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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.00854 |
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| _version_ | 1866912376354242560 |
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| author | Alexander, Abe Fritz, Lars |
| author_facet | Alexander, Abe Fritz, Lars |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Impermanent loss and loss-vs-rebalancing I: some statistical properties Alexander, Abe Fritz, Lars Statistical Finance 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. |
| title | Impermanent loss and loss-vs-rebalancing I: some statistical properties |
| topic | Statistical Finance |
| url | https://arxiv.org/abs/2410.00854 |