# 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**

**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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