  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.
