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The Economics of Automated Market Making and Decentralized Exchanges

Ciamac Moallemi – Professor, Columbia University

Thu, 30-Nov-2023 / 4:00pm / Packard 202

Abstract

Automated market making (AMM) protocols such as Uniswap have recently emerged as an alternative to the most common market structure for electronic trading, the limit order book. Relative to limit order books, AMMs are both more computationally efficient and do not require the participation of active market making intermediaries such as high frequency traders. As such, AMMs have emerged as the dominant market mechanism for trust-less decentralized exchanges (DEXs) implemented through smart contracts on programmable blockchain platforms such as Ethereum. In cryptocurrency markets, the aggregate trading volume on the Uniswap DEX exceeds that of the much better known Coinbase centralized exchange.

We develop a model the underlying economics of AMMs from the perspective of their passive liquidity providers (LPs). Our central contribution is a ‘Black-Scholes formula for AMMs’. Like the Black-Scholes formula, we consider the return to LPs once market risk has been hedged. We identify the main adverse selection cost incurred by LPs, which we call ‘loss-versus-rebalancing’ (LVR, pronounced ‘lever’). LVR captures costs incurred by AMM LPs due to stale prices that are picked off by better informed arbitrageurs. In a continuous time Black-Scholes setting, we are able to derive closed-form expressions for this adverse selection cost. Qualitatively, we highlight the main forces that drive AMM LP returns, including asset characteristics (volatility), AMM characteristics (curvature / marginal liquidity, fee structure), and blockchain characteristics (block rate). Quantitatively, we illustrate how our model’s expressions for LP returns match actual LP returns for the Uniswap v2 WETH-USDC trading pair. Our model provides tradable insight into both the ex ante and ex post assessment of AMM LP investment decisions. LVR can also inform the design of the next generation of DEX market mechanisms — in fact, in the short time since our work has been released, ‘LVR mitigation’ has already emerged as the dominant challenge among practitioners in the AMM protocol designer community.

This talk is joint work with Jason Milionis (Columbia CS), Tim Roughgarden (Columbia CS / a16z crypto), and Anthony Zhang (Chicago Booth). It is based on the following two papers: https://moallemi.com/ciamac/papers/lvr-2022.pdf https://moallemi.com/ciamac/papers/lvr-fee-model-2023.pdf

Bio

Ciamac C. Moallemi is William von Mueffling Professor of Business in the Decision, Risk, and Operations Division and the director of the Briger Family Digital Finance Lab at the Graduate School of Business at Columbia University, where he has been since 2007. A high school dropout, he received S.B. degrees in Electrical Engineering & Computer Science and in Mathematics from the Massachusetts Institute of Technology (1996). He studied at the University of Cambridge, where he earned a Master of Advanced Study degree in Mathematics (Part III of the Mathematical Tripos), with distinction (1997). He received a Ph.D. in Electrical Engineering from Stanford University (2007). Prior to his doctoral studies, he developed quantitative methods in a number of entrepreneurial ventures: as a partner in a $200 million fixed-income arbitrage hedge fund and as the director of scientific computing at an early-stage drug discovery start-up. He holds editorial positions at the journals Operations Research and Management Science. He is a past recipient of the British Marshall Scholarship (1996), the Benchmark Stanford Graduate Fellowship (2003), first place in the INFORMS Junior Faculty Paper Competition (2011), and the Best Simulation Publication Award of the INFORMS Simulation Society (2014). Aside from his academic work, he regularly consults for fintech companies. His research interests are in the development of mathematical and computational tools for optimal decision making under uncertainty, with a focus on applications areas including market microstructure, quantitative and algorithmic trading, and blockchain technology.