# Rho - Dynamic Fixed Yield Product

Rho is * not* a stablecoin. Instead, it has been designed to be a dynamic fixed-yield product that acts as a liquidity reserve for synthetic portfolio theory assets and a backstop for some derivative positions. While these two terms appear to contradict each other, we will explain more below. Per dollar of minted Rho, the funds are positioned into 80% USDC, 10% ISA, 5% eITY3, and 5% eTY3. However, when minting Rho, the ISA used to mint the synthetic yield product backings are deposited into a Reserve Fund for Rho. Therefore, Rho is already over-collateralized by 10% worth of ISA at the time of mint. However, this over-collateralized portion is a synthetic backing at the time of mint. It acts as a long-term hedge and growth multiplier as it is slowly released into the Rho contract to begin appreciating the asset throughout the variable time-locked interval of 1 year. This synthetic backing sets Rho's fixed income portion close to 10% YoY.

Multiple realized volatility stabilizers have been implemented to ensure stable and increasing collateral backing during times of volatility. In addition, we are insuring a growing Reserve balance that will allow for a fixed Reserve allocation of 10% per Minted Rho transaction and a dynamic and scalable Reserve balance based on realized volatility per time-locked period. This further reinforces return characteristics over the long term and helps stabilize the ISA ecosystem.

#### Rho Collateral Optimization

However, to further improve upon our Artificial Theta Value Proportionate to Reserve (ATVR) dynamic, we have introduced not only at mint over-collateralization but have also introduced a protocol balancing metric we’ve created using a cross weighted NCO and HERC optimization model we’ve designed called EERNCO - Equal Entropy Risk Nested Clusters Optimization. EERNCO essentially takes a retractive methodology of each core asset weighting and rebalances the summation of asset liquidity on the protocol using forward volatility modeling consisting a self established feature engineered temporal fusion transformer model to track millions of generative random noise data to simulate a vast number of market randomness points to optimize protocol liquidity. This reduces unforeseen volatility noise and random risk involved across different assets at a portfolio basis. This effectively solves cyclical isolated asset variance, randomness quandaries, and data leakage which construes results.

The protocol liquidity gets rebalanced weekly using our EERNCO methodology to ensure liquidity is best optimized for our asset mints, as well as overall protocol health in terms of treasury volatility. To put this into a more tangible form, below is one of our backtest portfolios utilizing traditional crypto assets used to quantify the methodology. Note, the weightings pictured below are just a singular week snapshot, they get rebalanced weekly and therefore change accordingly.

This backtest example exhibited a 1 year forward Volatility measure of just 116.76% with a 70:30 asset to liquidity reserve value - which is extremely low for crypto. For comparison, over the same period of time, SOL, XRP, BNB exhibited isolated annualized volatility of over 150%. The model balances further optimized with projected CDaR. This is further reduced by the establishing of inverse minted asset hedges proportioned based off the supply and demand of each mintable asset. The break down of conditional drawdown at risk per asset is as follows at a 95% confidence level.

Based off of the long|short ratio of a particular asset, notional value participating in a particular asset rebalance of liquidity through Rho collateral would be as follows:

And a change in interest rates for shorts against the underlying of:

I = Initial notional value of the underlying assets contained in the rebalance

PeV = Peak estimated volatility for the collection of assets

P = Average period of shorts

h = Hedge Rate - which is calculated by taking the trailing change in volatility. While variable, it is initially set at 30% which would be 1.3, representing a 30% buffer for outlier changes in long|short demand for any given asset.

A = Annual base interest rate - 8% for our example.

NOTE: These base level calculations are further constrained with specific IF/THEN statements unique to each asset’s volatility profile to refine absolute value changes in notional value of the underlying liquidity when a EERNCO rebalnce occurs.

#### Backtest Data

Utilizing traditional crypto assets, our EERNCO model's full backtest can be seen below. We ran 500m trials that included randomized entropy levels on real-world data with weekly rebalances utilizing a 14d look back optimization window from 2020-10-15 to 2022-08-15. It outperformed the base equal weight liquidity 18.83x to 12.73x - with a peak high of over 60x return on optimized liquidity and interest rate balancing.

Below is the cumulative drawdown exposure each asset contributed to the protocol portfolio throughout the test period. These assets on their own are incredibly volatile and can put extreme pressure on a protocol if they are not appropriately weighted and rebalanced to ensure adequate short/long incentivization. This also shows how certain assets are more closely correlated than others, leading to cyclical long/short demand. While periods of range trading exist, some random periods of divergence can harm protocol liquidity without modeling.

The next metric is the sustained drawdown periods of each asset over time. AVAX had a more substantial and rapid decline period at the start of the testing window, however it did stabilize 200 days into the period with the rest of the market - with the exception of SOL. SOL during this test had an additional 10 periods of decline while the remainder of the assets had stabilized, which shows the need for the need for entropy risk management. Without it, liquidity likely would have been drained.

The following graph depicts the daily return range which shows the random nature of outlier moves to both the upper and lower bounds of each token.

Finally, below are the cumulative returns each token individually expressed during the testing period - again showing extreme outlier moves with minimal correlations between assets.

