AARR Metrics

The AARR (Average Annualized Reflection Rate) metrics are a key feature of the EternETH Reflect protocol, providing insights into the token's reward performance over different time periods. This document explains how AARR is calculated, the formulas used, and the underlying logic.

What is AARR?​

AARR stands for Average Annualized Reflection Rate. It represents the average rate of return for token holders in the form of Ethereum reflections, expressed as an annualized percentage.

AARR Time Periods​

The dashboard displays three AARR metrics:

1. AARR7: 7-day average

2. AARR30: 30-day average

3. AARR365: 365-day average

Calculation Process​

The AARR calculation involves several steps and uses data from token transfers and reflections.

Step 1: Daily Data Collection​

For each day, the following data is collected:

• Minted tokens

• Burnt tokens

• Circulating supply

Step 2: Daily Growth Calculation​

For each day, the daily growth rate is calculated:

dailyGrowth = fee / circulation

Where:
fee = (adjustedMinted + burnt) * 0.1
adjustedMinted = minted / 0.88

Step 3: Annualized Growth Calculation​

The daily growth is then annualized:

annualizedGrowth = (1 + dailyGrowth)^365 - 1

Step 4: AARR Calculation​

The AARR for each time period is calculated by taking the average of the annualized growth rates for the respective number of days:

AARR7 = average(annualizedGrowth) for the last 7 days
AARR30 = average(annualizedGrowth) for the last 30 days
AARR365 = average(annualizedGrowth) for the last 365 days

Detailed Formula Breakdown​

1. Adjusted Minted Calculation:

   adjustedMinted = minted / 0.88

   This adjustment accounts for the 12% fee on transactions.

2. Total Activity Calculation:

   totalActivity = adjustedMinted + burnt

3. Fee Calculation:

   fee = totalActivity * 0.1

   10% of the total activity is taken as a fee.

4. Circulation Update:

   circulation = previousDayCirculation + minted - burnt

5. Daily Growth Rate:

   dailyGrowth = fee / circulation

6. Annualized Growth Rate:

   annualizedGrowth = (1 + dailyGrowth)^365 - 1

7. AARR Calculation:

   AARR = average(annualizedGrowth) for the specified period

Logic Behind AARR​

The AARR metrics provide a way to measure the performance of the reflection mechanism over different time periods. By annualizing the daily growth rates, it allows for easy comparison and understanding of the token's reward potential.

• AARR7 gives a very recent snapshot of performance, useful for understanding short-term trends.

• AARR30 provides a medium-term view, smoothing out short-term fluctuations.

• AARR365 offers a long-term perspective on the token's performance, giving the most stable and comprehensive view.

These metrics help token holders understand the potential returns from holding EternETH tokens and how those returns may vary over time based on trading volume and other factors affecting the reflection mechanism.

Considerations​

• AARR is based on historical data and does not guarantee future performance.

• The metrics are sensitive to trading volume and token supply changes.

• Extreme market conditions or large one-time events can significantly impact these metrics, especially the shorter-term ones (AARR7 and AARR30).