Visualizing Metastability

Visualizing Metastability for Neutral Dollar (NUSD)

Key Takeaways

  • Neutral Dollar is a basket of stablecoins which inherits attractive properties due to its metastable design. Our aggregate product allows for portfolio diversification benefits and the construction of an efficient rebalancing mechanism to closely track collateralized stablecoins. We can make generalized assessments about its superiority after measuring its simulated behavior over multiple time periods.
  • Neutral Dollar can track the U.S. Dollar and generally has less price movements, proving its worthiness as a better stablecoin than any underlying constituent.
  • Potential downside risk is mitigated due to diversification, indicating that a Neutral Dollar can serve as a hedge against idiosyncratic capital loss and a solution for stablecoin portfolio management.
  • In order for Neutral Dollar to become more volatile than any stablecoin alternative, a great deal of imbalance would need to occur, the probability of which is unlikely. This is due to market activity forcing a balanced composition in the open-end structure.
  • By diversifying exposure and introducing new stablecoins into the Neutral Dollar basket, we’re able to be competitive in the marketplace. The process of coin additions does not detract value from the basket itself.

Analysis, Interpretation, and Summaries

At Neutral, we are designing an aggregate basket of stablecoins which has a more subdued risk profile than any single stablecoin project today, and can expect this to hold for the foreseeable future. Financial theory highlights that an aggregate product can have lower volatility than any individual constituent, and we can showcase this visually in the context of Neutral Dollar. We can assess the stability of our token in comparison to underlying stablecoins across various metrics surrounding price and risk.

Furthermore, our innovative product construction is designed to be liquidity- and exchange- neutral, meaning it is possible to create new Neutral Dollar tokens by collateralizing supported stablecoins. While Neutral Dollar is equal-quantity weighted, trading-based activity can drive slight imbalances due to market behavior. To address potential concerns, we utilized optimization techniques to identify weighting compositions of the underlying assets that would result in higher volatility of the basket. Then, rigorous simulation was conducted to see how the basket effectively balances in response to market pricing. Lastly, we blended these analyses to account for the addition of another stablecoin to the basket, taking into the account how it would affect the behavior of the newly constituted Neutral Dollar. Our findings across many dimensions show how Neutral Dollar is a superior and better digital dollar to use for any stablecoin-related purposes.

To start, the composition of Neutral Dollar (NUSD) will initially comprise four stablecoins: USDC, PAX, TUSD, and DAI. The proposition of these stablecoins imply that each is valued at 1 U.S. Dollar. However, the price of each stablecoin won’t be reflective of this: trading activity can force deviations from this reference. There are idiosyncrasies such as credit risk, inflows/outflows, redemption qualities, and counterparty behavior that distinguish stablecoins from one another. By combining these stablecoins together, we reduce the overall exposure to these idiosyncrasies and can produce a more stable token that fluctuates more closely to the intended value.

Shown below are the historical prices of the underlying constituents along with Neutral Dollar. We expect these stablecoin prices to hover around 1 U.S. Dollar.

Based on this chart, we see that these stablecoins are actually not priced at exactly $1. In fact, these stablecoins can trade from to $.98 to $1.08. The prices will tend to roughly float around $1, but fluctuate depending on the market’s perception of the quality of the specific stablecoins. When we want to identify which stablecoin would be the best, we could visually try to interpret which stablecoin would have the less movements. Understandably, it’s hard to tell exactly which stablecoin is better when all of them are overlaid in a graph, so we generate analytics to assess the stability of each within this time period. The first measure we can interpret this price behavior with is price volatility, which is a general measure of the movement of asset prices in a period of time. Additionally for our purposes, we also calculate the volatility of each stablecoin relative to Neutral Dollar, to demonstrate the power of a metastable basket.

We can see from this table that the PAX has 29% more volatility than NUSD, the second most robust stablecoin in this time period. Similarly, we can also interpret that DAI possesses more than twice the volatility of our stablecoin. Based on this table, we can conclude that Neutral Dollar is clearly a more compelling product than the rest.

