# Calculation
This document contains the formulas used to calculate the data like APY, Volume, and TVL for Napier Protocols.
### Annual Percentage Yield (APY)
The annual percentage yield (APY) is the interest rate or yield earned on your investment in one year, including compounding interest. A higher APY is better as your return will be higher.
#### Net APY[](https://docs.pendle.finance/ProtocolMechanics/PendleMarketAPYCalculation#underlying-apy)
**Net APY** is the overall annual percentage yield after considering all yields and any other rewards on yield-bearing tokens.
$$
\text{Net APY} = \text{Interest APY} + \text{Reward APR}
$$
Net APY comes in two part, below are how to calculate each of them.
#### **Interest APY**
**Interest APY** represents the 7-day moving average yield rate of the underlying asset. This approach allows a more accurate indication of the underlying yield over a period of time, which can help traders to better estimate the Future Average Interest APY.
$$
\text{Interest APY} = \left(1 + \text{7-day yield}\right)^{365/7} - 1
$$
#### Reward APR
**Reward APR** is the estimation of the current APR for the **rewards** of the underlying assets. Rewards = returns in the reward token, and it’s not auto-compounding by default.
$$
\text{Reward APR} = \frac{\text{Annualized rewards (in underlying units)}}{\text{Current asset value}}
$$
#### **Implied APY**
**Implied APY** is the market consensus of the future APY of an asset. This value is calculated based on the ratio of the price of YT to PT and the formula is shown below. When used in conjunction with the Underlying APY, Implied APY can be used to establish the relative valuation of an asset such as YT and PT at their current price, and help traders determine their trading strategies.
The value of Implied Yield is numerically equivalent to the to Fixed Yield APY.
$$
\text{Implied APY}
\= \Bigl(1 + \frac{\text{YT Price}}{\text{PT Price}}\Bigr)^{\frac{365}{\text{Days to Expiry}}} ;-; 1
$$
**PT Price** is how much PT you can get from 1 underlying asset.
$$
\text{PT Price} = \frac{\text{PT Amount}}{\text{Underlying Amount}}
$$
**YT Price** is derived from PT Price.
$$
\text{YT Price} = 1 - \text{PT Price}
$$
#### **Effective Implied APY**
**Effective Implied APY** is the APY based on the actual rate that the user used to swap.
$$
\text{ptExchangeRate}
\= 1 + \frac{\text{ptAmount}}{\text{ytAmount}}
$$
$$
\text{Effective Implied APY}
\= ptExchangeRate^{\frac{365}{\text{Days to Expiry}}} ;-; 1
$$
#### **Fixed APY**
**Fixed APY** is the guaranteed yield you will receive by holding PT. This value is numerically equivalent to the Implied APY.
$$
\text{Fixed APY} \equiv \text{Implied APY}
$$
#### **Effective Fixed APY**
**Effective Fixed APY** is the Fixed APY based on the actual rate that the user used to swap.
$$
\text{Effective Fixed APY} \equiv \text{Effective Implied APY}
$$
#### Fixed Maturity Profit
**Fixed Maturity Profit** is the profit at maturity, expressed in the underlying token.
$$
\text{Fixed Maturity Yield} = \text{PT Received} - \text{Input Amount (base asset)}
$$
#### **Long (Yield)APY**
**Long (Yield) APY** is the approximated return (annualized) from buying YT at the current price, assuming underlying APY remains constant at its current value. This value can be negative, meaning that the total value of all the future yield based on the Underlying APY will be less than the cost of buying YT.
