options. Likewise, indicators based on Gaussian statistics such as Bollinger Bands are pretty useless during large market swings, which occur far more often than one intuitively assumes.
Let us now turn to a hypothetical "hooking" algorithm. We assume that the central bank (or stablecoin) will buy or sell the asset it is pegged to whenever the price moves outside a specified range. In mathematical terms, we can use the method of moments to expand the distribution. (The "moments" are the expected values drawn from the distribution, where the first three are usually called mean, variance, and skewness)
Suppose we want the pegged currency or stablecoin to remain in the range a < u < b relative to the base u, for example, say we want the pegged currency to stay on the basis of 1% = (ua)/u=-(ub)/u. Let us assume that the market falls below this range and the central bank has to buy underlyings to compensate. How much you need to buy depends on the price. The expected price is given by the variance of the distribution. In a worst-case scenario, the peg falls to zero, requiring the central bank or stablecoin to buy back its entire reserves, which requires the central bank or stablecoin to have reserves equal to its entire market cap in the underlying.
**Therefore, the notion that an algorithmic stablecoin will use an amount of collateral that is less than the full market cap of the pegged currency is absolutely false. **However, if you hold the entire market capitalization reserve, this is "fully collateralized" and requires no buying and selling, but only the issuance of new pegged units in line with the acquisition of the underlying asset.
The concept of fully collateralized stablecoins has been explored, often referred to as "bonding on the blockchain" or sometimes "tokenization". If the assets are deposited in a properly regulated and audited manner, new units of linked assets that correspond to bond issues or deposits can be issued directly. The key words here are "proper regulation and auditing". Any form of fractional reserve in these deposits creates a systemic risk of peg failure. It is auditing and trust in that auditing and regulatory regime that creates certainty.
Financial firms are known for lending collateral on their balance sheets, sometimes leading to events such as rehypothecation and commingling. Rehypothecation is the practice of multiple parties claiming the same asset on their balance sheet, such as the lender and the borrower both counting the asset, which results in double counting. This creates systemic risk when market conditions force loans to be called back. Blending is the practice of substituting one asset for another in an audit. This creates systemic risk when pledged alternative assets cannot be bought and sold at expected prices.
Financial firms don't like having large amounts of capital on their balance sheets, often referred to as "trapped capital," because it is believed that productivity can be increased if this capital is loaned out. However, this is the promise of cryptocurrencies - **everything is fully and systematically capitalized through cryptographic guarantees. **Cryptocurrency loans must use some form of multi-signature and escrow proxy so that when the loan needs to be recovered, it can be done fully and systematically without risk. Likewise, the practice of mixing assets must be banned if we want to achieve stability in the face of market volatility.
In conclusion, the only form of reasonable stablecoin or token that represents another asset without systemic risk is the fully collateralized type. The reason for creating such stablecoins is to enhance fiat currencies and give them the cryptographic certainty, fast settlement times, and international transportability of cryptocurrencies.
It would make sense for such bonds to be issued by the Federal Reserve or the European Central Bank. It is very important that the collateral behind the stablecoin cannot be re-hypothecated, and that the collateral is actually the underlying asset and not mixed with other assets with their own market movements. We encourage regulators to focus on the topic of rehypothecation and hybridization, so as not to bring the failure modes of traditional finance into the future of digital finance.
*The views and opinions expressed here are those of the authors and do not necessarily reflect the views of SparkDAO. Every investment and transaction involves risks, and you should have your own judgment when making decisions!
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