Uniswap V3
https://arxiv.org/pdf/2106.12033.pdf https://www.youtube.com/watch?v=mtd4JphPcuA here is an in-depth calculation example for liquidity provider returns in Uniswap v3 using concentrated liquidity, along with a comparison to the previous example using Uniswap v2's uniform liquidity distribution:
Scenario:
Consider a DAI/ETH pool on Uniswap v3 with the following initial reserves:
Reserve of DAI = 10,000 DAI
Reserve of ETH = 100 ETH
The pool price is initially 100 DAI per ETH.
A liquidity provider (LP) decides to concentrate their liquidity within a specific price range, for instance, between 90 DAI per ETH and 110 DAI per ETH.
Calculating Pool Tokens Received:
Since the LP is concentrating liquidity, they will receive more pool tokens compared to Uniswap v2's uniform distribution. The exact number of pool tokens depends on the current pool price and the width of the chosen price range.
Calculating LP Returns:
Assume the same events occur as in the Uniswap v2 example:
Price Increase: The price of ETH rises to 120 DAI per ETH.
Trading Volume: There is a total trading volume of 1,000 DAI worth of ETH trades within the LP's chosen price range.
Fee Rate: The fee rate for the pool is set at 0.3%.
Calculating Fees Earned:
Due to the concentrated liquidity, the LP earns more fees from trades occurring within their chosen price range:
Fees Earned = (Trading Volume within Price Range) * (Fee Rate)Fees Earned = (1,000 DAI) * (0.3%) = 3 DAIThe LP still earns 3 DAI in fees, but the concentrated liquidity allows them to capture a larger portion of the fees generated from trades within their chosen price range.
Calculating Impermanent Loss:
Impermanent loss is likely to be lower with concentrated liquidity as the LP's capital is focused on a narrower price range. However, it is still important to consider the potential for impermanent loss.
Impermanent Loss = (Current Pool Price - Initial Pool Price) * (LP's Share of Pool)Impermanent Loss = (120 DAI/ETH - 100 DAI/ETH) * (LP's Share of Pool)The value of the LP's share of the pool will depend on the specific price range they chose and the overall distribution of liquidity across different price ranges.
Comparing LP Returns with Uniswap v2:
Comparing the net returns of the LP in Uniswap v2 and Uniswap v3, it is expected that the LP in Uniswap v3 will experience a higher net return due to the benefits of concentrated liquidity. The concentrated liquidity allows the LP to capture a larger portion of the fees generated from trades within their chosen price range, and it also reduces the impact of impermanent loss.
Conclusion:
Concentrated liquidity in Uniswap v3 offers several advantages over Uniswap v2's uniform liquidity distribution, including:
Capital Efficiency: Concentrated liquidity allows LPs to utilize their capital more efficiently by focusing on relevant price ranges.
Impermanent Loss Mitigation: Concentrated liquidity can mitigate impermanent loss by reducing exposure to price fluctuations outside of the chosen price range.
Fee Optimization: Concentrated liquidity can lead to higher fee earnings for LPs due to their ability to capture a larger portion of fees generated from trades within their chosen price range.
Overall, concentrated liquidity represents a significant improvement in liquidity provision, providing LPs with greater control over their risk management and return potential.
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