The Paradox of Just-in-Time Liquidity in Decentralized Exchanges: More Providers Can Lead to Less Liquidity 

Speaker: Agostino Capponi (Columbia University)

We study just-in-time (JIT) liquidity provision within decentralized exchanges (DEXs). In contrast to passive liquidity providers who deposit assets into liquidity pools before observing order flows, JIT providers take a more proactive approach. They monitor pending orders prior to their execution and swiftly supply liquidity, only to withdraw it within a single block. Our game-theoretical analysis uncovers a paradoxical scenario: an increase in liquidity providers, rather than enhancing liquidity as might be expected, can inadvertently reduce it. At the heart of our analysis lies the adverse selection problem encountered by passive liquidity providers, stemming from the presence of informed arbitrageurs. Unlike passive liquidity providers, JIT providers can decide on the provision of liquidity after analyzing the order flow. This second-mover advantage mitigates their adverse selection costs, potentially leading to crowding out passive liquidity providers, especially if order flows are not very sensitive to changes in pool liquidity.  We show that these detrimental effects can be mitigated via a two-tiered fee structure which transfers a part of a JIT LP's fee revenue to passive LPs, or by fostering a competitive environment among JIT LPs.

Discussant: Sarit Markovich (Northwestern University, Kellogg)

Liquidity pooling beyond constant functions

Speaker: Fayçal Drissi (University of Oxford)

Popular automated market makers (AMMs) use constant function markets (CFMs) to clear the demand and supply of liquidity. In this talk, we recall the microstructure of CFMs, and we propose a general framework, called the arithmetic liquidity pool (ALP), to describe decentralised liquidity pooling where available reserves determine the price of liquidity and price dynamics. We derive conditions to prevent arbitrages from round-trip trades in the ALP, and we demonstrate that CFMs are a subset of ALP. Next, we describe the economics of ALPs; we derive the equilibrium fees that liquidity pools charge to liquidity takers when the size of the pool reserves is fixed, and we derive the equilibrium size of the pool reserves when the fee levels are fixed. As a specific case study, we investigate competition and equilibrium reserves within the Uniswap ecosystem. Finally, we propose a family of computationally efficient dynamic ALP strategies where the price of liquidity maximises the expected profit of LPs based on assumptions over the demand for liquidity and risk preferences. Transaction data from Binance and Uniswap v3 are used to show that liquidity provision is not a loss-leading activity in an ALP that implements our strategy.

Discussant: Tarun Chitra (Gauntlet)

The Economics of Automated Market Making and Decentralized Exchanges

Speaker: Ciamac Moallemi (Columbia Business School)

Automated market makers (AMMs) have emerged as the dominant market mechanism for trading on decentralized exchanges implemented on blockchains. However, they leak value due to stale prices to arbitrageurs, a phenomena called "loss-versus-rebalancing" (LVR) by Milionis et al. (2022). In the first part of this talk, we develop a model for arbitrage profits that accounts for both swap fees and discrete, Poisson block generation. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. We show that arbitrage profits are proportional to the square root of interblock time, the cube of volatility, and the reciprocal of the fee. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of time that an arriving arbitrageur finds a profitable trade, and can be viewed as splitting LVR between arbitrage profits and fees paid to liquidity providers.

In the second part of the talk, we leverage these results to present a single mechanism that targets two important unsolved problems for AMMs: reducing losses to informed orderflow, and maximizing revenue from uninformed orderflow. The ``auction-managed AMM'' works by running a censorship-resistant onchain auction for the right to temporarily act as “pool manager” for a constant-product AMM. The pool manager sets the swap fee rate on the pool, and also receives the accrued fees from swaps. The pool manager can exclusively capture some arbitrage by trading against the pool in response to small price movements, and also can set swap fees incorporating price sensitivity of retail orderflow and adapting to changing market conditions, with the benefits from both ultimately accruing to liquidity providers. We prove that under certain assumptions, this AMM should have higher liquidity in equilibrium than any standard, fixed-fee AMM.

This talk includes joint work with Jason Milionis (Columbia CS), Tim Roughgarden (Columbia CS / a16z crypto), Anthony Zhang (Chicago), Austin Adams (Uniswap Labs), Sara Reynolds (Uniswap Labs), and Dan Robinson (Paradigm). It is based on the following two papers:
https://moallemi.com/ciamac/papers/lvr-fee-model-2023.pdf
https://moallemi.com/ciamac/papers/am-amm-2024.pdf

Discussant: Andrew Papanicolaou (North Carolina State University)

Scalable, Frequent Batch Auctions with Multiple Numeraires

Speaker: Geoff Ramseyer (Stanford University)

Frequent batch auctions have been much studied as a mechanism for reducing latency competition in financial markets. Instantiating this mechanism requires computing a market-clearing price---a straightforward computational task when there are only two assets in each batch (i.e., a volatile stock and a stable numeraire). However, many settings, such as foreign exchange markets or the modern decentralized finance ecosystem, lack a common numeraire, and instead feature simultaneous trading between all (or most) pairs of a large set of assets. Treating each pair separately leaves a large class of risk-free ``cyclic'' arbitrage opportunities and complicates the problem for end-users of routing trades.  Competition to claim these opportunities causes significant computational stress on today's decentralized exchanges.

