Impermanent loss and Loss-vs-Rebalancing II

ArXiv ID: 2502.04097 “View on arXiv”

Authors: Unknown

Abstract

This paper examines the relationship between impermanent loss (IL) and loss-versus-rebalancing (LVR) in automated market makers (AMMs). Our main focus is on statistical properties, the impact of fees, the role of block times, and, related to the latter, the continuous time limit. We find there are three relevant regimes: (i) very short times where LVR and IL are identical; (ii) intermediate time where LVR and IL show distinct distribution functions but are connected via the central limit theorem exhibiting the same expectation value; (iii) long time behavior where both the distribution functions and averages are distinct. Subsequently, we study how fees change this dynamics with a special focus on competing time scales like block times and ‘arbitrage times’.

Keywords: Automated Market Makers, Impermanent Loss, Loss-versus-Rebalancing, Arbitrage, DeFi

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper uses advanced stochastic calculus (Brownian motion, SDEs) and statistical theory (distributions, CLT) to model AMM dynamics, but relies on conceptual numerical simulations rather than real-world data or specific backtesting protocols.
  flowchart TD
    A["Research Goal:<br>Investigate IL vs. LVR in AMMs<br>featuring fees & block times"] --> B["Methodology:<br>Theoretical Modeling &<br>Statistical Analysis"]
    B --> C["Computational Processes:<br>Simulate Discrete Block<br>vs. Continuous Time Regimes"]
    B --> D["Data Inputs:<br>Market Volatility,<br>Fee Parameters, Block Times"]
    C --> E{"Analysis of<br>Time Regimes"}
    D --> E
    E --> F["Outcome 1:<br>Three distinct regimes identified:<br>Identical (Short), Dist. but same mean (Int.),<br>Different mean (Long)"]
    E --> G["Outcome 2:<br>Fee dynamics & Arbitrage<br>Time Scales analysis"]
    F & G --> H["Key Finding:<br>LVR & IL coincide at t=0,<br>diverge over time; Fees bridge<br>block time vs. continuous limits"]