What is impermanent loss?

The shortfall a liquidity provider takes when the prices of the two assets they deposited move apart, measured against simply holding them.

It affects anyone supplying liquidity to a dex pool. The loss becomes permanent on withdrawal, and trading fees earned may or may not offset it.

The name is unhelpful. Nothing about the loss is temporary except in the narrow sense that it disappears if the price ratio returns to where you entered. A clearer description is divergence loss: the more the two assets move apart, the further behind holding you end up, and the effect is entirely mechanical rather than a matter of bad luck.

How it works

A constant product pool holds two assets and enforces that the product of the two reserves stays fixed as trades occur, the formula described in the Uniswap v2 documentation. When an outside price moves, arbitrageurs trade against the pool until its ratio matches, and they take the difference. The pool ends up holding more of whichever asset fell and less of whichever asset rose.

That rebalancing is automatic and always in the wrong direction for the depositor. You are, in effect, selling the winner as it rises and buying the loser as it falls. The shortfall depends only on how far the price ratio moved, not on the path it took to get there.

For a constant product pool, if the price ratio changes by a factor of k, the value of your position relative to holding is 2 times the square root of k, divided by 1 plus k. Run a few values and the shape is clear.

Fees are the offset. A pool earning a share of every trade can out-earn the shortfall when volume is high and prices are range-bound, and cannot when one asset trends hard. Concentrated liquidity designs raise both the fee income and the divergence exposure within the chosen range.

Example

Worked arithmetic on the constant product formula. You deposit 1 ETH and 2,000 USDC when ETH trades at $2,000, so your position is worth $4,000 and the product of reserves is 2,000.

ETH then rises to $4,000. Arbitrage rebalances the pool until the ratio matches, leaving about 0.707 ETH and 2,828 USDC, since 0.707 times 2,828 still equals roughly 2,000. Your position is now worth 0.707 times $4,000 plus $2,828, which is $5,657.

Had you simply held, you would have 1 ETH worth $4,000 plus 2,000 USDC, which is $6,000. The difference is $343, or 5.7 percent, matching the table above. Fees earned over the period are subtracted from that shortfall.

Why it matters when you buy

Advertised pool yields are quoted as fee income and rarely net of divergence, so a headline rate is not a return. If you are choosing between providing liquidity and holding, the comparison depends on how far the pair moves, which is a volatility question. The liquidity view shows measured market conditions per asset, and stablecoin yield risks covers how advertised yields are constructed.

Related terms

• liquidity pool: the contract your deposit sits in
• automated market maker: the pricing rule that rebalances it
• lp token: the claim you redeem to realize the loss
• concentrated liquidity: narrower ranges, higher fees and exposure
• yield farming: incentives layered on top of fees
• volatility: the variable that drives the shortfall

Questions

Does the loss go away if I wait?

Only if the price ratio returns to where you entered. Otherwise it is realized in full when you withdraw, whatever the pool is called.

Is a stablecoin pair immune?

Nearly, while both hold their pegs, because the ratio barely moves. If one depegs, the pool rebalances into the failing asset exactly as it would with any other divergence.

Do fees usually cover it?

Sometimes. High volume against a range-bound pair favors the provider, and a strong trend in one asset does not. It is an empirical question per pool, not a rule.