I will discuss my work on instantiating frequent batch auctions at scale in this multi-numeraire setting. Instead of a single clearing price, clearing each batch requires computing the equilibrium of a linear Arrow-Debreu exchange market. I demonstrate that these equilibria can be computed empirically efficiently (i.e. ~0.5-1s) on reasonably large sets of numeraire assets (~50) and very large markets (millions of limit orders).  This type of market mechanism eliminates the risk-free ``cyclic'' arbitrage opportunities and avoids requiring end-users to explicitly route trades.  This mechanism also has the added benefit of eliminating one of the key computational performance bottlenecks of today's decentralized exchanges. I will then discuss the qualitative tradeoffs in how this mechanism interacts with other market mechanisms, such as the constant-function market makers prevalent in today's decentralized finance ecosystem, and their impact on the equilibrium computation problem.

Based on joint work with Mohak Goyal, Ashish Goel, and David Mazières. Papers available at https://www.usenix.org/conference/nsdi23/presentation/ramseyer and https://arxiv.org/abs/2210.04929

Discussant: Ayan Bhattacharya (University of Chicago)

Thorough mathematical modeling and analysis of Uniswap v3

Speaker: Emmanuel Gobet (École Polytechnique)

Automated Market Makers have emerged quite recently, and Uniswap is one of the most widely used platforms. In this work, starting from its open-source code, we provide a detailed and exact description of the mechanisms of the protocol, so that we can analyze the Impermanent Loss of a liquidity provider by detailing its evolution, with no assumption on the swap trades or liquidity events that occur over the time period.  We also investigate the behavior of collected fees under mild assumptions on the latent price; the value of the collected fees then coincides with an integral of call and put prices. Last, we study when a Liquidity Provider should optimally exit from a Uniswap v3 liquidity pool.

Discussant: Fayçal Drissi (University of Oxford)

Geometry of DeFi and Maximal Extractable Value

Speaker: Tarun Chitra (Gauntlet)

The formal understanding of how decentralized finance (DeFi) mechanisms compare to their centralized alternatives has dramatically improved over the past few years. However, much of the analysis has focused on analytic, non-canonical properties of mechanisms like constant function market makers, lending protocols, and perpetual exchanges. However, there has been little in the way of understanding general geometric and algebraic properties of these systems. In this talk, we’ll start by illustrating recent convex geometric results about constant function market makers. We will then consider a geometric view of maximal extractable value (MEV) as a stochastic process on the Birkhoff polytope. This representation allows one to utilize algebraic tools to provide concrete bounds on the difference between worst-case and average-case MEV. These bounds can be made analytically tractable and useful for practical protocols when smoothness assumptions are placed on agent utilities and policies. We will conclude with open problems that we hope will inspire others to move beyond coordinate-dependent analysis of DeFi.

Discussant: William Cottrell (University of Chicago and Jump Trading)

Implied Impermanent Loss: A Cross-Sectional Analysis of Decentralized Liquidity Pools

Speaker: Andrew Papanicolaou (North Carolina State University)

We propose a continuous-time stochastic model to analyze the dynamics of impermanent loss in liquidity pools in decentralized finance (DeFi) protocols. We replicate the impermanent loss using option portfolios for the individual tokens. We estimate the risk-neutral joint distribution of the tokens by minimizing the Hansen–Jagannathan bound, which we then use for the valuation of options on relative prices and for the calculation of implied correlations. In our analyses, we investigate implied volatilities and implied correlations as possible drivers of the impermanent loss and show that they explain the cross-sectional returns of liquidity pools. We test our hypothesis on options data from a major centralized derivative exchange.

Discussant: Anthony Lee Zhang (University of Chicago, Booth)

Trust at Scale: The Economic Limits of Cryptocurrencies and Blockchains

Speaker: Eric Budish (University of Chicago, Booth)

Satoshi Nakamoto (2008) invented a new kind of economic system that does not need the support of government or rule of law. Trust and security instead arise from a combination of cryptography and economic incentives, all in a completely anonymous and decentralized system. This paper uses a simple three-equation argument to show that this new form of trust, while ingenious, is deeply economically limited. A zero-profits condition on the providers of blockchain trust and an incentive-compatibility condition on the system’s security against attack together imply an equilibrium constraint that the recurring, “flow” cost of blockchain trust must be large relative to the one-off, “stock”-like benefit of attacking the system. Moreover, this equilibrium cost of blockchain trust scales linearly with the value secured — which means that if cryptocurrencies and blockchains were to become more economically useful than they have been to date, then their costs would have to grow to absurd levels. There is a way out of the flow-stock argument but it is premised on the risk of economic collapse, which is itself a serious problem – pick your poison. The key contrast between Nakamoto trust and traditional trust grounded in rule of law, and complementary sources such as reputations, relationships and collateral, is the economies of scale that arise from credible deterrence as in Hayek (1960) and Becker (1968): Society or a firm pays a fixed cost to enjoy trust over a large quantity of economic activity at low or zero marginal cost.

Discussant: Ciamac Moallemi (Columbia Business School)