# Ensuring Fairness with Time-Weighted Average Balance (TWAB)

When it comes to generating yield, how the yield is calculated is important for token holders to understand. AQTIS employs something called Time-Weighted Average Balance (TWAB).

This idea takes into account the relative inflows and outflows you make to your LST over time to ensure an accurate picture can be created of how much yield your tokens accrue.

TWAB is a common mechanism used throughout the DeFi world. Below we go into more detail about assumptions and how it is typically calculated.

Assumptions for User A buying qETH, and the TWAB of that investment.

Fixed APY: 10%

Initial token purchase: 100 ETH

Additional tokens bought after 20 days: 30 ETH

Total days held: 30

Price of 1 ETH at the time of purchase: $1650

To calculate the TWAB of the above assumptions, we would follow these steps:

Calculate Daily Interest Rate: The daily interest rate can be calculated by taking the annual rate and dividing it by days in the year, 365. The daily interest rate for a 10% APY LST would be: 10 ÷ 365 ≈ 0.0274%

The daily interest rate is 0.0274% based on the assumptions above.

Calculate Time-Weighted Average Balance (TWAB): The TWAB is calculated by taking the average balance over the time period, weighted by the number of days each balance was held. In this instance:

For the first 20 days, User A has 100 ETH.

For the next 10 days, Bob has 100 + 30 = 130 ETH

The TWAB equation would look like this: ((100 × 20) + (130 × 10)) ÷ 30 TWAB = (2000 + 1300) ÷ 30 = 3300 ÷ 30 = 110 ETH

Calculate Rewards: Now that we have the TWAB for User A, we can calculate the yield rewards over the 30 days qETH was held. To do this, we would do the following:

TWAB × Daily Interest Rate × 30 days = 110 × 0.000274 × 30 days ≈ 0.9036 ETH

To calculate the dollar value of the rewards, simply multiply the amount of ETH by the current market price. In this example, ETH is worth $1,650 USD. Multiplying 0.9036 ETH by 1,650 would lead to a dollar reward of $1490.94.

In summary, User A would earn approximately 0.9036 ETH as a reward over the 30-day period with a 10% fixed APY, using the Time-Weighted Average Balance method.

The dollar value of this reward would be approximately $1490.94 USD.

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