Now, we would be doing a huge disservice to stop our analyses here, as it is quite incomplete. First, the time period during which all underlying stablecoin-price data was available in October 2018. At the moment of this writing, not even 6 months of historical data can be used for testing which can make our claim less meaningful if we don’t know if our statements can hold over time. Second, substantiated evidence in finance cannot be based on a single time period, but must be assessed over several. This is the same concept as finding out a strategy that would do well in crypto markets in 2017 vs. applying the same strategy in 2018 — there will be wildly different results which could potentially multiply your wealth or obliterate it. Given the scarcity in available historical data, we need a way to assess if Neutral Dollar can be robust throughout time. Fortunately, we can do this by calculating metrics on a rolling period.

A rolling period is a method to eliminate biases towards any specific range of time. It’s a more methodical way to assess whether future performance is reliable on past performance or not. While there are still other associated risks when implementing this (just as any approach will never ‘guarantee’ a certain return), we can effectively remove this time bias. In the first graph and table, we only sampled a single time period and made a claim that Neutral Dollar is superior. Now for rolling periods, we sample every 5 minutes a 12-hour window of historical data — effectively creating over 30,000 time periods to assess against. The findings from this experiment setup can better reinforce or dispute our statements.

In addition, we introduce two metrics we can evaluate along with volatility in order to get a better sense of overall price stability:

  • Deviation: as in, how much that stablecoin strayed away from the reference of 1 U.S. Dollar.
  • Fluctuation: meaning the total movement of price.

We evaluated across these rolling time periods which stablecoin had the maximum and minimum statistic as these measures all consider both upwards and downwards price directions.

The left chart shows Neutral Dollar rarely has the most deviation from one dollar — only happening in 0.3% of all the time periods we evaluated. The next best stablecoin is PAX, having maximum deviation occurring 2.5% of the time. DAI often has the most deviation as 40% of the time it is the least stable token within the basket. On the right pie chart, Neutral Dollar shines in that majority of the time the aggregate basket has the lowest deviation value from 1 U.S. Dollar. Interestingly, DAI has the minimum amount of deviation 14.2% of the time, possibly indicating that there are time periods where DAI is very stable and time periods where DAI is very volatile, indicating that it has different exposure risks than the fiat-backed stablecoins.

A very similar story can be told here: Neutral Dollar actually never had the most fluctuation in a 12-hour window, and 39.8% of the time had the least amount of fluctuations.

When assessing volatility, Neutral Dollar never had the maximum volatility, and it had the lowest volatility of any underlying stablecoin 44.1% of the time.

To conclude our findings when it comes to price stability, we see that Neutral Dollar is very robust across the multiple time periods we tested in comparison to other stablecoins. This gives us assurance that Neutral Dollar is stable in terms of price, resulting in a better stablecoin which is both less volatile and more closely references a U.S. dollar value than any individual stablecoin can.

We can further extend our analyses even more by focusing on metrics that can assuage users, particularly downside movements. All the metrics prior showcased how Neutral Dollar is more stable in terms of price, considering movements both up and down. When we want to detail what potential risks are, we are far more concerned about downside movements that associate with a loss of capital. Selected are two metrics to analyze this potential, the first being Value at Risk (VaR). VaR is a method to contextualize with a certain level of confidence, what could be the potential loss in a given time period. There are many methods to evaluate the distribution of losses by estimating the probability density function, but the general idea is similar in that VaR always looks at potential drawdowns in one’s holdings.

Source: Wikipedia

For our experiment, we computed a historical daily 95% VaR metric across the available data we have. Not much assessment can be made from the graph below because the overlaid data can get messy, though we can see brief moments where the potential capital loss on these stablecoins can range between 2 and 6 cents.

We can also conduct a similar analysis of using rolling periods that we applied for the price metrics. Because this metric is focused on the left tail distribution of returns, we are most concerned about the most potential loss amongst each stablecoin. Below is a pie chart of the amount of times each stablecoin had the largest value at risk, on average, across the windows we sampled.

Across the time periods we sampled, it seemed that Neutral Dollar never would have the largest tail risk. PAX would be the next most assuring stablecoin, having the maximum 95% VaR 9.9% of the time. DAI poses the most risk for capital loss in this basket, which is supported by the line graph above with its periodic spikes. The power of aggregation shows that a basket can remove some possibility of large drawdowns in your portfolio based on individual stablecoin risk.

