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Impermanent Loss & LP Risk Modeling

Concrete IL math, hedging, and the LVR (Loss-Versus-Rebalancing) view of concentrated liquidity.

30 min · advanced · part of DeFi Deep Dive: Lending, AMMs & Yield

The Cost of Being an LP

Liquidity providing looks like a passive income strategy. You deposit two assets, you earn trading fees, you withdraw later. In practice, there is a structural cost that most beginner LPs ignore until it has eaten a meaningful fraction of their position: **impermanent loss**. The name is misleading. IL is "impermanent" only in the sense that it would vanish if the price ratio returned to where it was when you deposited. The moment you withdraw, whatever IL exists at that moment becomes permanent. For most LP positions held through a meaningful price move, the loss is realized. The deeper framing — recent academic work refers to it as **Loss-Versus-Rebalancing (LVR)** — is that an LP is structurally adverse-selected against arbitrageurs. Every time the off-chain market price moves, an arbitrageur takes value out of the pool by trading until the pool's implied price matches the external price. That value is the LP's cost. Fees earned from organic (non-arbitrage) trading need to exceed this cost for LPing to be net-profitable. This lesson walks through the math of IL with concrete numbers, gives you a hedging primer, and explains why concentrated-liquidity LPs face a particularly sharp version of the problem via LVR.

Also in this lesson

  • 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.

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Educational only — not financial advice.