Unscramble: pledge stable currency changes stable currency, do so graph what?

Original title:Visualization of Neutral Dollar (NUSD) metastability
By: Neutral team
Translation & amp; Proofread: zhou jin, ViolaH, ah jian

& have spent The key points 

The -neutral Dollar is a stable currency basket, and because of its metastability in design, it inherits some of the attractions of stable currencies. This combination products can make people benefit through portfolio diversification, as well as build closely tracks mortgage stable currency price efficient rebalancing mechanism (rebalancing mechanism). After a long simulation run, we can make an overall assessment of its superiority.

The -neutral Dollar was trading in line with the Dollar and was generally less volatile, proving to be a more suitable stable currency than other potential competitors.

- potential downside risk is mitigated due to its diversified nature, suggesting that Neutral Dollar can hedge against specific capital losses and is a viable option for stable Dollar portfolios.

- only when there are a lot of unweighted orders in the market will Neutral Dollar experience greater volatility than other stable currencies, which is extremely unlikely as market activity will eventually reach unwinding.

- we were able to compete in the market by diversifying currencies and introducing the new stable currency into the Neutral Dollar basket. The process of introducing a new stable currency does not reduce the value of the basket itself.

& have spent Stability analysis of Neutral Dollar & NBSP;

In Neutral, we are designing a stable currency basket that is less risky than any single stable currency today and can be expected to remain so for some time. Financial theory emphasizes that portfolio volatility can be lower than that of any product in a portfolio, and we can intuitively demonstrate this in the context of Neutral Dollar.We can evaluate and compare the stability of the money we create with the stability of the money in the portfolio around various indicators of price and risk.

In addition, our innovative product structure is designed to achieve liquidity neutrality and exchange neutrality, which means that new Neutral dollars can be created by collateralizing the stable currency backed by the Dollar. Although Neutral Dollar has the same weighting across stable currencies, transaction-based activity can lead to a slight imbalance.In order to solve this potential problem, we use optimization measures to determine the weight composition of related assets to smooth out the fluctuations caused by these assets.We then performed a rigorous simulation to see how the basket could be unwound based on market pricing. Finally, we combined the above analysis to consider how adding another stable currency to the basket would affect the behavior of the newly constructed Neutral Dollar. Various studies have shown that Neutral Dollar is a superior and better digital Dollar than any stable currency for a variety of purposes.

First, Neutral Dollar (NUSD) will include four stable currencies: USDC, PAX, TUSD, and DAIThe term stability coin implies that each of these stability COINS is worth a dollar. However, the price of a stable currency does not reflect this: trading activity may cause the price of the currency to deviate from this reference value. Factors such as credit risk, inflow or outflow, redemption requirements, and counterparty behavior determine the differences between stable currencies. By combining these stable currencies, we have generally smoothed out the explosion of these factors and produced more stable currencies whose value fluctuates closer to expectations.

Here are the historical prices for the correlated and Neutral Dollar currencies. We expect these stable currencies to hover around $1.

According to this chart, we find that the price of these stable currencies is not actually $1. In fact, they trade from $0.98 to $1.08. The price will fluctuate around $1, but will vary according to market expectations about the quality of the stable currency.If we want to determine which is the best stable currency, we can try to visually see from the graph which currency has the least volatility.But obviously, whenWhen some stability COINS are superimposed on the graph, it is difficult to determine exactly which currency is the best, so we need to specifically evaluate the stability of each stability coin in this period. The first tool that allows us to explain this price volatility isPrice volatility, a general measure of changes in asset prices over time. In addition, to achieve this goal, we also calculated the volatility of each stable currency relative to Neutral Dollar, which can reflect the effect of the metastable basket.

From this table we can see that PAX is the second stable currency during this period and its volatility is 29% higher than NUSD. Similarly, we can see DAI's volatility more than double that of our stable currency. From this, we can conclude that Neutral Dollar is clearly more attractive than other products.

