Quant Memo
Core

LP Range Selection and Rebalancing

Concentrated liquidity AMMs let a provider choose the exact price range their capital is active in, and that choice trades off fee income against how often the price wanders outside the range and stops earning anything at all.

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Prerequisites: Delta-Neutral Liquidity Provision

In a concentrated liquidity AMM like Uniswap v3, a liquidity provider doesn't have to spread capital across every possible price from zero to infinity — they can pick a specific band, say $1,800 to $2,200 for ETH, and their capital only earns trading fees while the price stays inside that band. Pick a narrow band and the same dollar of capital earns far more in fees per trade, because it's concentrated where trading actually happens. Pick too narrow a band and the price frequently drifts outside it, where the position earns nothing and sits fully in one asset until someone actively moves the range back.

A narrow range multiplies fee income while the price stays inside it, but it also multiplies the fraction of time the position spends inactive once the price wanders out. Range width is a direct trade-off between capital efficiency and how often you have to actively manage the position.

The trade-off in one picture

price narrow range: high fee density, exits often wide range: lower density, stays active current price
The narrow band earns more fees per dollar while price stays inside it, but goes idle the moment price exits — the wide band trades fee density for staying active longer.

Worked example

An LP has $100,000 to deploy into an ETH/USDC pool with ETH at $2,000. Two options:

Narrow range ($1,900-$2,100, a 10% band): concentrated capital earns roughly 4x the fee rate of a full-range position while active, but backtests on recent volatility suggest price stays inside this band only about 55% of the time before needing a manual rebalance.

Wide range ($1,600-$2,400, a 40% band): earns closer to 1.3x the full-range fee rate, but stays inside the band around 90% of the time.

Expected fee capture (rough): narrow ≈4×0.55=2.2\approx 4 \times 0.55 = 2.2 full-range-equivalent units; wide ≈1.3×0.90=1.17\approx 1.3 \times 0.90 = 1.17 units. On paper the narrow range wins on expected fees — but every time it exits the band, the LP must actively rebalance (a transaction cost, plus the position sits idle until it does), and each rebalance also realizes the paper loss from being on the wrong side of concentrated liquidity's version of impermanent loss.

What this means in practice

Active LPs treat range selection as an ongoing job, not a set-and-forget decision — narrower ranges need frequent rebalancing (and the gas or transaction costs that come with it) and are better suited to lower-volatility pairs like stablecoin-to-stablecoin, where the price rarely leaves even a tight band.

Backtesting a range width against historical volatility only works if future volatility resembles the past — a range sized for calm markets can spend most of a volatile period sitting idle out-of-range, earning nothing while still carrying the concentrated position's exposure to whichever asset the price has drifted toward.

Related concepts

Practice in interviews

Probability →Market Making →

Further reading

  • Adams et al., Uniswap v3 Core (concentrated liquidity)
  • Loesch et al. (2021), Impermanent Loss in Uniswap v3
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