Impermanent loss
Impermanent loss is the difference between the value of a liquidity pool position and the value the same tokens would have if you had simply held them. It appears whenever the prices of the two pooled tokens move apart, and it is measured before trading fees.
Impermanent loss calculator
How it works
A constant-product pool, the design used by Uniswap v2 and most of its forks, holds two tokens and keeps the product of their quantities fixed (x × y = k). In a 50/50 pool that means the two sides are always worth the same amount in dollars. The pool has no view of outside prices. It only learns a new price when someone trades against it, and that someone is usually an arbitrageur who buys the underpriced token from the pool until its price matches other venues.
The result is that a liquidity provider (LP) is continuously selling the token that rises and buying the token that falls. Impermanent loss is the gap this creates between the pool position and a wallet that held the original tokens untouched.
For a 50/50 constant-product pool, the gap depends only on how far the price ratio between the two tokens has moved since you deposited. If the ratio has changed by a factor r:
Impermanent loss = 2 × √r ÷ (1 + r) − 1
The calculator above applies this formula. It takes the price change of each token, so it also handles the case where both tokens move: what matters is the ratio, not the direction of the market. If both tokens double, r = 1 and the loss is zero.
| Price change of one token (other flat) | Price ratio r | Pool vs. holding |
|---|---|---|
| +10% | 1.10 | −0.11% |
| +25% or −20% | 1.25 or 0.80 | −0.62% |
| +40% | 1.40 | −1.40% |
| +50% | 1.50 | −2.02% |
| +100% or −50% | 2.00 or 0.50 | −5.72% |
| +200% | 3.00 | −13.40% |
| +400% or −80% | 5.00 or 0.20 | −25.46% |
A doubling and a halving produce the same shortfall, because both are a factor-of-two change in the ratio. For small moves the loss grows roughly with the square of the price change, so a move twice as large costs about four times as much.
A worked example
You deposit $10,000 into a pool of a volatile token and USDC: $5,000 of each. The token then doubles and USDC stays at $1. These are the calculator's default inputs.
- If you had held: $5,000 × 2 + $5,000 = $15,000
- In the pool: $10,000 × √2 = $14,142.14
- Shortfall: $14,142.14 ÷ $15,000 − 1 = −5.72%, or $857.86
The pool position is up $4,142 in dollars, which is why the loss is easy to miss. The right benchmark is holding the same tokens, not the $10,000 you started with.
Now the bad direction. The token falls 80% instead. Holding is worth $1,000 + $5,000 = $6,000. The pool is worth $10,000 × √0.2 = $4,472.14, a shortfall of −25.46%. The pool kept buying the token on the way down, so you end up with mostly the asset that lost value.
Fees have to cover this. Suppose the pool advertises 20% APY. Over one month that is about 20% ÷ 12 = 1.67% if the rate holds. A month in which the token doubles costs 5.72%, more than three months of that yield. A 40% move, by contrast, costs 1.40%, less than the 4–5% that is sometimes quoted for it.
What it means in practice
Advertised APY is gross. It counts fees and reward tokens and subtracts nothing for impermanent loss, so the net return of an LP position is the yield actually earned minus the shortfall against holding.
Pair choice sets most of the exposure. Two tokens that move together, such as two stablecoins or ETH and a liquid staking version of ETH, keep the ratio near 1, where the curve is almost flat. A volatile token paired with a stablecoin sits on the steep part of the curve every time the market moves.
The name "impermanent" refers to the fact that the endpoint gap closes if the ratio returns to where it was when you deposited. That only describes the endpoint. Research on loss-versus-rebalancing (LVR) measures what the pool gives up to arbitrageurs on every price update along the way. For a constant-product pool it scales with variance: roughly σ² ÷ 8 of pool value per year, so about 2% at 40% annualized volatility, 8% at 80% and 18% at 120%. Doubling volatility quadruples the drag, while fee income only grows with volume.
Concentrated liquidity (Uniswap v3 and similar) multiplies both fee income and impermanent loss inside the chosen range. If price leaves the range, the position is entirely in the weaker token and stops earning fees.
When it matters most
Impermanent loss matters most in sharp, one-directional moves in a volatile pair, and when realized volatility is well above what the pool's fee level was set for. Those are also the weeks when trading volume and displayed APY spike, so the headline yield tends to look best exactly when the loss is largest.
Stablecoin pools are usually safe from it, with one exception: a stablecoin depeg. If one coin in a two-stablecoin pool loses its peg, arbitrageurs sell it into the pool and withdraw the healthy coin, and LPs end up holding mostly the broken one.
Common misconceptions
"It isn't a real loss until I withdraw." The shortfall exists at every moment and is realized when you withdraw. If the ratio comes back, the endpoint gap closes, but the value already handed to arbitrageurs along the path does not come back.
"Fees always cover it." In calm, high-volume pools of correlated assets they often do. In volatile pairs a single large move can cost more than months of fees, and fees accrue slowly while the loss arrives in days.
"If the price goes up, I can't have impermanent loss." Direction does not matter. A doubling costs exactly as much as a halving, and if both tokens rise by different amounts the ratio still moves.
"Impermanent loss means I lost money." It means you have less than if you had held. A pool position can be up in dollars and still show a large impermanent loss.