Definition
Impermanent loss is the shortfall a liquidity provider has compared with simply holding the same tokens, caused by a change in the price ratio of the tokens in the pool.
How it works
In an automated market maker pool, traders buy the token that is rising from the pool and sell the token that is falling into it. As a result, the pool holds less of the token that gained and more of the token that lost. When a liquidity provider withdraws, they get back a different mix than they deposited, and that mix is worth less than the original tokens would be worth if they had simply been held.
For a standard 50/50 constant-product pool, the loss depends only on how far the price ratio moved, not on the direction: impermanent loss = 2 × √r ÷ (1 + r) − 1, where r is the new price ratio divided by the old one. A doubling (r = 2) gives about −5.7%, a fourfold rise (r = 4) gives −20%, and a fall to half (r = 0.5) gives the same −5.7% as a doubling. Pools with other weights or concentrated liquidity follow different formulas.
The loss is called impermanent because it shrinks if the ratio returns to where it started. It becomes realized once the provider withdraws at a different ratio. Trading fees earned by the pool can offset it partly, fully or not at all, so the yield shown for a pool is not the provider's net result.
Example (hypothetical numbers)
Suppose you deposit 10 Token X at $100 each and 1,000 stablecoins worth $1 each into a 50/50 pool, $2,000 in total.
Token X doubles to $200 (r = 2). Simply holding would be worth 10 × $200 + $1,000 = $3,000.
The pool rebalances to about 7.071 Token X and 1,414.21 stablecoins, which are worth 2 × $1,414.21 ≈ $2,828.43.
Impermanent loss = $2,828.43 ÷ $3,000 − 1 ≈ −5.7%, matching 2 × √2 ÷ (1 + 2) − 1, or about $171.57 before fees.
The position still gained in dollars, but it earned less than holding; only trading fees could close the gap.
Common mistakes
- Comparing the pool's value with the original deposit instead of with simply holding the same tokens.
- Assuming the loss will disappear because it is called impermanent.
- Looking at the fee yield alone without estimating the loss from a large price move.
Related calculators
This glossary is for education only and is not investment advice. Examples use hypothetical numbers.