Automated Market Makers and Loss-versus-Rebalancing (LVR): a Deep Dive into Decentralized Finance

Tutorial at EC'24

Introduction to the topic

In recent years, automated market makers (AMMs) have emerged as an alternative to the most common market structure used for electronic trading, the limit order book (LOB). AMMs are currently the dominant market structure for the on-chain exchange of digital assets. One advantage of AMMs over LOBs is computational efficiency: AMMs generally have minimal storage needs and require only lightweight computations, as opposed to the relatively complex data structures and matching logic typically used by large-scale LOBs. Second, LOBs are not well-suited to "long-tail" assets (i.e., those with thin trading markets), as they generally require the participation of active market makers. In contrast, AMMs rely largely on passive liquidity providers (LPs). There is a well-developed theory for the design and analysis of LOBs; what would an analogous theory look like for AMMs?

The focus of the tutorial will be on the adverse selection costs incurred by liquidity providers in automated market makers, and in particular the concept of "loss-versus-rebalancing" (LVR) introduced recently by Milionis, Moallemi, Roughgarden, and Zhang (2022). We will discuss multiple ways to interpret LVR, and then develop the necessary math to give a closed-form expression for LVR in AMMs (e.g., σ²/8 for the ubiquitous “x*y=k” AMM made famous by Uniswap, where σ denotes the volatility of the price process).

The primary goals of this tutorial are to learn about the market structure of AMMs, the reasons why LVR is an important quantity in decentralized finance, how LVR applies to data, and the mathematics that are best suited for reasoning about and predicting LVR.


Jason Milionis, Ciamac C. Moallemi, and Tim Roughgarden


Part 1: AMMs and the multiple facets of LVR

This part of the tutorial will focus on a conceptual understanding of the market structure posed by AMMs, as well as the multiple structural results. No knowledge of AMMs will be assumed.

Part 2: Mathematical characterization of the AMM design space

The second part of the tutorial will delve into the mathematical details underlying the structural characterizations and conceptual understanding of AMMs.

Part 3: Characterizing LVR in a Black-Scholes-style model

The final part of the tutorial will introduce just enough mathematics to derive a characterization of LVR in the most basic model studied in continuous-time finance.