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Liquid Staking Tokens in Automated Market Makers

Krzysztof Gogol, Robin Fritsch, Malte Schlosser, Johnnatan Messias, Benjamin Kraner, Claudio Tessone

TL;DR

The paper analyzes the profitability of providing liquid staking tokens (LSTs) as liquidity on automated market makers (AMMs), combining a theoretical framework with empirical measurements. It develops LVH and LVS as core LP-loss metrics and derives closed-form fee-return conditions across CFMM variants (CPMM, CLMM, Stableswap, Cryptoswap) for rebase and reward LSTs, using price dynamics parameterized by the staking rate $r$ and volatility $\sigma$. Empirically, it studies Ethereum LST pools (stETH, wstETH, cbETH, rETH) across Curve and Uniswap v3, finding that trading fees often offset impermanent loss (LVH) but rarely compensate for loss-versus-staking (LVS); this raises questions about the sustainability of current LST-AMM liquidity levels and the broader role of CRV rewards and CLMM rebalancing. Overall, the work provides a structured, quantitative assessment of LST liquidity on AMMs and highlights practical implications for DeFi design and staking economics, including potential impacts on LST price stability and depegging risk.

Abstract

This paper studies liquid staking tokens (LSTs) on automated market makers (AMMs), both theoretically and empirically. LSTs are tokenized representations of staked assets on proof-of-stake blockchains. First, we model LST-liquidity on AMMs theoretically, categorizing suitable AMM types for LST liquidity and deriving formulas for the necessary returns from trading fees to adequately compensate liquidity providers under the particular price trajectories of LSTs. For the latter, two relevant metrics are considered: (1) losses compared to holding the liquidity outside the AMM (loss-versus-holding, or "impermanent loss"), and (2) the relative profitability compared to fully staking the capital (loss-versus-staking) which is specifically tailored to the case of LST-liquidity. Next, we empirically measure these metrics for Ethereum LSTs across the most relevant AMM pools. We find that, while trading fees often compensate for impermanent loss, fully staking is more profitable for many pools, raising questions about the sustainability of the current LST liquidity allocation to AMMs.

Liquid Staking Tokens in Automated Market Makers

TL;DR

The paper analyzes the profitability of providing liquid staking tokens (LSTs) as liquidity on automated market makers (AMMs), combining a theoretical framework with empirical measurements. It develops LVH and LVS as core LP-loss metrics and derives closed-form fee-return conditions across CFMM variants (CPMM, CLMM, Stableswap, Cryptoswap) for rebase and reward LSTs, using price dynamics parameterized by the staking rate and volatility . Empirically, it studies Ethereum LST pools (stETH, wstETH, cbETH, rETH) across Curve and Uniswap v3, finding that trading fees often offset impermanent loss (LVH) but rarely compensate for loss-versus-staking (LVS); this raises questions about the sustainability of current LST-AMM liquidity levels and the broader role of CRV rewards and CLMM rebalancing. Overall, the work provides a structured, quantitative assessment of LST liquidity on AMMs and highlights practical implications for DeFi design and staking economics, including potential impacts on LST price stability and depegging risk.

Abstract

This paper studies liquid staking tokens (LSTs) on automated market makers (AMMs), both theoretically and empirically. LSTs are tokenized representations of staked assets on proof-of-stake blockchains. First, we model LST-liquidity on AMMs theoretically, categorizing suitable AMM types for LST liquidity and deriving formulas for the necessary returns from trading fees to adequately compensate liquidity providers under the particular price trajectories of LSTs. For the latter, two relevant metrics are considered: (1) losses compared to holding the liquidity outside the AMM (loss-versus-holding, or "impermanent loss"), and (2) the relative profitability compared to fully staking the capital (loss-versus-staking) which is specifically tailored to the case of LST-liquidity. Next, we empirically measure these metrics for Ethereum LSTs across the most relevant AMM pools. We find that, while trading fees often compensate for impermanent loss, fully staking is more profitable for many pools, raising questions about the sustainability of the current LST liquidity allocation to AMMs.
Paper Structure (44 sections, 48 equations, 9 figures, 2 tables)

This paper contains 44 sections, 48 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology and Contribution
  3. Related Work
  4. Background
  5. Liquid Staking Tokens
  6. Rebase-LST.
  7. Reward-LST.
  8. Risks of LSTs
  9. Constant Function Market Makers (CFMMs)
  10. Constant Product (CPMM).
  11. Constant Product with Concentrated Liquidity (CLMM).
  12. Stableswap Invariant.
  13. Cryptoswap Invariant.
  14. The Theory of LSTs on AMMs
  15. Suitable types of AMMs for LSTs
  16. ...and 29 more sections

Figures (9)

  • Figure 1: Required returns for different staking rates.
  • Figure 2: Historical portfolio values for the stETH-ETH pool on Curve v1: LPing in the pool (blue line), holding the initial position (orange line), and fully holding the LST (blue line). The red line indicates the average staking rate.
  • Figure 3: Historical 7 day moving average of LVH and LVS for the stETh-ETH pool on Curve v1. Color green marks periods with no loss-versus-staking (LVS) and color yellow periods with no loss-versus-holding (LVH)
  • Figure 4: Historical portfolio value of Staker (red line), HOLD (orange line), LPs (blue line) and LST holder (green line) for the cbETH-ETH pool on Curve v2, denominated in ETH
  • Figure 5: Historical market value of stETH - rebase-LSTs pegged to 1 ETH, denominated in ETH
  • ...and 4 more figures