Now, let's stop the analysis -- because it's incomplete.First, data on stable currency prices only date back to October 2018. At the time of this writing, the length of the data interval we can use for testing is less than six monthsAll this analysis would be meaningless if we did not know whether our results would hold up in the long run. Second, results based on a single period cannot be used as reliable evidence in finance. It's like a trading strategy -- the same strategy can make you rich in 2017 or lose money in 2018. Given the lack of historical data, we need a way to determine whether Neutral Dollar can be stable over time. Fortunately, we can do this by calculating the metrics for the rolling period.

A rolling period is a method of eliminating deviations within any given time range. Rolling periods are a more scientific way of assessing the relationship between future performance and past performance. While there may be other risks associated with using this approach (as there is no guarantee of a return for any method), we can effectively eliminate this time bias. In the first chart, we sampled just one time period to see the advantage of Neutral Dollar. Now, with rolling periods, we sample historical data over 12 hours every 5 minutes -- so we can effectively create more than 30,000 periods to evaluate. The results of this experiment can better reinforce or correct our conclusions.

At the same time, we introduce two analyzable indicators and volatility to better understand the overall price stability:

deviationThe extent to which a stable currency deviates from a given dollar price;

Volatility (fluctuation)It means the overall movement of prices.

We calculated the percentage of sample points with the maximum or minimum deviation of each stable currency over the rolling period, which took into account both upward and downward price movements.

As you can see from the graph on the left, the Neutral Dollar has rarely been the biggest currency to move away from the Dollar -- only 0.3% of the time. The next best stable currency is the PAX, at 2.5%. DAI was the most frequently deviated from the dollar -- it was the most volatile for 40 percent of the time. As shown on the right, the Neutral Dollar was the least biased currency most of the time. Interestingly, DAI was the least biased 14.2 percent of the time,This may indicate that DAI is very stable in some time periods and very unstable in others, indicating that its risk factors are different from those of fiat notes.

Here's a very similar example: Neutral Dollar has never been the most volatile currency in any given 12 hours and was the least volatile currency in 39.8% of the time.

When assessing volatility, Neutral Dollar has never been the most volatile currency and has been the least volatile of all stable currencies for 44.1% of the time.

Overall, on the price stability front, we found the Neutral Dollar to be very strong compared to other stable currencies over the periods we testedWe are confident that Neutral Dollar is price stable, so we can create a better stable currency that is less volatile and more representative of Dollar value than any single stable currency.

We can extend our analysis (especially to the downward phase of prices). All of the above indicators show that Neutral Dollar is more stable in price, both up and down. When we want to understand in detail what the potential risks are, we pay more attention to the downside phase because it can cause property damage. We use two indicators to describe the potential risk in this scenario. The first is called value at risk (VaR). VaR USES a specific level of confidence to simulate a scenario to calculate the potential loss over a period of time. Many methods can estimate the distribution of losses by estimating the probability density function, but in general they are similar because VaR always focuses on an individual's potential loss.

In our experiment, we calculated the daily VaR of the available historical data at 95% confidence. The chart below doesn't give much of an estimate because of the confusion caused by overlapping data, but we can get an idea of the potential capital loss for these stable currencies, which could range from 2 to 6 cents.

We can also perform a similar analysis of the data previously constructed using the rolling period method. Because this measure focuses on the left-tail distribution of returns, we are most concerned with the maximum potential loss for each stable currency. Below is a pie chart showing the average number of times each stable currency had the maximum value at risk during our sampling phase.

Neutral Dollar doesn't seem to have the biggest tail risk over our sampling period. PAX, the moment of maximum VaR only accounts for 9.9% of the sampling time, which is expected to become the second reliable stable currency. From the cyclical peaks in the line chart above, DAI has the greatest risk of capital loss among these stable currencies. Portfolio performance suggests that a basket of currencies eliminates the risk of asset deflation associated with investing in a single stable currency.

Although VaR is widely used to measure risk, its limitation is that it sometimes fails to measure expected losses in the presence of adverse effects. If returns do not follow a normal distribution (a fat tail), VaR may not be the best description of potential capital losses at the time.

