# Yield Calculation

## Understand Yield in Stella

In Stella, the definition of **"Yield"** is the **remaining value** of the position in US dollars at the time of closing the position after repaying the debts and returning the leveragoors’ initial input.

$$
\text{Yield} = \text{PositionValue}-\text{BorrowValue}-\text{InputValue}
$$

Where the value of each part is calculated as follows

$$
\text{PositionValue} = \text{LPTokenAmount} \cdot \text{Price}*{\text{LPToken}} + \text{RewardTokenAmount} \cdot \text{Price}*{\text{RewardToken}}
$$

$$
\text{BorrowValue} = \text{BorrowAmount} \cdot \text{Price}\_{\text{BorrowToken}}
$$

$$
\text{InputValue} = \text{InputAmount} \cdot \text{Price}\_{\text{InputToken}}
$$

### Annualized Yield

In Stella, we need to calculate the annualized yield in order to determine how much profit should be shared between the lenders and leveragoors

$$
\text{Yield}*{\text{APR}} = \frac{\text{Yield}}{(\text{BorrowValue}+\text{InputValue})} \cdot \frac{365\cdot24\cdot60\cdot60}{(\text{ts}*{\text{close}}-\text{ts}\_{\text{open}})}
$$

> $$\text{ts}\_{\text{close}}$$ = timestamp at the the time of closing the position
>
> $$\text{ts}\_{\text{open}}$$ = timestamp at the time where the position was opened

### Example

<figure><img src="/files/Nj6CL0jDl0ipaBKwBry6" alt=""><figcaption></figcaption></figure>

* Alice input 1000 USDC and open a position with leverage 4x on Uniswap V3 ETH/USDC 0.3% strategy by borrowing 2 ETH and 1000 USDC where ETH\@1000
* As time passed for **exactly 30 days**, Alice's position accrue the trading fee and her current position composition is 2.1 ETH + 2100 USDC where ETH price is still the same @1000
* Alice closes the position getting the yield of **$200 over 30 days**
* So, Alice's position yield is

&#x20;                $$\textsf{= }  (\textsf{2.1} \cdot \textsf{$1000} + \textsf{$2100}) - (\textsf{2} \cdot \textsf{$1000} + \textsf{$1000}) - (\textsf{$1000}) \ \textsf{= } \textsf{$4200} - \textsf{$3000} - \textsf{$1000} \ \textsf{= } \textsf{$200}$$

* **Yield = $200**
* **Annualized Yield** = **60.83%**


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