[Paper Review] FLAIR: A Metric for Liquidity Provider Competitiveness in Automated Market Makers

Jason Milionis, Xin Wan+1 more|arXiv (Cornell University)|Jun 15, 2023

Financial Markets and Investment Strategies4 citations

TL;DR

This paper introduces FLAIR, a novel metric for measuring liquidity provider (LP) competitiveness in automated market makers (AMMs), which quantifies fee-adjusted, instantaneous returns relative to capital deployed. By capturing dynamic LP behavior and competition, FLAIR complements existing metrics like LVR and enables ex-post performance evaluation and forward-looking optimization of liquidity provision strategies.

ABSTRACT

This paper aims to enhance the understanding of liquidity provider (LP) returns in automated market makers (AMMs). LPs face market risk as well as adverse selection due to risky asset holdings in the pool that they provide liquidity to and the informational asymmetry between informed traders (arbitrageurs) and AMMs. Loss-versus-rebalancing (LVR) quantifies the adverse selection cost (Milionis et al., 2022a), and is a popular metric to evaluate the flow toxicity to an AMM. However, individual LP returns are critically affected by another factor orthogonal to the above: the competitiveness among LPs. This work introduces a novel metric for LP competitiveness, called FLAIR (short for fee liquidity-adjusted instantaneous returns), that aims to supplement LVR in assessments of LP performance to capture the dynamic behavior of LPs in a pool. Our metric reflects the characteristics of fee return-on-capital, and differentiates active liquidity provisioning strategies in AMMs. To illustrate how both flow toxicity, accounting for the sophistication of the counterparty of LPs, as well as LP competitiveness, accounting for the sophistication of the competition among LPs, affect individual LP returns, we propose a quadrant interpretation where all of these characteristics may be readily visualized. We examine LP competitiveness in an ex-post fashion, and show example cases in all of which our metric confirms the expected nuances and intuition of competitiveness among LPs. FLAIR has particular merit in empirical analyses, and is able to better inform practical assessments of AMM pools.

Motivation & Objective

• To address the gap in existing metrics by quantifying LP competitiveness, which is orthogonal to flow toxicity and adverse selection.
• To provide a dynamic, ex-post measure of individual LP performance that captures strategic positioning and timing in AMM pools.
• To enable practical assessment and optimization of liquidity provision strategies using a metric that reflects real-world competitive dynamics.
• To offer a framework for comparing LP strategies and identifying optimal liquidity deployment under varying market conditions.
• To support future market design by enabling comparative analysis across different AMM structures and traditional exchanges.

Proposed method

• FLAIR computes fee liquidity-adjusted instantaneous returns by normalizing fee income by the effective capital deployed over time.
• The method uses tick-spacing and price path data to calculate the minimum and maximum ticks for liquidity placement, accounting for discrete price levels in AMMs like Uniswap v3.
• It models both passive and fully-competitive LPs: passive LPs cover the full range from min to max price, while competitive LPs dynamically adjust positions based on observed price changes.
• The aggregate FLAIR of a pool is computed via an integral over time, reflecting fee income divided by the effective liquidity range and capital deployed.
• The metric is robust to rounding and tick-spacing effects, with convergence to full-range positioning when price volatility is high or tick-spacing is coarse.
• FLAIR is applicable point-in-time, over arbitrary periods, and to portfolios or entire pools, enabling back-testing and forward-looking strategy optimization.

Experimental results

Research questions

• RQ1 How can LP competitiveness be quantified in a way that complements existing metrics like LVR, which measure adverse selection?
• RQ2 To what extent does dynamic, competitive liquidity provisioning improve LP returns compared to passive, full-range positioning?
• RQ3 How do factors such as fee rate, timing of deployment, and liquidity concentration affect instantaneous LP competitiveness?
• RQ4 Can FLAIR be used to identify optimal liquidity range and deployment timing for maximizing returns in AMMs?
• RQ5 In what ways can FLAIR inform portfolio optimization and market design across different market structures?

Key findings

• FLAIR successfully captures the dynamic nature of LP competitiveness, showing that strategic positioning significantly affects returns beyond passive liquidity provision.
• Fully-competitive LPs achieve higher FLAIR than passive LPs when price movements are frequent and within a narrow tick range, due to better capital efficiency.
• The metric confirms that higher fee rates and better timing of deployment increase FLAIR, reflecting improved competitiveness.
• When price paths are stable or tick-spacing is coarse, FLAIR converges to the full-range case, validating the model’s consistency under extreme conditions.
• FLAIR enables meaningful comparison of LP strategies and supports back-testing for optimal capital deployment, with potential applications in portfolio optimization.
• The metric is generalizable and could be adapted for use in traditional exchanges, enabling cross-market structural comparisons.