Calculating the Expected Value of the Impermanent Loss in Uniswap

  • What is the impermanent loss in concentrated AMMs like Uniswap v3 and Sushiswap’s Trident
  • What is the expected magnitude of the impermanent loss for a given token pair.

Expected Impermanent Loss in AMMs

(That’s the correct expression, thanks to Leo Liu @PlanetHunter_HS for pointing out my mistake)
Try it yourself here: https://www.desmos.com/calculator/dmnrp2jde7

Expected Impermanent Loss

Data taken from Coingecko.com on 2021/10/01. Error bars = standard error of the mean.
Expected Impermanent Loss for tokens denominated in either USDC (left) or ETH (right). That a lot of curves, hope the labels help.
Expected LP returns for tokens denominated in either USDC (left) or ETH (right).

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Guillaume Lambert

Guillaume Lambert

Asst professor in Applied Physics at Cornell. LambertLab.io PI and proud father. Interests: Biophysics, Math, Crypto, and Options (often all at the same time).