Impermanent loss is how much less a liquidity pool deposit is worth than the same tokens would be if you had kept them in a wallet. It happens when the prices of the two pooled tokens move apart. In a standard 50/50 pool, a doubling of one token leaves the deposit about 5.7% behind holding, and a fivefold move leaves it about 25.5% behind. You measure the loss against holding, not against what you put in. So a pool position can go up in dollars and still show impermanent loss. Trading fees can make up some or all of the gap. In the largest public study of concentrated-liquidity pools, they did not.
How the loss arises
An automated market maker (AMM) lets people trade tokens against a liquidity pool instead of matching buyers with sellers. Avalanche Support says a "constant mathematical formula" sets the price between the two tokens. The most common formula is the constant product: the pool's two balances, x and y, must always multiply to the same number, k (x × y = k).
When a token's price changes on the wider market, the pool's price is briefly out of line with it. Arbitrage traders buy the cheaper token from the pool until the two prices match again. That means the pool keeps selling whichever token is rising and buying more of whichever is falling. The liquidity provider ends up with more of the weaker asset and less of the stronger one. Avalanche Support says the loss is "driven by the disparity between the external market price of an asset and its price within the liquidity pool."
The formula and what it gives
For a 50/50 constant-product pool, NIF Academy gives this formula:
Impermanent loss = 2 × √r / (1 + r) − 1
Here r is the new price ratio divided by the starting ratio. The result is negative, and its size is the loss compared with holding. A move of r and a move of 1/r give the same loss, so a halving costs as much as a doubling.
| Price change of one token (r) | Loss versus holding |
|---|---|
| 1.25x | 0.6% |
| 1.5x | 2.0% |
| 2x or 0.5x | 5.7% |
| 3x | 13.4% |
| 4x | 20.0% |
| 5x | 25.5% |
NIF Academy gives the 2x, 0.5x and 5x figures. The other rows are worked out from the same formula. All of them leave out fees and rewards.
A $10,000 worked example
NIF Academy's example starts with 2 ETH at $2,500 each and $5,000 in USDC, so $10,000 in total. ETH then doubles to $5,000. Arbitrage leaves the pool position with about 1.41 ETH and about $7,071 in USDC, worth about $14,142. The original tokens held in a wallet would be worth $15,000. The $858 difference is 5.7% of the holding value.
To get the dollar gap for any 50/50 deposit:
Gap = deposit × ((1 + r) ÷ 2 − √r)
On $10,000 this gives $858 at 2x, $429 at 0.5x and $7,639 at 5x. The formula assumes one token moves while the other, such as a stablecoin, holds its value.
Impermanent loss in dollars: pool versus holding
How much would your deposit trail simply holding after one token's price changes?
| Your deposit, split 50/50 at entry | New price ÷ old price of the moving token (r) | Gap versus holding |
|---|---|---|
| 10,000 USD | 2 x | 858 USD |
| 10,000 USD | 0.5 x | 429 USD |
| 10,000 USD | 5 x | 7,639 USD |
- The deposit is split equally in value between the two tokens at entry.
- Only one token's price changes. The other token holds its value.
- r is the new price of the moving token divided by its old price.
- Trading fees and reward tokens are left out.
The result applies to a standard 50/50 constant-product pool and leaves out trading fees.
When "impermanent" becomes permanent
The loss shrinks back to zero only if the price ratio returns exactly to where it was when you deposited. If you withdraw at any other ratio, the loss is locked in. The word "impermanent" describes that one narrow case.
Do trading fees cover it?
Fees are what liquidity providers earn in exchange for taking this risk. Whether they cover the loss depends on how much trading the pool sees and how far prices move.
The main dataset is a paper by Stefan Loesch, Nate Hindman, Mark B. Richardson and Nicholas Welch, published on arXiv on 17 November 2021. It studied 17 pools on a concentrated-liquidity decentralised exchange, chosen by size, which together held 43% of that exchange's total value locked. From each pool's launch to the study's cut-off date:
- Liquidity providers earned $199.3 million in fees.
- They lost $260.1 million to impermanent loss.
- In total, they would have been $60.8 million better off holding.
The paper also says concentrated liquidity raises both the fees a provider can earn and the impermanent loss they face. Narrow price ranges make both effects larger.
Later research describes the same cost in a different way. In "Automated Market Making and Loss-Versus-Rebalancing" (first posted 11 August 2022, last revised 20 August 2026), Jason Milionis, Ciamac C. Moallemi, Tim Roughgarden and Anthony Lee Zhang split a provider's return into two parts: market exposure, plus fees minus losses to arbitrageurs. When they applied this to an ETH-USDC pool, market-risk exposure explained more than 99.99% of the variance in provider returns. Put simply, a pool position mostly behaves like holding the tokens. The fee edge is small and has to be weighed against what arbitrage takes.
Where the risk is smaller or larger
- Correlated or stable pairs. If two tokens tend to move together, r stays close to 1 and the loss stays small. NIF Academy calls stablecoin pools "the closest thing DeFi has to a low-risk yield." It adds that they still carry smart-contract risk and depeg risk, which have nothing to do with impermanent loss.
- One token you expect to rise sharply. The pool keeps selling that token as it climbs. A 5x move costs about a quarter of the holding value before fees.
- Concentrated ranges. Fees and losses are both larger than in a full-range pool.
- Compensation schemes. Avalanche Support notes that some platforms pay providers extra tokens or extended earnings to offset impermanent loss. It says these schemes vary and are not guaranteed.
A quick check before depositing: work out the loss for the price move you think is plausible, using the table or the formula above. Then ask whether the pool's realistic fee income over the same period would cover it. For the role itself, see what a liquidity provider does.
The formulas here hold only for 50/50 constant-product pools before fees, and the fee-versus-loss totals come from one 2021 study of 17 pools.
