Hedging Uniswap V3
PowerMaker enables anyone the ability to hedge impermanent loss on Uniswap. This is possible by minting a power perpetual through the PowerMaker AMM and matching the positive gamma with negative gamma of a Uniswap LP share.
Hedging Process
Hedging the impermanent loss of a Uniswap LP simply entails canceling out the negative gamma of a LP share with the positive gamma of a power perpetual.
For the example above we take a ETH/USDC LP position with the following parameters:
So to hedge the following Uniswap LP position we:
Calculate the price of a Power Perpetual Token
Becuase every Power Perpetual Token (PPT) is a quadratic contract. We know that it will square the price of an underlying asset, “squared leverage.” In fact, we also know that the gamma will always be a constant 2 (this useful for the next step).
The price of a PT = (Price of the underlying asset)².
If ETH = $1825.53, then the price of a PT = (1825.53)² = 3332559.78
2. Calculate the value of a Uniswap LP
With Uniswap V3, the valuing a LP share get a bit more tricky as there is a lower bound and upper bound which refer to the prices between which the liquidity is concentrated on the AMM.
The value of a Uniswap LP is defined as:
3. Calculate the gamma of Uniswap LP
Assuming that the price of the underlying asset is with in the lower and upper bound 0, then the gamma will be:
If the price of ETH = $1825.53, then the gamma of the Uniswap LP is:
4. Calculate the number of Power Tokens.
Using the positive gamma value and price of a Power Token we find the number of Power Tokens needed to hedge a Uniswap LP position.
Which is the gamma of Uniswap over the negative gamma of a Power Token. Therefore the number of PT needed is:
Total Returns
After analyzing the on-chain data for the 7 days block.timestamp we can chart the value of the hedged portfolio versus a non-hedge portfolio or “LP Value.” We show that the hedge portfolio [ETH/USDC LP] consistently outperforms across wide and tight bounds.
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