Liquidity, where
the arithmetic works
Range orders in pools where the fee tier more than covers the volatility cost. We size bands to the tick grid rather than to a round percentage, and we decline the pools where the arithmetic loses, which is most of them.
A liquidity position earns fees and pays loss-versus-rebalancing. The test is a single inequality: fee APR must exceed volatility squared over eight, multiplied by the position's concentration. Concentration scales both sides, so tightening a band never improves the ratio; it only scales the bet.
That inequality is why we hold stable-stable pools and decline volatile pairs. At ETH's realised volatility of roughly 53%, a ±20% band carries a 36% annual drag and needs two turns of its own TVL trading every day to break even. The deepest ETH/USDC pool runs 0.58. The pool is not mispriced; it is simply not a business.
Where both legs are dollars, volatility is near zero, the drag effectively vanishes, and fee income is close to pure return. That is a narrow universe, and it is the one we operate in.
The test
| Volatility | Full range | ±50% | ±20% | ±10% |
|---|---|---|---|---|
| 30% | 1% | 5% | 12% | 23% |
| 53%, ETH | 4% | 15% | 36% | 72% |
| 100% | 12% | 52% | 130% | 255% |
| 150%, small cap | 28% | 117% | 292% | 575% |
Annual loss-versus-rebalancing by volatility and band width. The fee APR has to clear the cell.