Liquidity pools and impermanent loss

What is a liquidity pool?

A liquidity pool is a smart contract holding two tokens that traders can swap against, the engine behind AMM-based decentralized exchanges such as Uniswap. In Uniswap v2 a liquidity provider deposits both tokens in equal value and receives pool tokens representing a pro-rata share of the reserves. A 0.30% fee on every trade is added to the reserves, so each LP's share slowly grows if the pool is busy.

The price inside the pool is set by the constant-product rule x × y = k. Prices only change when someone trades, and Uniswap's documentation explains that when the pool's price diverges from prices elsewhere, arbitrage traders step in until the two line up. Those arbitrage trades are what create impermanent loss.

What is impermanent loss, in plain terms?

Say ether rises on every other exchange. Arbitrage traders buy the now-cheap ether from your pool and pay in the other token until the pool's price catches up. The pool — and therefore your share of it — ends up holding less ether and more of the other token. You kept a smaller stake in the asset that went up.

Uniswap's own documentation shows it with small numbers. An LP owns 1% of a pool holding 100 ETH and 10,000 DAI, so their share is 1 ETH plus 100 DAI. ETH then rises from 100 to 120 DAI. The LP can now withdraw about 0.9129 ETH and 109.54 DAI, worth 219.09 DAI. Had they just held 1 ETH and 100 DAI, they would have 220 DAI. The 0.91 DAI gap is impermanent loss.

It is called impermanent because, as Uniswap notes, it vanishes if the price returns to where it was when the liquidity was added. It becomes a permanent, realized loss if you withdraw while the price is still away from that level.

How large can impermanent loss get?

For a standard 50/50 constant-product pool, the loss depends only on how far the price ratio has moved from your entry, not on the direction. The figures below are our calculations from the constant-product formula, before fees; we checked them against Uniswap's worked example above, which the same calculation reproduces exactly.

Two patterns stand out. Small moves cost little, but the loss accelerates as the move grows. And a halving hurts exactly as much as a doubling, because what matters is the ratio between the two tokens.

Can trading fees make up for impermanent loss?

Sometimes. Fees accumulate with every trade, while impermanent loss depends on how far prices drift. A busy pool whose two tokens move together — two dollar stablecoins, for instance — can collect fees with little rebalancing. A quieter pool pairing a volatile token with a stablecoin can lose more to price moves than it earns.

Uniswap's documentation is candid that the trade-off between fee income and losses from directional moves is hard to know without knowing how much trading will happen. Advertised pool returns are usually based on past fees and say nothing about future price moves.

Concentrated liquidity adds another variable. In Uniswap v3 you choose a price range. While the price is inside it, your capital works harder; once the price leaves the range, your position stops earning fees and ends up entirely in one of the two tokens until the price comes back.

What mistakes do new liquidity providers make?

• Counting only the fees. Always compare the LP position with what you would have had by holding, not with what you started with in dollars.
• Thinking "impermanent" means "temporary". It is only temporary if prices return. Many never do.
• Ignoring the pair. A pool with a volatile, thinly traded token exposes you to large ratio moves and to that token's own risks, including a rug pull.
• Setting a narrow range and walking away. In concentrated pools a price move can push you out of range, where you earn nothing.
• Forgetting contract risk. Pool contracts can be exploited; see the main risks of DeFi.