#### Example

Using the core portfolio above, let’s say an investor wants to short 3 assets on ethereal. Since we have been using standard tokens, we will run through this example with dollar amounts. However, our synthetic assets utilize ISA and have different volatility profiles when compared to this example, so this is just to offer a bit of clarification. The same logic applies to the long side of assets to incentives short interest - simply take the inverse of the following principles.

The investor intends to short ETH, BTC, and SOL with a notional value worth $15,000 vs the core protocol asset value of $1.5m across the three targeted assets and has a 1 week volatility forecast rating of 20.41%.

Weights of volatility contribution per token can be seen in the figure directly below.

**The required total collateral needed for these three short positions would be:**

**The max collateral this investor would need would be:**

**At an interest rate of:**

This would result in a net interest revenue for the aggregate pool of longs of $58.15 for the 7 day period.

For interest periods above 2 weeks, the protocol portfolio would include this new risk and volatility profile in its weekly rebalance to reflect the incoming volatility skew. For example, if the incoming short interest in the above example was $100,000 instead of $15,000, the total protocol exposure would shift from the balanced starting point in the first figure on page 1, to the portfolio exhibited below.

This increases the annualized volatility of the protocol liquidity by nearly 2x. Therefore, by including the portfolio in a rebalance and taking the weight of the hedge into place by converting it into short delta exposure, the protocol is able to withstand volatility outside the expected move. In the $100,000 example, this would result in a 2 week rate of 0.7527% on a $165,703.09 loan resulting in $494.55 worth of interest for the aggregate pool of longs. The slight change in expected collateral is due to the volatility profile changing based off the historical timeline as things don’t scale linearly. The included hedge rate of 30% is repurposed into additional short exposure at the same ratio of the protocol balanced portfolio. As such, ethereal liquidity is hedged against these outlier moves.

Based off of the structured volatility of each underlying asset, the timeline of the hedge is either structured to coincide with the expiry of the interest period - or set to a variable take profit/stop loss of a multiple of a volatility move outside of the expected. For example, if the move in volatility is expected to be 20% for the period, the 30% hedge with take profit on a 30% to 50% above the expected (20%/50 = 10% + 20% = 30% take profit move) on a non linear scale due to momentum.

**Breaking ATVR Down:**

We have examined traditional market volatility rates to uncover ways to artificially generate similar systems to help deleverage and reduce underlying capital risk exposure to derive a specific type of growth product. However, this does not undermine the tangible counterparts used to generate protocol stability on the USDC underlying portion of Rho through the EERNCO methodology but instead lends to Rho’s underlying risk factions.

To begin to break this down, we have looked at a 1.3 standard deviation move in the market and the effects that it would have on traditional derivative products as it closely mirrors the 20% capital exposure risk on Rho itself. Moves within the market have a roughly 80.6% chance of staying within the 1.3 range. However, the same cannot be said for crypto, where many orders of magnitude greater moves are not uncommon. However, the more critical piece missing in crypto is controlling risk beyond just position sizing. For example, you have various Greeks in traditional investing that can help you manage a position and its inherent risk to the trade itself and your overall portfolio. As such, we have examined various avenues of replicating specific derivative-based tools to help neutralize volatility and stablize or increase the floor price of Rho and improve both the Reserve and Treasury balances.

Three such instruments are Theta decay, DvegaDtheta (Veta), and the overall correlation to the Treasury as a whole (Beta). Now the purpose of this article is not to decipher these terms, as you can do that through research on your own time. But in summary, time, realized volatility, and correlation all play a role in the price action of Rho – in retrospect to platform-based inflation, to ensure a stable or upwards trending price.

**To utilize all of these metrics, the following equation was derived:**

**R =**Rho Units Minted**C =**Collateral Weight in USDC Percentage**e =**Percentage Weight in eTY3**ei =**Percentage Weight in eITY3**i =**Percentage Weight in ISA**B =**Total ISA Emission Units Per Period**A =**Starting ISA nEmissions Balance**Ii =**ISA Starting Price Per Period**If =**ISA Final Price Per Period (If becomes the next cycle Ii Value)

Now, this was left non-simplified to isolate each piece separately and experiment with it individually to comprehend the specific weighting in the overall formula. It is also a “dirty” calculation undergoing continual revision to factor additional data points and optimize emission usage while also introducing other fail-safes beyond the Reserve and fee manipulation.

To summarize these separate theories, the acronym *ATVR* was created, which stands for *Artificial Theta Value with respect to Reserve.* **At its core,** **we are prioritizing growth and stability in regards to the minimum amount of total emissions relative to realized volatility levels needed to maintain a positive correlation concerning platform-based inflation and available liquid POL on the protocol to backstop assets and derivatives.**

This effect is greatly amplified by the introduction of a time-lock on mints/redeems as not only does it allow for realized volatility to converge towards zero, but it also allows for a more powerful Theta effect which bolsters the underlying contract and, therefore, Rho's value. This "Theta" value also allows for the rebalance strategies to begin realizing their returns, which will make up 42% of the return percentage for Rho year over year, as can be seen below. Pairing this with a dynamically adjusting rate that funnels consistently and predictably into the Reserve further solidifies its growth trajectory.

