Impermanent Loss in Uniswap v3 (2111.09192v1)

Abstract: 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.

• The paper quantifies impermanent loss in Uniswap V3, demonstrating that nearly half of liquidity providers incur net negative returns.
• It analyzes 17 pools covering 43% TVL, revealing that total fees ($199.3M) fell short against an impermanent loss of $260.1M.
• The study refines the risk framework by differentiating between minimum and actual impermanent loss, guiding future liquidity provision strategies.

Impermanent Loss in Uniswap V3

The paper on impermanent loss (IL) in Uniswap V3 provides an in-depth examination of the economic implications of providing liquidity within the framework of a concentrated liquidity AMM. Automated Market Makers (AMMs), particularly Constant Function Market Makers like Uniswap, have become a vital component in decentralized finance due to their ability to facilitate trading between cryptocurrency pairs without the need for traditional order books. However, liquidity providers (LPs) face non-negligible risks like impermanent loss, which defines the financial disadvantage faced by LPs as compared to merely holding their assets unchanged ("HODLing").

A key feature of Uniswap V3 is leveraged liquidity provision, which allows LPs to concentrate their capital within specific price ranges, thus enhancing capital efficiency. This paper focuses on quantifying impermanent loss within this new framework, especially in the context of uncorrelated cryptocurrency pairs.

Quantitative Insights

The authors analyzed 17 liquidity pools on Uniswap V3, representing about 43% of the total value locked (TVL) in the protocol, and found striking results. Over the analyzed period, the total fees accrued by liquidity providers were approximately $199.3 million. However, the aggregate impermanent loss was calculated at$260.1 million. Consequently, liquidity providers on average were financially worse off by $60.8 million compared to if they had chosen to HODL the assets instead.

The paper also highlights that the impermanent loss surpassed the fees in nearly all pools, leading to negative net returns for 49.5% of liquidity providers studied. Notably, the authors found no statistically significant evidence to suggest that more active LPs, who frequently adjusted their positions, experienced better returns than those who did not.

Theoretical Implications

The paper advances the theoretical understanding of impermanent loss in the context of leveraged AMMs. By introducing the concepts of minimum and actual IL, the researchers offer a refined framework to gauge the unavoidable risks in liquidity provision. Minimum IL is defined as the loss incurred while the asset remains within the defined price range, unaffectable by sophisticated trading strategies. In contrast, actual IL encompasses both in-range and out-of-range losses, representing the full extent of the financial impact on LPs.

Speculations on Future Developments

This research indicates that, under the current Uniswap V3 model, liquidity provision may not present a lucrative strategy for many participants due to the prevailing impermanent loss factors. As decentralized finance (DeFi) continues to evolve, there may be attempts to innovate new AMM designs aiming to mitigate IL or devise strategies optimizing liquidity provisioning to be a more profitable endeavor. Subsequent research may focus on enhanced segmentation of liquidity providers to identify specific strategies or automated algorithms that outperform HODLing, thereby closing the gap noted in this paper.

In sum, while Uniswap V3's use of concentrated liquidity provides a layer of sophistication and potential fee opportunities, it also amplifies the associated risks, particularly impermanent loss. The paper's findings prompt a reevaluation of liquidity strategies and suggest a need for further development in LP optimization techniques and AMM protocol designs to offer truly sustainable economic opportunities within the DeFi landscape.