A limitation to VaR is that while it is widely adopted as a proper risk measure, at times VaR may not appropriately quantify the expected loss during an adverse effect. Mainly if the distribution of returns are not normal (fat-tailed), then VaR may not be the best description of the potential capital loss at the time.

Outlining a complication with VaR. Sub-additivity is not accounted for. Source

Stablecoins tend not to follow behaviors similar to other assets, mainly because arbitrage will typically force prices to converge towards a redeemable value. We now introduce the second risk measure, which is expected shortfall, or conditional Value at Risk (cVaR). cVaR is a measure that describes how bad things could get in such an adverse event. Specifically, the conditional loss is considered so that there’s a more appropriate understanding of what could be the potential, expected drawdown. For our purposes, we use the same parameters as we did with VaR to compute a rolling cVaR calculation.

On a rolling basis, cVaR looks to be quite similar to VaR — typically, arbitrage will occur before a stablecoin price drops too far by someone willing to bear the implied credit risk.

Comparing across rolling time periods, we see that Neutral Dollar never has the highest cVaR metric across all the stablecoins. When looking at the pie graph between VaR and cVaR, USDC and DAI increase their maximum counts a bit more, indicating a larger expected loss and larger distribution tails in their trading behavior.

The intention of the analysis so far is to show how an aggregate product can be superior in price stability and risk exposure when compared to underlying assets across many measures of time. The idiosyncrasies of individual constituents are mitigated in a basket, showcasing how Neutral Dollar serves as a better unit of account and medium of exchange than any other stablecoin.

If Neutral Dollar is better than the underlying due to diversification properties from aggregation, how can we show that our construction process is robust? Our process is unique in that creation of a new token does not require all the components, but only requires a single constituent. Thus, any activity can drive imbalance to the weighting of the basket. One might believe that if there is too much imbalance in the basket, then aggregation may fail to procure any meaningful benefits. To address these concerns we compute, using optimization algorithms, how incremental misweightings would affect volatility. We can also show that such events are also very unlikely due to arbitrage behavior.

The intention for Neutral Dollar is to be equal-quantity weighted, which means an ideal Neutral Dollar token consists of 25% DAI, PAX, USDC, and TUSD each. When new Neutral Dollar tokens are minted, this weighting can deviate. To look at these potential effects, we evaluated several different composition weightings of Neutral Dollar and the volatility compared to an equal basket. Below are the worst volatiles you can expect relative to an ideal composition.

On the x-axis are the max-min weights, which highlights the degree of imbalance. Starting at a 5% difference, a sample composition might be 27.5% DAI, 22.5% PAX, 22.5% TUSD and 27.5% USDC. The incremental volatility of Neutral Dollar as a result would increase roughly 10%. The behavior of the basket is that the volatility monotonically increases as the misweighting increases. From the first table we showed that the PAX has 29% more volatility than NUSD, so this also shows that there has to be some meaningful deviation in the basket (roughly between ~35% of a difference between max and min weights) for Neutral Dollar to be worse than an underlying stablecoin in its current composition.

To show that the higher-volatility basket compositions are unlikely to happen, we need to provide context about arbitrage and how a basket can provide a more meaningful environment. Typically (ignoring fiat off-ramping or other complex strategies), arbitrage on stablecoins can happen across exchanges where prices are different or when prices deviate from $1. The former is hindered, especially due to fragmented pools of liquidity. The latter is more risky because, as we have seen, pricing can differ greatly due to perceived market risks. Neutral Dollar allows for price discovery mechanisms, both on the fair market price of the basket, as well as the underlying constituents. Conceptually, liquidity becomes pooled since it is now combined under one product (addressing the first) and arbitrage can take place between the fair market price of the basket to the fair price of an individual stablecoin, rather than an implied value based on redeemability (addressing the second).

Our pricing mechanism ensures that the fair price of the basket doesn’t deviate from the aggregate value, and that arbitrage should remove any meaningful deviation of weights in the basket. We simulated the effect of creation and redemptions on Neutral Dollar to see what the weights would look like based on rational and incentivized market activity.