This Artificial Theta Value is proportionate to ISA's trailing realized volatility rate — i.e., when the price decreases, this implies volatility is rising. Therefore the variable emission rate would increase proportionally to the decline. This keeps Rho more stable during these periods and allows for continual liquidity optimization. However, if ISA is stable, this additional ATV would begin appreciating the Rho proportionately to the price moves of ISA. This structure, paired with adding a time lock on redeems, would decrease the inherent 10% risk due to ISA exposure — despite the fact Rho is already over-collateralized at the time of mint.

**By default, Rho will have very little downside pressure for the first 15 months as it is over collateralized at the time of mint, and due to the platform based growth measures that have been implemented - any initial downwards ISA pressure will have an effect lasting less than one month, thus ensuring a stay of value near the mint value.** That being said, should volatility arise, another benefit is the ability to apply a multiplier to the overall formula. This, in *theory*, would allow the time-to-base stability to be shorter on substantial collapses — potentially up to two-three times as quickly.

Furthermore, the dynamic ATV, over time, increases its correspondence to the platform Beta. Therefore, it has an inherent correlation to the Treasury balance on a more permanent basis than relying solely on a predetermined floor price. At the same time, Rho pulls a secondary correlation to the changes in notional value of longs|shorts on the protocol for all assets, thus diversifying risk across multiple market types. These three items, paired with the time locking of certain Rho redemptions, prohibit arbitrage potentials but replicate multiple important stability mechanisms found in traditional marketplaces–essentially causing ethere.al to back Rho and vice versa. It also stabilizes the risk-to-return profile to match more closely with even something as “unexotic” as a SPY position.

**Rho Return Metrics on Liquidity Provisions:**

10% over-collateralized at the mint provides a fixed return from the Reserve per period.

5-20% dynamic emission rate allocation per period of realized volatility. Increasing price means lower realized volatility - which means the ISA in the Rho contract increases in value, therefore requiring fewer emission allocations to reach return objectives. Conversely, a decreasing price means more realized volatility - which equates to a decreasing ISA value that dictates additional emission allocations to stabilize and lead to an increasing price floor for Rho. This is similar to how the Treasury supports the price of ISA through buybacks at a dynamic price floor using 75% of the platform swap fees collected. To further bolster the Reserve and return dynamic, the Rho Reserve receives 25% of the 0.3% swap fee on the platform.

15-20% on the 80% USDC backing through EERNCO liquidity management and long|short incentivization.

1-4% through fee-based collateral additions to the Rho Reserve.

The above return estimates increase the longer Rho is time-locked as this is a multiple-based system that achieves the highest level of base growth around year three. You can view the baseline model of month-over-month performance in the chart below.

Our estimated YoY return for Rho for period 1 is 40-45%. However, when the platform reaches its natural deflationary stage after 1.8 years, performance is expected to increase sizably as ISA unit counts become scarcer. By that point, a host of additional synthetic products will be available to mint using ISA, further increasing the demand. In addition, long-term liquidity hedges will begin to achieve their maximum decay rate, increasing the return for that period. This corresponds with additional hedge positions starting to reach their prime rate, thus continuing the cycle YoY as various expiry dates unroll within the mint cycles. Finally, however, the momentum will begin to reach a critical point of expansion, given that the increased capital reserves would have since allowed for extensive diversification. All of these factors build off one another, and as such, transform ethere.al into an investment and hedge conglomeration that begins to transform investors into a synthetic type of protocol share owner. Once we reach this point, the possibilities for increased technical development, asset types, investment vehicles, and more increase tenfold.

**How to Mint Rho**

Rho is minted using USDC under the Rho tab on ethere.al. No additional tokens are required as the contract will automatically make all divisions. In addition, upon minting, Rho will be automatically time-locked for 15 months. This ensures that the total investable capital is available for bridging. Currently, bridge allotments are made every quarter, which means if you mint January 1 - your Rho allocation will be appreciated based on platform-specific mechanisms. However, on March 31, period 1 of Rho mintage will be completed, at which point the USDC value would be used to begin backstoping and balancing mints and option liquidity which would begin the second yield cycle. Congruently, period 2 for RHO mintage would start as period one closes and last for another quarter. As the total minted value of Rho increases, we will be able to shrink the periods from 1 quarter to possibly one month, which will allow for additional mint and option liquidity and faster turn-over rates.

Nine months after the conclusion of your mint period, you will be able to choose to either compound your current stake for another 12 months if you are satisfied with the current and future predicted return metrics, request redemption for your yields generated, or redeem the total value of your position. You will have three months to decide your action. However, once those three months conclude, the contract will automatically reinvest your stake for another 12 months if you have taken no action.

At the time of mint, you will receive a receipt called sRHO. This receipt is what proves your ownership and also allows you to leverage your Rho stake across the platform as a whole by using it as collateral for both options and short positions. You will be able to redeem sRHO for ISA before your designated expiry date if you wish.

The EERNCO model is testable through our API. Please request an authentication key to examine.

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