Trail notes
- Impermanent loss is how much less a liquidity position is worth than if you had simply held the same tokens.
- In a 50/50 constant-product pool it depends only on how far the price ratio moves, not on which direction.
- The formula is IL = 2 × √r ÷ (1 + r) − 1, where r is the new price ratio divided by the starting one.
- Fees and rewards can offset it, but only if they add up to more than the loss over the time you stay in.
What impermanent loss actually measures
When you provide liquidity to a two-token pool, you hand the pool a mix of both tokens. As prices move, arbitrage traders buy whichever token is cheap in the pool and sell whichever is expensive. The pool automatically ends up holding more of the token that fell and less of the token that rose.
Impermanent loss (IL) is the gap between the value of your pool share and the value you would have had if you had just held your original tokens in a wallet. It is measured against holding, not against your starting dollars. You can make money in dollar terms and still have impermanent loss.
It is called “impermanent” because if prices return exactly to where they were when you deposited, the gap disappears. In practice, prices rarely return to exactly the same ratio when you happen to withdraw, and once you withdraw, the loss is realized. Many people prefer the term divergence loss.
The formula for a 50/50 constant-product pool
For a pool that keeps equal value in two tokens and uses the constant-product rule (x × y = k), impermanent loss depends only on r, the price ratio’s change: the new price of token A in terms of token B, divided by the price when you deposited.
IL = 2 × √r ÷ (1 + r) − 1
The result is a negative percentage: how much less your pool share is worth than holding. Fees are excluded; we add them back later.
| Price ratio change (r) | What happened (hypothetical) | Impermanent loss vs holding |
|---|---|---|
| 0.5 | Token A halves against Token B | −5.72% |
| 1.0 | No change | 0.00% |
| 1.25 | Token A up 25% | −0.62% |
| 1.5 | Token A up 50% | −2.02% |
| 2 | Token A doubles | −5.72% |
| 3 | Token A triples | −13.40% |
| 4 | Token A quadruples | −20.00% |
Two patterns stand out. Small moves cost little: a 25% move costs about 0.62%. Large moves cost a lot, and the cost grows faster than the move. And the formula is symmetric: halving (r = 0.5) costs exactly the same as doubling (r = 2), because what matters is how far the two prices diverge.
Worked example with real arithmetic
This is why impermanent loss is easy to miss. The position grew, so it can feel like a win. The honest comparison is with what you would have had without the pool. Our DEX and liquidity pools guide explains the rebalancing mechanics in more detail.
Fees vs impermanent loss
Liquidity providers earn trading fees, and sometimes reward tokens, to compensate for impermanent loss. Whether a position comes out ahead depends on three things together: how much fee income the pool generates relative to its size, how far prices diverge, and how long you stay in.
Fee rates you see quoted are usually backward-looking. They describe what a pool earned, not what it will earn. Reward tokens add another layer: their value can fall at the same time as the pool’s other token. Read yield farming 101 for how to stress-test those numbers.
Where the formula does not apply
The table above is for 50/50 constant-product pools only. Other designs behave differently:
- Weighted pools (for example 80/20) have smaller impermanent loss for the same move, in exchange for other trade-offs.
- Concentrated liquidity, where you provide liquidity only within a price range, magnifies both fees and impermanent loss. If price leaves your range, you end up holding entirely the weaker token.
- Stablecoin-to-stablecoin pools have little impermanent loss while both hold their pegs, and a large one if one of them depegs. See stablecoin depeg risk.
Impermanent loss ignores smart contract risk, gas costs to enter and exit, the chance that one token goes to zero, and taxes. A pool that looks fine on the IL table can still lose money for other reasons.
As of 2026-10-30 the CRA has published no DeFi-specific guidance on liquidity pools, LP tokens or impermanent loss. How deposits, withdrawals and fee income are treated is not addressed on its crypto-asset pages, so keep detailed records and consider professional advice. See DeFi transactions and tax.
Your checklist
Questions people ask
What is impermanent loss in simple terms?
Impermanent loss is the amount by which a liquidity pool position is worth less than simply holding the same tokens, caused by the pool rebalancing toward the token that fell as prices move.
How do you calculate impermanent loss?
For a 50/50 constant-product pool, IL = 2 × √r ÷ (1 + r) − 1, where r is the change in the price ratio. For example, r = 2 gives −5.72% and r = 4 gives −20.00%, before fees.
Is impermanent loss permanent?
It becomes permanent when you withdraw at a different price ratio from when you deposited. If the ratio returns to its starting point, the loss disappears, but there is no guarantee it will.
Can trading fees make up for impermanent loss?
Sometimes. Fees and rewards offset impermanent loss only if, over the time you stay in, they add up to more than the loss from price divergence, and both fee volume and prices can change.
Sources and dates
- Decentralized finance (DeFi) — ethereum.orgreference
No date shown on page · checked 2026-10-31. Overview of DeFi building blocks on Ethereum. - Introduction to smart contracts — ethereum.orgreference
No date shown on page · checked 2026-10-31. What a smart contract is and how it executes. - Information for crypto-asset users and tax professionals — Canada Revenue Agencyin force
Page date 2025-10-29 · checked 2026-10-30. CRA's current crypto-asset guidance set (replaced the older 'Guide for cryptocurrency users'). - Keeping books and records of crypto-assets for tax filing — Canada Revenue Agencyin force
Page date 2025-11-10 · checked 2026-10-30. What to record per transaction, wallet addresses, yearly balances; export platform history; keep records at least six years.
Education only. Nothing on this page is financial, investment, tax or legal advice, or a recommendation to buy, sell, stake, lend or borrow any crypto-asset. Crypto-assets can lose some or all of their value and are not covered by CDIC. Canadian rules change: check the dated sources above and talk to a qualified professional about your situation. Full disclaimer.