A stable currency does not have the same effect as other assets because arbitrage usually forces prices to converge to redeemable value. Now let me introduce to you the second method of measuring risk -- "expected loss value" or "conditional value at risk" (cVaR). CVaR is a measure of how bad things can get in a bad event. Specifically, the potential and expected asset losses can be better understood when conditional losses are taken into account. For the sake of argument, we'll use the same arguments as VaR to calculate the scrolling cVaR.

On the basis of the rolling period method, cVaR looksIt is not quite the same as VaR - usually arbitrage occurs when someone is willing to take on the implied credit risk before the price of a stable currency falls sharply.

By comparing different periods of rolling period, we can see from the figure that Neutral Dollar did not have the highest cVaR value among all stable currencies. When comparing the pie chart of VaR and cVaR, we found that the maximum cVaR value of USDC and DAI was slightly higher than the maximum VaR value, indicating that USDC and DAI had higher expected loss and tail distribution in the trading behavior.

So far, the analysis in this paper has been intended to show that, in terms of intertemporal weight based on multiple time dimensions, portfolio products have advantages over underlying assets in terms of price stability and risk exposure. The weakness of a single stable currency against a basket of currencies makes Neutral Dollar a better unit of account and medium of exchange than other stable currencies.

& have spent Neutral Dollar currency weighting & NBSP;

If the diversification from the portfolio makes the Neutral Dollar better than the basket, how can we prove that our construction process is robust? What's special about this process is that it doesn't take all the elements to make a new token, just a single element. As a result, any activity can lead to an imbalance in the weight of currencies in the basket. One might feel that there are too many causes of imbalances in a basket of currencies to achieve any meaningful benefit from a currency portfolio. To address these issues, we use optimization algorithms to calculate how incremental misweighting will affect volatility. We can also prove that such an event is unlikely because of arbitrage.

The goal of Neutral Dollar is equal volume weighting, which means the ideal Neutral Dollar token is 25% DAI, PAX, USDC, and TUSD. This ratio may deviate when new Neutral Dollar tokens are minted. To investigate the potential impact of this divergence, we assess the volatility of several different stable currency portfolios and compare them in equal amounts. The chart below shows the expected maximum volatility of an ideal portfolio.

The X-axis is the difference between the maximum and minimum weights in the basket, indicating the degree of imbalance. Taking a 5% "max-min" weight difference as an example, the sample composition might be 27.5% DAI, 22.5% PAX, 22.5% TUSD, and 27.5% USDC. Therefore, the incremental volatility of Neutral Dollar will increase by about 10%. The performance of this currency combination is that the basket's volatility increases (in one direction) as the currency weights in the basket move away from the perfect average. We can see from the first table that PAX is 29% more volatile than NUSD, so this also suggests that there must be some meaningful bias in the basket (the difference between the maximum and minimum weights is about 35%) that would make such a basket Neutral Dollar perform worse than the single currency in the basket.

To prove that this more volatile currency combination will not occur, we look at the environment in which arbitrage occurs and how a currency basket can provide a better environment.

In general (ignoring cryptographic currency conversions and other complex policies), arbitrage between exchanges occurs when prices are not the same or when the price of a stable currency deviates from the dollar. The former is harmful, especially when liquidity is more diffuse; The latter is riskier because, as we have seen, pricing can vary widely depending on the perceived market risk.

Neutral Dollar can support a price discovery mechanism, both against the market price of the basket itself and against the prices of the currencies in the basket. Conceptually, liquidity is already concentrated in one product (the first problem is solved), and one can arbitrage between the market price of a basket of currencies and the market price of a single stable currency without having to base it on the implied value generated by the repo activity (thus solving the latter problem).

Our pricing mechanism ensures that the market price of the basket does not deviate from the value of the set, and that arbitrage eliminates any meaningful bias in the weighting of the basket. We simulated the impact of casting and repo on Neutral Dollar to see what the weighting would look like in a rational and incention-based market activity.

