Impermanent loss and loss-vs-rebalancing I: some statistical properties
Abstract
There are two predominant metrics to assess the performance of automated market makers and their profitability for liquidity providers: 'impermanent loss' (IL) and 'loss-versus-rebalance' (LVR). In this short paper we shed light on the statistical aspects of both concepts and show that they are more similar than conventionally appreciated. Our analysis uses the properties of a random walk and some analytical properties of the statistical integral combined with the mechanics of a constant function market maker (CFMM). We consider non-toxic or rather unspecific trading in this paper. Our main finding can be summarized in one sentence: For Brownian motion with a given volatility, IL and LVR have identical expectation values but vastly differing distribution functions.
Keywords
Cite
@article{arxiv.2410.00854,
title = {Impermanent loss and loss-vs-rebalancing I: some statistical properties},
author = {Abe Alexander and Lars Fritz},
journal= {arXiv preprint arXiv:2410.00854},
year = {2025}
}