My friend Pim van Vliet, who runs some great low-volatility funds at Robeco, has a casual interest in crypto. My paper on Thorchain was long and replete with parochial concepts, so he asked ChatGPT to summarize it and sent me the summary. I found it was probably better than I would have written. I don’t think ChatGPT is going to fundamentally change the world anymore than word processors, databases, or the internet have, but they are great at summarizing. Below is ChatGPT’s summary of the paper I recently posted on SSRN.
Comments and questions appreciated.
Promotes two practical ways to measure LP’s gamma expense, aka theta:
Markout theta: LP PnL from net token flows marked to a future price, minus fees.
Liquidity-Variance (LVR) theta: a Black–Scholes–style gamma cost proportional to liquidity × price variance.
These estimators have the same expected value but use different inputs and can be computed solely from swap event logs, thereby avoiding costly CEX data joins.
Proposes theta/fees (expense-to-revenue ratio) as the correct cross-pool LP performance metric, avoiding ambiguous metrics like APY and raw PnL, or PnL in basis points.
v2 LPs are profitable: average theta/fees ≈ 0.58 (expenses well below revenue).
v3 LPs are unprofitable:
5 bp pools: theta/fees ≈ 1.14
30 bp pools: theta/fees ≈ 1.10
These losses are:
Stable over time
Invariant to fee tier (5 vs 30 bp)
Invariant to blockchain latency (Ethereum vs Arbitrum/Base)
Not explained by excess liquidity once pool-specific anomalies are controlled.
Identifies JIT / ephemeral liquidity spikes that can distort daily estimates.
Shows that simple filters (median liquidity, excluding extreme spikes) recover results comparable to high-frequency markouts.
Demonstrates that three to six months of data are sufficient to reduce the simple estimator standard errors to those generated by the most costly 5-second markout PnL estimator (~0.1 in theta/fees).
Arbitrage profits exceed LP losses on v3 pools.
Roughly:
50–55% of arb profits come from large, rare trades
~50% of total arb profit comes from reversing uninformed retail trades, not from LP gamma extraction.
Lower block times and dynamic or higher fees do not improve LP profitability.
Front ends that divert order flow to off-chain auctions reduce LP revenue without reducing LP theta.
Sustainable AMMs require:
Honest measurement of LP gamma costs
Mechanisms that retain or internalize retail flow
Recognition that arbitrage adapts endogenously to fees and latency.
Profitable AMMs are possible (v2 proves this), but v3 equilibrium liquidity provision is structurally loss-making.
Progress is blocked less by theory than by systematic under-measurement and misreporting of LP performance.
“You can’t fix what you don’t measure.”
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