We can see from this chart that the weight of the single currency in Neutral Dollar fluctuates around 25%, while the difference between the maximum and minimum weight during this period is only about 2%. Currencies, in particular, will be weighted a bit differently due to the volatility of underlying asset prices, but over time their weights should fluctuate around the expected level. With the popularity of Neutral Dollar, we can expect the weighting mismatch to get smaller relative to collateral. Because of arbitrage, currency weightings are limited to a certain range, so an unbalanced basket is not expected. From these findings, we can conclude that Neutral Dollar is not only robust, but can also form a more dynamic structure to promote liquidity.

& have spent Add new currency to Neutral Dollar 

In the final section we will show how Neutral Dollar can be affected if another currency is added to the basket. It is vital to ensure that our products maintain a competitive edge and increase diversity as the basket of currencies grows. For now, our rebuilding of Neutral Dollar is based on a rigorous process that ensures the overall product is based on lower volatility and risk without sacrificing the benefits of liquidity.

We can assess the feasibility of adding different stable currencies to a Neutral Dollar design by evaluating the different basket components. One of the indicators we assessed was whether the stable currency would have a diversification effect.We can evaluate by pairwise pairingIf a currency has a negative or low correlation with other components, it is likely to be added to the basket. Below is a sample diagram of correlation coefficients to identify which stable currencies behave similarly to others in USDT, USDC, TUSD, PAX, GUSD, and DAI. As long as a stable currency has more attractive properties, it is a potential complement to our future portfolio.

As an example of this assessment, we can see from this chart that DAI has a low correlation with the price movements of other stable currencies. In addition, as the figure shows, DAI is actually more unstable in the tests than fiat notes. However, further internal analysis suggests that the Neutral Dollar basket containing PAX, TUSD, and USDC is actually more volatile than the basket with DAI (in fact, the four-currency basket is 5% less volatile than the three-currency basket).This may be counterintuitive to some, as DAI is less stable, but its weak correlation to other currency market movements suggests a big difference in DAI's exposure. All the characteristics of the assets in the composite basket actually reduce concentrated risk in the portfolio.The finding also illustrates the power of diversification -- bringing together volatile components can actually produce a more attractive portfolio of risk than any single component.

We would also like to mention briefly the governance of increasing money. We can resort to a more open system in the future, but also want to take into account factors other than volatility such as liquidity and volume. In this section, we wanted to make our restructuring approach more transparent in order to give people a sense of our desire to create quality products.

Once we found a high-quality candidate token, we pooled it into Neutral Dollar. New stable currencies added to the basket are added gradually to ensure that they do not cause any problems. Market participants will pledge the new stability COINS to our system until prices reach equilibrium.

The chart below details the expected process of integrating USDT into our product, which is to move the Neutral Dollar from a 4-currency to a 5-currency combination.

Over time, the USDT collateral will gradually tilt toward equal weights, while the weights of other existing collateral will converge to 20 percent. Neutral Dollar provides an additional secondary layer of liquidity and adjusts prices through a more stable mechanism to manage risk while avoiding balance sheet losses. The pricing mechanism is an incentive for traders to maintain the balance between the fair value of a basket of currencies and the underlying components without consuming the backed collateral. The beauty of these structures is that Neutral Dollar can add a supported stable currency to a basket of currencies, creating a better product for consumers and gaining a competitive advantage in the market against potential future stable currencies.

If readers think we've provided enough evidence that Neutral Dollar can be the new stable currency standard based on being a better tool, then so be it. We've shown how Neutral Dollar can beat other stable currencies in many ways, including price and risk. We also point out that consumers may have concerns about imbalances in a basket of currencies, but because of market behaviour such concerns are not a real issue. Finally, we outlined how to add a currency to the Neutral Dollar basket and achieve further improvement. If we can see our products play a role in the blockchain ecosystem and promote growth, we will be truly delighted.

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