Impermanent Loss in Uniswap v3

AMMs are autonomous smart contracts deployed on a blockchain that make markets between different assets that live on that chain. In this paper we are examining a specific class of AMMs called Constant Function Market Makers whose trading profile, ignoring fees, is determined by their bonding curve. This class of AMM suffers from what is commonly referred to as Impermanent Loss, which we have previously identified as the Gamma component of the associated self-financing trading strategy and which is the risk that LP providers wager against potential fee earnings. The recent Uniswap v3 release has popularized the concept of leveraged liquidity provision - wherein the trading range in which liquidity is provided is reduced and achieves a higher degree of capital efficiency through elimination of unused collateral. This leverage increases the fees earned, but it also increases the risk taken, ie the IL. Fee levels on Uniswap v3 are well publicized so, in this paper, we focus on calculating the IL. We found that for the 17 pools we analyzed, covering 43% of TVL and chosen by size, composite tokens and data availability, total fees earned since inception until the cut-off date was $199.3m. We also found that the total IL suffered by LPs during this period was USD 260.1m, meaning that in aggregate those LPs would have been better off by USD 60.8m had they simply HODLd.