Impermanent loss
The badly named cost of supplying liquidity. It is not impermanent, it is not a loss in the ordinary sense, and it is the reason most providers underperform holding.
Supply two assets to a pool and you earn a share of trading fees. You also end up with a different mix of assets than you deposited, and that rebalancing has a cost. The cost is called impermanent loss, and both words are wrong.
Why the composition changes
The pool keeps the product of its two balances constant, so arbitrageurs trade against it whenever the outside price moves. They buy whichever asset has become cheap in the pool. You, as a provider, are automatically selling the asset that is rising and buying the one that is falling.
Deposit 1 ETH and 100 USDC into a pool when ETH is worth 100 USDC. Your deposit is worth 200 USDC, and k = 100.
ETH then doubles to 200 USDC on the wider market. Arbitrage rebalances the pool to roughly 0.707 ETH and 141.4 USDC (0.707 × 141.4 ≈ 100).
Your pool share is worth 0.707 × 200 + 141.4 = 282.8 USDC.
Had you simply held 1 ETH and 100 USDC, you would have 200 + 100 = 300 USDC.
The gap is 17.2 USDC, about 5.7%. That is impermanent loss, before fees.
Why the name is wrong twice
It is called impermanent because the gap closes if prices return to where they started. They frequently do not, and withdrawing crystallises the difference exactly as selling crystallises a paper loss. It is called a loss although you may still be up in absolute terms — you simply have less than holding would have given you. Both features of the name systematically make it sound smaller than it is.
The shape of it
- Price changes 1.25× → roughly 0.6% below holding
- Price changes 1.5× → roughly 2.0% below holding
- Price changes 2× → roughly 5.7% below holding
- Price changes 4× → roughly 20.0% below holding
- Price changes 5× → roughly 25.5% below holding
The effect is symmetric: a halving costs the same as a doubling. It depends only on the ratio of the two prices changing, which is why pools of two assets expected to move together — two dollar stablecoins, or an asset and its staked version — carry so much less of it.
When fees make up for it
Providers are paid a share of every trade. Whether that beats the divergence cost depends on volume relative to pool size, and on how far prices move over the period.
A pool paying an eye-catching annual percentage is usually doing so because the assets in it are volatile, because rewards are being paid in a token whose price is falling, or both. A yield quoted without the price behaviour of the underlying pair is not information.
The position you actually hold
Mathematically, supplying liquidity resembles having sold a straddle: you are paid a premium — the fees — and you lose when the price moves substantially in either direction. Anyone who has read the options stage will recognise the payoff, and it is a far better mental model than thinking of it as a deposit.