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feat: add docs for APR calculation (#232)
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* feat: add staking APR

* feat: try making equations appear

* feat: change to image

* feat: fix explanation
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mattverse authored Nov 21, 2023
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41 changes: 41 additions & 0 deletions docs/overview/integrate/apr.md
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sidebar_position: 11
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# APR Calculation

## Introduction
APR for each pools is a metric that indicates the expected annualized return on investment for liquidity providers. APRs are calculated differently for CL pools and normal pools due to their distinct operational mechanisms.

## Concentrated Liquidity Pools

### Calculation:
- **APR for CL Pools**:
![](../../assets/apr-cl.png)
Where:
- **Spread Reward per Unit Liquidity**: This is the reward earned from the spread for providing liquidity, expressed per unit.
- **Incentive Reward per Unit Liquidity**: This is any additional incentive reward for providing liquidity, also expressed per unit.
- **Base Price**: The standardized value of one unit of liquidity in the pool, used to convert the reward values into a comparable base.
- **Seconds in a Year**: Represents the total number of seconds in a year, used for annualizing the return. It's calculated as \( 365.25 \times 24 \times 60 \times 60 \) to account for leap years.
- **Calculation Time Duration**: The duration in seconds over which the rewards were calculated

## CFMM Liquidity Pools(Balancer pools, Stableswap Pools)

1. **Standard APR Calculation** (for 1 day, 7 days, and 14 days):
- The APR is calculated for each time frame using the formula:
![](../../assets/apr-normal.png)
- Where:
- `Distribured Amount_timeframe` is the sum of distributed rewards for the time frame (1 day, 7 days, or 14 days).
- `Exponent` is a factor related to the coin denomination.
- `Liquidity` is the total liquidity in USD for the pool, adjusted by the percentage bonded (if applicable).
- `Coin Price` is the current price of the coin.
- The multiplier \(36500\) annualizes the rate.

2. **Superfluid APR Calculation** (if applicable):
- The Superfluid APR is calculated additionally for pools where it's relevant, using the formula:
![](../../assets/apr-superfluid.png)
- Where:
- \(\text{Staking APR}\) is the APR from staking.
- `Superfluid Percentage` is the percentage of the pool that is superfluid.
- `Superfluid Risk Factor` is a risk adjustment factor.
- `APR_14d` is the 14-day APR calculated as above.

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