Rudy DeFi Insight — How to hedge Impermanent Loss?

DeFi protocols such as Uniswap, SushiSwap or PancakeSwap have experienced explosive growth in volume and liquidity. These liquidity protocols allow virtually anyone with funds to become a market maker and earn trading fees. A permanent loss occurs when you provide liquidity to a liquidity pool and the price of the assets you contribute changes compared to when you contributed them. The greater this change, the higher your exposure to a permanent loss. To tackle the impermanent loss, Opyn has released Squeeth, the first power perpetual that gives traders perpetual exposure to ETH². It provides global option-like exposure (pure convexity, pure gamma) without the need for strike prices or expiration dates, consolidating much of the liquidity of the options market into a single ERC20 token.

Authors: Christian Viehof, Valentin Kalinov

What is impermanent loss?

Impermanent loss describes the temporary loss of funds that liquidity providers occasionally suffer due to the volatility of a trading pair. It also illustrates how much more money someone would have if they had simply kept their assets in their wallet instead of providing liquidity. Liquidity pools often consist of two assets — and while one might be a stablecoin like USDC, the other might be a more volatile cryptocurrency like ETH. Let’s imagine that after a provider deployed an equal amount of liquidity in USDC and ETH the price of ETH suddenly increases. This creates a compelling opportunity for arbitrage, as the price of ETH in the liquidity pool is now cheaper than on alternative exchanges like Coinbase. To ensure that the ratio of USDC to ETH remains balanced, other traders buy ETH at a discounted price until equilibrium is restored. After arbitrage, a liquidity provider may end up holding a larger amount of USDC and slightly less ETH. The impairment loss evaluates the loss in value of the assets if withdrawn compared to what they would be worth if they were kept deployed in the liquidity pool. The loss becomes permanent only when a liquidity provider decides to withdraw its tokens from the pool.

Losses to liquidity providers due to price variation chart
Figure 1: Impermanent loss due to price variation (source: https://bit.ly/3lmaUjB)

Power perpetuals and Squeeth

A power perpetual is a perpetual derivative indexed to power of the price of some underlying instrument. We will assume this underlying instrument is Ether since Squeeth is an ETH power perpetual. If the price of ETH doubles, the ETH² power perp 4Xs, the ETH³ power perp 8Xs, and the ETH⁵ power perp 32Xs. In the context of power perpetuals, the funding fee is called a premium yield to reflect that this cost generally represents a premium being paid from longs to shorts in return for options-like exposure.

Squeeth payout function chart
Figure 2: Squeeth payout (source: https://bit.ly/3MwFx1Y)

The concept of perpetual options completely eliminates expiration dates from regular options. Since multiple expiration dates are no longer required, liquidity will be less fragmented. However, there are still multiple perpetual options for different strike prices. This means that liquidity is still fragmented across different portfolios of option contracts, and traders still have to choose between multiple strike prices.

Power Perpetuals solve this problem and are a more specific implementation of Everlasting Options without strike prices. A power perpetual is a perpetual derivative that is linked to a power of the price of an underlying asset, such as ETH. For each power p, the ETH^p power perpetual is kept in line with a funding fee paid at regular intervals (as opposed to premiums for options). Quadratic power perpetuals like Squeeth provide global, option-like exposure (pure convexity, pure gamma) without the need for strike prices or expiration dates, and have the ability to consolidate much of the liquidity of the options market into a single instrument like an ERC20.

Squeeth (squared ETH) is a power perpetual that tracks the price of ETH². It works similar to a perpetual swap where you bet on ETH² rather than ETH. Long Squeeth offers traders a leveraged position with unlimited ETH² upside, protected downside and no liquidations. Squeeth buyers pay a funding rate for this position. In contrast, Short Squeeth is a short ETH² position backed by ETH. Traders earn a funding rate for taking this position, which is paid by Long Squeeth holders.

Opyn total value locked chart on DeFi Lama
Figure 3: Opyn DefiLlama entry (source: https://defillama.com/protocol/opyn)

How to hedge impermanent loss

Now let’s go through a process of how to hedge the impermanent loss of a Uniswap V3 liquidity position using Squeeth.:

1. step: Buy an amount of Squeeth with equal curvature (gamma) as your Uniswap V3 liquidity position

2. step: Sell enough ETH perpetual futures to equalize the delta from your Uniswap V3 position as well as your Squeeth holdings

The resulting position will still have some leftover cubic and higher-order terms since the impermanent loss can be displayed as a Taylor series and Squeeth only eliminating the second-order term (ETH²):

Consider the Uniswap V3 liquidity position below. The aim is to buy enough Squeeth to hedge the gamma of the LP and sell enough ETH perpetuals to offset the change in the price of ETH.

USDC/ETH Uniswap V3 Liquidity Position schreenshot
Figure 4: USDC/ETH Uniswap V3 LP (source: https://bit.ly/3LlN2HC)

This Uniswap liquidity position has a virtual liquidity L² = 1398. The value of a Uniswap position bounded between (3747, 5024) at a price of 4360.61 is:

Virtual liquidity formula

The delta and gamma of the Uniswap V3 LP are:

Delta function formula
Gamma function formula

The delta and gamma of the Squeeth power perpetual are:

The delta and gamma of the Squeeth power perpetual formula
Gamma

To fully hedge the position, we need to:

  • Buy 0.0012 Squeeth (half the option gamma since Squeeth gamma is 2) to hedge the gamma from the Uniswap V3 position
  • Sell 10.59 ETH perpetual futures to hedge the delta from Squeeth
  • Sell 1.448 ETH perpetual futures to hedge the delta from the Uniswap V3 position

The table and figure below display the overall performance of the hedge. The hedge works great as long as the price of ETH does not change more than 10%. If the price of ETH changes more, rebalancing is necessary.

