Impermanent Loss is a popular concept when it comes to automated market makers and decentralized exchanges like Uniswap. This term is often defined as the percentage loss a liquidity provider would experience for a given price movement. This means that, as an LP, your position may fall in value due to volatility, causing a loss compared to holding these assets outside of the pool. This article will spell out the concept in mathematical logic and explain all the assumptions involved. We consider a market with liquidity L and amounts x and y of assets X and Y respectively. We also have P as the price of X in terms of Y, and a price movement P1 = P.d where d >0 According to the definition of IL touched upon, we establish a generic formula for IL: where: V1 is the value of your position in the pool at the price P1 (x,y move with price) Vh is the value of your assets at the price P1 if you keep them outside of the pool We also consider V0 as the initial value of your hol...
Uniswap is currently the leading decentralized exchange in the blockchain world. In this article, I am going to explain the Curve of Real Reserve on Uniswap V3 in mathematical logic. This paper assumes you are familiar with automated market makers between two assets X and Y defined as a trading function, meaning a relationship between its reserves x and y. First, we consider a market with liquidity L and amounts x and y of assets X and Y respectively. And, we also have P as the price of X in terms of Y. It follows immediately that: In the earlier version, Uniswap V2, liquidity was distributed across the entire price range (0,∞), leading to inefficient liquidity utilization since much of the assets in the pool are never touched. The graph looks like this: Now, on version V3, liquidity providers are capable of providing liquidity in a fixed price range, saying [Pa, Pb] for example. This feature is called concentrated liquidity. If the price does not fall outside of the range, you ca...