Impermanent Loss

Deposit equal value of two tokens into an AMM pool and one of them doubles in price — a liquidity provider (LP) doesn't get to fully enjoy that gain the way a simple holder would. The pool's pricing formula automatically sold some of the appreciating token into the depreciating one along the way, to keep the pool balanced. That built-in underperformance versus just holding both tokens is impermanent loss.

Why it happens

A constant-product pool ($x \times y = k$) rebalances automatically: as one token's price rises relative to the other, arbitrageurs buy the now-underpriced token from the pool until the pool's ratio matches the outside market price again. That arbitrage is exactly what makes the pool track fair value — but from the LP's chair, it means the pool is always selling the winner and buying the loser as prices move, the opposite of what a buy-and-hold investor would choose to do.

$$\text{IL} = \frac{2\sqrt{r}}{1 + r} - 1$$

In words: if $r$ is the ratio of how much one token's price has changed relative to the other since deposit, this formula gives the percentage loss versus simply holding — it's zero when $r = 1$ (no price change) and grows (more negative) the further the price ratio drifts in either direction.

Worked example

An LP deposits $10,000 ($5,000 of ETH, $5,000 of USDC) into an ETH/USDC pool. ETH then doubles in price relative to USDC — so $r = 2$.

1. Impermanent loss. $\frac{2\sqrt{2}}{1+2} - 1 = \frac{2.828}{3} - 1 \approx -0.0572$, about -5.7%.
2. Holding value. $5,000 of ETH is now worth $10,000; $5,000 of USDC is still $5,000. Total if held: $15,000.
3. LP position value. $15,000 scaled down by the loss, $1 - 0.057 = 0.943$, gives roughly $14,150 — about $850 less than simply holding, purely from the pool's automatic rebalancing, before counting any trading fees earned.

What this means in practice

LPs are compensated for taking this risk through trading fees earned on every swap that passes through the pool, and the real question for any LP position is whether accumulated fees outpace the impermanent loss over the holding period — for volatile pairs this is far from guaranteed, which is why LPs gravitate toward pairs expected to stay correlated (stablecoin pairs, or two versions of the same asset) where the price ratio barely moves and impermanent loss stays small.