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APY & APR

APY and Fee APR are two critical metrics that every liquidity provider (LP) should pay close attention to when participating in decentralized finance (DeFi) protocols. At Steer, we understand the significance of these metrics, which is why we provide them to our users.

What is Fee APR and how is it calculated?

The Fee APR is a general standard to measure any strategy preformance, it focuses on the fees generated through the underlying strategy.

At Steer, we calculate fees earned over time and compare them to the assets used to determine fees vs the current liquidity. We then normalize this value with tend to give the average fees earned in relationship to the underlying liquidity per second. This enables us to project returns over a given period of time. We determine the collective fee return per assets held using market value. However, please note that we do not factor in any impermanent profit/loss in this calculation.

This calculation is purely a measure of the rate of fees generated by a given strategy.

Formula -

fees0=cumulativeFees0[currentSnapshot]cumulativeFees0[currentSnapshot1]fees0 = cumulativeFees0[currentSnapshot] - cumulativeFees0[currentSnapshot - 1]
fees1=cumulativeFees1[currentSnapshot]cumulativeFees1[currentSnapshot1]fees1 = cumulativeFees1[currentSnapshot] - cumulativeFees1[currentSnapshot - 1]
totalFees=fees1+(fees0conversion0For1)totalFees = fees1 + (fees0 * conversion0For1)
totalAssets=totalHoldingsToken1+(totalHoldingsToken0conversion0For1)totalAssets = totalHoldingsToken1 + (totalHoldingsToken0* conversion0For1)
periodReturn=totalFees/totalAssetsperiodReturn = totalFees / totalAssets

On each tend we emit the vault’s current holdings of token0 and token1, the total supply of tokens, and the pool’s current sqrtPriceX96 (for the pool conversion rate). We also generate the cumulative fees generated in each token. From these values we can determine the increase in fees, put in terms of one token for comparison.

We then divide this value by the duration of the current tend (this snapshot’s timestamp to the previous snapshot timestamp) to get a return per second value. This value is averaged out with all previous tend’s return per second values, and can be applied to a period of time like a year to give the Fee APR.

Pros of Fee APR:

- Gives dependable fee returns over time
- Values are smoother over time
- If LPs exit at the price they entered at, this will be similar to market return
- Better for comparison across pools and protocols

Cons of Fee APR:

- Does not reflect the change in value of the underlying assets
- Does not include rebalancing fees (currently)

What is APY and how is it calculated?

APY is based on its token face value return over a year. This is calculated by measuring the vault's price per share over time and projecting this value out over a year.

The price of the share is determined by evaluating the vault's holdings in a single asset at time of valuation (each execution/tend), meaning impermanent losses and profits are recognized in this value.

Here is the formula -

conversion0For1=sqrtPriceX962/(2192)conversion0For1 = sqrtPriceX96 ** 2 / (2 ** 192)
PPS=(totalHoldingsToken1+(conversion0For1totalHoldingsToken0))/totalSupplyPPS = (totalHoldingsToken1 + (conversion0For1 * totalHoldingsToken0)) / totalSupply

On each tend we emit the vault’s current holdings of token0 and token1 (less performance fees), the total supply of LP tokens, and the pool’s current sqrtPriceX96 (for the pool conversion rate). From these values we are able to calculate the vault’s price per share.

With a collection of price per share values over different periods of time, we can average out these over the observed period or compare the latest snapshot with the vault’s initial state.

Pros of APY:

- Shows current trajectory of user deposit value increase over a period of time
- Represents raw returns for withdrawal

Cons of APY:

- Recognizes impermanent loss and profit when unhedged
- Values are very volatile and swing with market conditions

Steer Protocol provides both APY and Fee APR to our users to help them make informed decisions about their investment strategies. By displaying these metrics in an easy-to-understand format, we enable our users to compare different liquidity pools and choose the ones that align with their investment goals and risk tolerance.

If you would like to learn how you can understand the risk and potential of a given strategy further, please read out documentation around backtesting and risk analysis.