**Interest Returns:**\
The returns from interest for holding 1 YT until expiry:
$$
\text{interestReturns} = \left(1 + \text{underlyingInterestApy}\right)^{\text{yearsToExpiry}} - 1
$$
**Rewards Returns:**\
The returns from rewards (assumed linear over time):
$$
\text{rewardsReturns} = \text{underlyingRewardApy} \times \text{yearsToExpiry}
$$
**Total YT Returns:**\
The sum of interest and rewards returns:
$$
\text{ytReturns} = \text{interestReturns} + \text{rewardsReturns}
$$
**YT Returns After Fee:**
We have 2 type of performance fees: \
Performance Fee Before Maturity and Performance Fee After Maturity\
\
In this example we just assume all fees already calculated become X % on the YT Yield \
Let say X is 10 %
$$
\text{ytReturnsAfterFee} = \text{ytReturns} \times 0.9
$$
**Long Yield APY:**\
If you start with a YT priced at $$\text{ytReturnsAfterFee}$$, then after $$\text{yearsToExpiry}$$ you receive an additional $$\text{ytReturnsAfterFee}$$(in terms of the base asset). The APY is calculated by annualizing the total return:
$$
\text{longYieldApy} = \left(\frac{\ \text{ytReturnsAfterFee}}{\text{ytPriceInAsset}}\right)^{\frac{1}{\text{yearsToExpiry}}} - 1
$$
#### **Yield (P**oint) **Leverage**
**Yield (Point) Leverage** is the multiplied exposure on yield or points by holding YT beyond what your principal normally earns.
$$
\text{Yield (Point) Leverage} = \frac{1}{\text{Yield Price in YBT}}
$$
#### Napier Point APY
The **Napier Point APY** estimates the annualized yield derived from Napier Point incentives. It reflects the potential return users may receive based on their participation and TVL contribution.
The calculation begins with estimating the **total incentive value**, which is 15% of the protocol’s fully diluted valuation (FDV):
$$
\text{Total Incentive Value} = 15% \times \text{FDV}
$$
This value is then distributed proportionally across all eligible Napier Points, giving us the **point price**:
$$
\text{Point Price} = \frac{\text{Total Incentive Value}}{\text{Total Points}}
$$
Given the amount of points distributed each week, we can compute the **weekly return** in dollar terms:
$$
\text{Weekly Return} = \text{Weekly Point Distribution} \times \text{Point Price}
$$
To understand the yield relative to the total capital deployed, we divide the weekly return by the total value locked, resulting in the **weekly APR**:
$$
\text{Weekly APR} = \frac{\text{Weekly Return}}{\text{Total TVL}}
$$
Finally, the **Napier Point APY** is the annualized projection of this weekly APR, assuming consistent distribution:
$$
\text{Napier Point APY} = \text{Weekly APR} \times 52
$$
#### **Pool APY**
**Pool APY** is the overall APY from TwoCryptoNG Curve after considering all yields and any other rewards on LP positions.
$$
\text{Pool APY} = \text{Net Apy} + \text{PT Fixed Rate APY} + \text{LP Fees APY}
$$
### **Volume**
**Volume** is the the number of shares or contracts traded in an asset over a period of time.
$$
\text{Volume} = \sum\_{i} \text{Traded Asset}\_i
$$
### Total Value Locked (TVL)
#### TVL
**TVL (Total Value Locked)** is the total amount of assets currently deposited in the Napier protocol.
#### Pool TVL
**Pool TVL** is the total value locked within a specific liquidity pool.
#### PT and YT TVL
**PT and YT TVL** is the current value of the total issued amount of a specific PT and YT.
## AUM
#### Current AUM
**Current AUM** is the current value of assets under management by a specific curator.
$$
\text{Current AUM} = \sum\_{i=1}^{N} \text{TVL}\_{\text{curator}\_i}
$$
Where:
* $$N$$ is the total number of market curators.
* $$\text{TVL}\_{\text{curator}\_i}$$represents the TVL of the $$i^{th}$$market curator.
#### Cumulative AUM
**Cumulative AUM** is the total historical value of assets that a curator have been managed since inception.
$$
\text{Cumulative AUM} = \sum\_{i=1}^{N} \text{TVL}\_{\text{market}\_i}
$$
Where:
* $$N$$ is the total number created by curator.
* $$\text{TVL}\_{\text{market}\_i}$$ represents the TVL of the $$i^{th}$$ created by curator.
#### Cumulative Fees Earned
**Cumulative fees earned** are the total fees collected by a curator across all transactions over time.
$$
\text{Cumulative Fees Earned} = \sum\_{i} \text{Fee Received}\_i
$$
#### **Underlying Asset TVL**
**Underlying asset TVL** is the total value locked in the underlying assets across the protocol.