Impermanent Loss & LP Risk Modeling

What you'll learn

• The Cost of Being an LP
• IL Math: Concrete Numbers
• Concentrated Liquidity IL: It's Worse
• Loss-Versus-Rebalancing: The Academic View
• Hedging IL: A Practical Primer
• What to Remember

Key terms

Impermanent loss (IL)

The opportunity cost of providing liquidity to an AMM versus simply holding the underlying assets. Becomes permanent when the LP withdraws.

IL formula (50/50 pool)

For a constant-product LP, IL = 2·√r / (1 + r) − 1, where r is the new-price-to-old-price ratio. A 2x move yields ~5.72% IL; a 4x move yields ~20% IL.

Loss-Versus-Rebalancing (LVR)

A rigorous reformulation of LP cost as the value continuously extracted from the pool by arbitrageurs. Approximately σ² / 8 per year on a constant-product pool; recent academic work has formalized this.

Delta hedging

Offsetting the directional exposure of an LP position by taking an opposite (typically short) position in the underlying asset, usually via a perp. Requires continuous rebalancing because LP delta changes with price.

Concentrated-liquidity leverage

The effective capital efficiency multiplier produced by narrowing a V3/V4 LP range. Boosts both fees and IL/LVR exposure proportionally.

Range exit

On Uniswap V3/V4, the event when price moves outside an LP's chosen range. The position becomes 100% one asset and stops earning fees until rebalanced or price returns to range.

Static hedge

A one-time delta-neutralizing trade taken at LP deposit (typically a perp short for half the LP's underlying-asset value). Approximately neutral at entry but drifts as price moves.

Arbitrageur

A trader whose business is to keep AMM pool prices aligned with off-chain market prices by trading against pools whenever a profitable spread exists. The counterparty extracting LVR from LPs.