From this chart, we see that weights of individual constituents to Neutral Dollar should float around 25%, with the max-min weight difference only being roughly 2% across this time frame. There will be some deviation especially due to price volatility of the underlying, but over time should float around their intended weightings. As Neutral Dollar is popularized, we can expect relative misweightings to become smaller in proportion to the collateral. Because the weights should be range-bound due to arbitrage, we can expect imbalanced baskets to be highly unlikely. From these findings, we can conclude that Neutral Dollar is not only robust but can also form a more dynamic structure to foster liquidity.

The last aspect we want to cover demonstrates how Neutral Dollar might be affected if there were another coin added to the basket. It’s essential our product can maintain competitive edge and more stablecoins in our basket equals increased diversification. For now, reconstitution of our Neutral Dollar is based on a rigorous process which ensures the aggregate product is based on a lower volatility and risk profile without sacrificing the benefits of liquidity.

We can assess viable stablecoin candidates to be added into Neutral Dollar design by evaluating different basket compositions. One of the metrics we evaluate on is whether the diversification effect can be procured. We can ascertain this using pairwise correlations — a coin can be a likely candidate to be added to the basket if it has negative or low correlation relative to other constituents. Below is a sample correlation coefficient map that identifies which stablecoins behave similarly to others amongst USDT, USDC, TUSD, PAX, GUSD, and DAI. Some of these stablecoins may be potential additions to our basket in the future so long as they procure more attractive properties.

As an example of this evaluation, we see on this chart that DAI has low correlation to the price movements of the rest of the stablecoins. In addition, we have shown above that DAI actually is less stable than fiat-backed stablecoins in our testing. However, further internal analysis has shown that a Neutral Dollar basket consisting of PAX, TUSD, USDC actually has more volatility than a 4-coin basket with DAI included (in fact, a 5% increase based on our results). This may seem counterintuitive to some as DAI has less stability, but the correlation of market movements on DAI is weak which indicates that exposure risks on DAI are much different. Combining all these idiosyncrasies together across supported assets actually lowers these concentrated risks in the context of a portfolio. This finding also highlights the power of diversification — aggregating together volatile constituents can actually procure an attractive risk profile that is better than any standalone component.

We also wanted to mention briefly the governance regarding coin additions. Down the road we could resort to a more open system, but we also want to be considerate of other factors beyond volatility such as liquidity and volume. More on this to come as we want to be transparent on our reconstitution methodology for people to sense our desire to create quality products.

Once we have figured out a quality candidate token, we need to integrate it into the Neutral Dollar. Stablecoin additions into our basket will take place over a period of time, and are expected not to cause any issues. The high-level rationale is that our pricing mechanism will favor underrepresented weightings of stablecoins. Market participants will collateralize the new stablecoin into our system until prices reach to equilibrium.

Below is a graph detailing an event where we want to include USDT into our product — turning Neutral Dollar from a 4-coin to a 5-coin basket.

Over time, the USDT collateral will ramp towards equal quantity weighting, and the other existing collateral will converge as well to 20% weights. Neutral Dollar provides an additional, secondary liquidity layer and allows for a more robust process to skew/lean pricing for managing asset exposures while simultaneously avoiding balance loss.The pricing mechanism serves as an incentive for traders to maintain equilibrium between the fair value basket and the underlying constituents without draining the supported collateral. The beauty of these constructs allow Neutral Dollar to add newly supported stablecoins into the basket to create better products for consumers and obtain competitive advantages in the market against any upcoming stablecoins in the future.

We hope that we have shown enough evidence to demonstrate that Neutral Dollar can be a new stablecoin standard based on qualities of being a better instrument. We showcased how Neutral Dollar beats out other stablecoins across many dimensions across price and risk. We also addressed that a large misweighting in the basket is required for it to be a concern, and how this is not expected to be a problem due to market behavior. Lastly, we outlined how a coin would be added in the Neutral Dollar basket to improve it even further. We’re quite excited to see our product play out and promote growth in the crypto ecosystem.

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