Impact of ETH price change on the net profit and loss spreadsheet
Figure 5: Impact of ETH price change on the net profit and loss (https://bit.ly/3LlN2HC)
Impact of ETH price change on the net profit and loss chart
Figure 6: Impact of ETH price change on the net profit and loss (https://bit.ly/3LlN2HC)

The classification of Squeeth according to the ITC

ITSA tokenbase entry for Squeeth
Figure 7: The Squeeth Tokenbase entry (Source: https://itin.itsa.global/JN3FMVM54)

Economic Purpose (EEP): Squeeth is listed as a Derivative Token (EEP23DV) due to its option-style design.

Industry Type (EIN): The issuer of Squeeth is active in the field of Decentralized Derivatives, Synthetic Assets and Insurance (EIN06DF03).

Technological Setup (TTS): Squeeth runs under the Ethereum ERC-20 Standard (TTS42ET01) as an application layer token on top of the Ethereum blockchain.

Legal Clam (LLC): Squeeth does not entitle its holder to any legal claim or rights against the issuing organization; therefore, it is listed as a No-Claim Token (LLC31).

Issuer Type (LIT): The dimension “Issuer Type” provides information on the nature of the issuer of the token. Squeeth’s platform is built by a team of programmers and engineers. Its Issuer Type is a Private Sector Legal Entity (LIT61PV).

Regulatory Framework (EU) (REU): The dimension “Regulatory Status EU” provides information on the potential classification of a token according to the European Commission’s proposal for a Regulation on Markets in Crypto Assets (MiCA, Regulation Proposal COM/2020/593 final). Squeeth qualifies as a Utility Token (REU52) according to the definition provided in Article 3 (5) of Regulation Proposal COM/2020/593 final.

The International Token Standardization Association (ITSA) e.V.

The International Token Standardization Association (ITSA) e.V. is a not-for-profit association of German law that aims at promoting the development and implementation of comprehensive market standards for the identification, classification, and analysis of DLT- and blockchain-based cryptographic tokens. As an independent industry membership body, ITSA unites over 100 international associated founding members from various interest groups. In order to increase transparency and safety on global token markets, ITSA currently develops and implements the International Token Identification Number (ITIN) as a market standard for the identification of cryptographic tokens, the International Token Classification (ITC) as a standard framework for the classification of cryptographic tokens according to their inherent characteristics. ITSA then adds the identified and classified token to the world’s largest register for tokens in our Tokenbase.

  • The International Token Identification Number (ITIN) is a 9-digit alphanumeric technical identifier for both fungible and non-fungible DLT-based tokens. Thanks to its underlying Uniform Token Locator (UTL), ITIN presents a unique and fork-resilient identification of tokens. The ITIN also allows for the connecting and matching of other media and data to the token, such as legal contracts or price data, and increases safety and operational transparency when handling these tokens.
  • The International Token Classification (ITC) is a multi-dimensional, expandable framework for the classification of tokens. Current dimensions include technological, economic, legal, and regulatory dimensions with multiple sub-dimensions. By mid-2021, there will be at least two new dimensions added, including a tax dimension. So far, our classification framework has been applied to 99% of the token market according to market capitalization of classified tokens.
  • ITSA’s Tokenbase currently holds data on over 21000 tokens. Tokenbase is a holistic database for the analysis of tokens and combines our identification and classification data with market and blockchain data from external providers. Third-party data of several partners is already integrated, and API access is also in development.

Remarks

If you like this article, we would be happy if you forward it to your colleagues or share it on social networks. More information about the International Token Standardization Association can be found on the Internet, on Twitter, or on LinkedIn.

Christian Viehof is an Executive Director at the International Token Standardization Association (ITSA) e.V. and Chief Research Officer of Rudy Capital. He completed his Bachelor in Economics at the University of Bonn, the Hong Kong University and the London School of Economics and Political Science with a focus on Behavioral Economics and Finance. Currently pursuing his Master of Finance at the Frankfurt School of Finance and Management, you can contact him via christian.viehof@itsa.global and connect with him on Linkedin, if you would like to further discuss ITSA e.V. or have any open questions.

Valentin Kalinov is an Executive Director at International Token Standardization Association (ITSA) e.V., working to create the world’s largest token database, including a classification framework and unique token identifiers and locators. He has over five years of experience working at BlockchainHub Berlin in content creation and token analysis, as a project manager at the Research Institute for Cryptoeconomics at the Vienna University of Economics and token analyst at Token Kitchen. You can contact Valentin via valentin.kalinov@itsa.global and connect on Linkedin if you would like to further discuss ITSA e.V. or have any other open questions.

How to hedge impermanent loss article cover

--

--

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
International Token Standardization Association

The International Token Standardization Association (ITSA) is a not for profit organization working on holistic market standards for the global token economy.