UNISWAP: Impermanent Loss and Risk Profile of a Liquidity Provider

Abstract: Uniswap is a decentralized exchange (DEX) and was first launched on November 2, 2018 on the Ethereum mainnet [1] and is part of an Ecosystem of products in Decentralized Finance (DeFi). It replaces a traditional order book type of trading common on centralized exchanges (CEX) with a deterministic model that swaps currencies (or tokens/assets) along a fixed price function determined by the amount of currencies supplied by the liquidity providers. Liquidity providers can be regarded as investors in the decentralized exchange and earn fixed commissions per trade. They lock up funds in liquidity pools for distinct pairs of currencies allowing market participants to swap them using the fixed price function. Liquidity providers take on market risk as a liquidity provider in exchange for earning commissions on each trade. Here we analyze the risk profile of a liquidity provider and the so called impermanent (unrealized) loss in particular. We provide an improved version of the commonly denoted impermanent loss function for Uniswap v2 on the semi-infinite domain. The differences between Uniswap v2 and v3 are also discussed.