> ## Documentation Index
> Fetch the complete documentation index at: https://tech.ramses.xyz/llms.txt
> Use this file to discover all available pages before exploring further.

# Research

# The Goal

Ramses is committed to furthering the space of research and employs reputable scholars to implement sophisticated research-driven solutions.

# Relevant Research

Ramses contributors have published papers that are informative around systems akin to that of Ramses, providing value insights for users and developers alike

## [Impermanent loss and loss-vs-rebalancing I: some statistical properties](https://arxiv.org/html/2410.00854v1)

### **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.