What is impermanent loss?

Impermanent loss is the gap between what an AMM liquidity provider ends up with and what they would have had if they had just held the two tokens in a wallet. It is not a fee. It is a mathematical consequence of the way AMM pools rebalance as prices move. The name is misleading — the loss becomes permanent the moment you withdraw — and it is the single most important concept any would-be LP needs to understand.

Where the loss comes from

Consider a Uniswap v2 pool with ETH at 2,000 dollars. An LP deposits 1 ETH and 2,000 USDC, total value 4,000 dollars. The pool's formula keeps the product of the two reserves constant, so as ETH rises, the pool's ETH balance gets sold down in exchange for USDC, and vice versa.

Now suppose ETH doubles to 4,000. Traders arbitrage the pool: they buy ETH from the pool while it is still quoting the old price, dragging the pool's price up toward 4,000. When the dust settles, the pool rebalances to the new price. Plug into the formula: the LP's share is now roughly 0.707 ETH and 2,828 USDC, total value about 5,657 dollars.

If the LP had just held 1 ETH and 2,000 USDC, they would have 1 ETH at 4,000 plus 2,000 USDC, total value 6,000 dollars. The difference — 343 dollars, about 5.7 percent — is the impermanent loss. The LP did not lose money in absolute terms. They lost money relative to holding.

The formula, in one sentence

For a constant-product pool with price ratio change of r (from entry to exit), the impermanent loss is 2 times the square root of r, divided by 1 plus r, minus 1. The math works out to: the loss is about 0.5 percent if the price doubles in either direction, 2 percent if it quadruples, 5.7 percent at a five-x, and 13 percent at a ten-x.

The shape of the curve matters. Impermanent loss is symmetric — it does not care whether ETH goes up or down — and it grows roughly with the square of the log of the price move. Small moves are cheap. Big moves are painful.

Fees are the compensation

The whole reason anyone provides liquidity despite impermanent loss is that LPs earn trading fees. On a busy pair — ETH/USDC, ETH/USDT, stETH/ETH — fees can add up to several percent of the position's value per year, which often exceeds the expected impermanent loss at observed volatility. The question for an LP is whether expected fees exceed expected IL over the holding period.

In practice, on the highest-volume Uniswap v3 ETH/USDC pool, well-managed concentrated positions have historically earned enough fees to outperform simple holding. On long-tail pairs, or on pools where one token trends strongly against the other, LPs often lose. The average retail LP — especially in concentrated v3 positions they never rebalance — has been shown in several research papers to underperform holding.

Stable pairs and correlated assets

Impermanent loss is minimized when the two tokens in the pool move together. USDC/USDT is the canonical example: both assets are dollar-pegged, so the ratio barely moves, and LP fees are nearly pure yield. stETH/ETH is similar — Lido's liquid staking token trades close to ETH by construction, so the pool's ratio drifts only slowly.

Curve's StableSwap formula was designed specifically for these pairs, giving much tighter pricing near parity and much lower IL when prices hold. When stETH briefly depegged in mid-2022 during the 3AC and Celsius unwinds, Curve's stETH/ETH pool filled up with stETH as LPs effectively bought the depegged asset. That was a concentrated instance of impermanent loss turning permanent.

Concentrated liquidity amplifies it

Uniswap v3's concentrated liquidity lets an LP earn more fees on less capital — but if price leaves the chosen range, the position goes fully into the losing side of the pair. An LP providing ETH/USDC between 3,000 and 4,000 who does not adjust their range when ETH climbs past 4,000 ends up with pure USDC and no upside. The IL, in that case, is as bad as if they had sold at the top of the range and held dollars.

Active management — Arrakis, Gamma, Maverick, Merkl — tries to solve this by rebalancing the range, but rebalancing itself realizes losses. There is no free lunch.

What LPs can do about it

The standard mitigations are: provide to correlated pairs (stables, LST pairs); size positions you can afford to hold through the IL; treat LPing as a volatility-selling strategy rather than a yield strategy; and track your position in terms of "hold vs. LP" not "dollar PnL." Tools like Revert Finance make this comparison explicit.

For the sophisticated LP, impermanent loss is a feature of the contract being sold. An AMM LP is implicitly writing an option on the pair's relative price; the fees are the option premium. If the premium is priced above the fair value of the option, the LP makes money over time. If not, the LP loses, slowly or quickly.

Why it matters

"Liquidity provision" sounds passive and staking-like. It is neither. It is an active market-making strategy with a specific risk profile, and users who treat it as yield farming without understanding impermanent loss frequently end up worse than if they had just held. Fees make IL bearable; they do not make it disappear. The honest LP mental model is: you earn a spread on trades in exchange for bearing the convexity cost of the pool. Whether that trade is good depends on the pair, the fees, and the volatility.