Impermanent loss is the difference between what a liquidity provider’s deposited assets are worth if withdrawn from a pool, and what those same assets would be worth if the provider had simply held them in a wallet. It is calculated with the formula IL = 2×√d/(1+d) − 1, where d is the ratio between the token’s price at withdrawal and its price at deposit, according to Coinbase Learn’s glossary entry, BydFi’s guide (published 13 April 2026) and Speedrun Ethereum’s guide, all of which state the identical formula. Chainlink’s education page (last updated 6 April 2026) does not write out this closed-form equation, but demonstrates the same result through the constant-product formula and a worked numerical example, described below.
Why it happens
Most standard decentralized exchanges use a constant-product formula, written as x × y = k, where x and y are the quantities of the two pooled tokens and k is fixed after every trade, per Chainlink and Speedrun Ethereum. The pool itself does not know the external market price. When that outside price moves, the pool’s internal price only catches up because arbitrage traders step in: if ETH becomes more expensive on the open market than inside the pool, traders buy ETH from the pool until its internal price matches the outside one, per Chainlink. That buying removes ETH from the pool and adds the other token, so the liquidity provider ends up holding less of the asset that rose in price and more of the one that fell, per Chainlink and Speedrun Ethereum. The arbitrageur pockets the difference; the liquidity provider absorbs it as impermanent loss.
A worked example
Chainlink’s education article walks through a full example, dated 6 April 2026. A provider deposits 1 ETH and 1,000 USDC into a pool where 1 ETH is worth 1,000 USDC, for a total deposit value of 2,000 USDC. The pool already holds 10 ETH and 10,000 USDC, so the provider owns a 10 percent share, and the constant product k is 100,000 (10 × 10,000), per Chainlink.
Suppose ETH’s external price doubles to 2,000 USDC. Arbitrageurs buy ETH from the pool until its internal price also reads 2,000 USDC. After that rebalancing the pool holds roughly 7.071 ETH and 14,142 USDC — the product is still 100,000 — per Chainlink. The provider’s 10 percent share is now 0.7071 ETH and 1,414.2 USDC, worth 2,828.4 USDC combined. Had the provider simply held the original 1 ETH and 1,000 USDC, the ETH alone would be worth 2,000 USDC, for a total holding value of 3,000 USDC. The shortfall is 171.6 USDC, or 5.7 percent of the holding value — the impermanent loss, per Chainlink.
Checking the formula at other price levels
The formula depends only on the ratio d, not on the dollar level of the asset, and examples in this evidence confirm that across different scales. Chainlink’s example uses an ETH price of 1,000 USDC rising to 2,000 USDC. Speedrun Ethereum’s separate worked example starts from a different token price, per Speedrun Ethereum: ETH worth $3,000, alongside 3,000 USDC. When ETH doubles to $6,000, holding would be worth $9,000, while the pool position is worth roughly $8,484 (about 0.707 ETH worth $4,242 plus 4,242 USDC) — a loss of 5.7 percent, per Speedrun Ethereum. BydFi frames its example around a $10,000 total deposit value rather than a per-token price. Using the same formula, BydFi calculates 2 × √2 / (1 + 2) − 1 = −0.057, or a 5.7 percent loss, for a 2x price change, matching the result from Chainlink and Speedrun Ethereum at different dollar scales, per BydFi. BydFi’s guide adds that for a $10,000 deposit where one token doubles, “your pool value would be approximately $9,430 less than if you’d simply held the tokens” — wording that does not specify whether $9,430 is the resulting pool value or the size of the shortfall itself, and this page has not resolved that ambiguity beyond what BydFi states. The three figures land on the same 5.7 percent result for a 2x move even though they start from different scales — two expressed as a token price, one as a total deposit value — because the formula is a function of the ratio between old and new price, not of what the tokens or the deposit are worth in dollars.
The loss also scales the same way regardless of direction and grows faster than the price move itself. Speedrun Ethereum’s table gives impermanent loss of 0.6 percent for a 1.25x price ratio, 2.0 percent for 1.5x, 5.7 percent for 2.0x, 13.4 percent for 3.0x and 25.5 percent for 5.0x. BydFi separately reports 20 percent impermanent loss for a 4x price change and 42 percent for a 10x change, figures consistent with the same formula. Both outlets agree the loss is symmetric: a token doubling produces the same percentage loss as its counterpart halving, per BydFi and Speedrun Ethereum.
What “impermanent” does and doesn’t mean
The common misreading is that the loss is automatically temporary. It is only reversible if the price ratio returns to its deposit-time level before the provider withdraws, at which point the loss disappears and the provider keeps whatever trading fees accrued in the meantime, per Coinbase Learn and Chainlink. Speedrun Ethereum is explicit that in volatile markets the loss typically does not revert, and becomes permanent, realized, the moment the provider exits at a diverged price. Until withdrawal, it functions as an unrealized loss, per Speedrun Ethereum.
Trading fees earned while providing liquidity can offset some or all of the loss, but none of the outlets in this evidence supply audited, real-world figures showing how often that actually happens for a given pool. BydFi offers an illustrative model — a pool earning 50 percent APY generates roughly 4.2 percent in monthly fee income, which would offset a 5 percent impermanent loss in five to six weeks — but this is a hypothetical calculation from BydFi’s guide, not a reported outcome of an actual pool.
Ways to reduce exposure
Coinbase Learn’s glossary suggests reducing impermanent loss by choosing less volatile pairs, such as stablecoins or BTC, using established automated market makers, and starting with a small allocation to limit exposure. Chainlink and BydFi both point to stablecoin pairs such as USDC/USDT and correlated pairs such as stETH/ETH as ways to keep the price ratio close to 1, since impermanent loss shrinks toward zero as the ratio stays near its deposit-time level. BydFi also describes Bancor as offering full impermanent-loss protection after 100 days of continuous liquidity provision, a figure reported by BydFi alone in this evidence. Coinbase separately describes an “Impermanent Loss Protection” mechanism as a form of insurance for liquidity providers that requires locking tokens into a farm to activate.
Speedrun Ethereum notes that Uniswap v3’s concentrated liquidity, which lets providers focus capital in a specific price range, can amplify impermanent loss within that range and exposes the provider entirely to one asset if the price moves outside it. Speedrun Ethereum also cites research by Bancor and IntoTheBlock finding that over 51 percent of Uniswap v3 liquidity providers were unprofitable once impermanent loss exceeded their fee income — a figure this page has not verified against the underlying research, since only Speedrun Ethereum’s characterization of it is in evidence.
What this page does not tell you
The formula IL = 2×√d/(1+d) − 1 applies to standard 50/50 constant-product pools, the Uniswap v2 style of automated market maker. It does not directly describe the loss inside a Uniswap v3 concentrated-liquidity position, where Speedrun Ethereum says the effect is magnified within the chosen range and total once the price exits it.
The formula measures only the loss from price divergence. It leaves out trading fees earned along the way, which can partly or fully offset the result in practice. None of the sources here supply audited data from a real, on-chain pool showing how often fees actually cover the loss over a stated period; every fee-offset figure in this evidence, including BydFi’s 4.2-percent-a-month example, is an illustrative calculation, not a reported outcome.
Every numeric example used here — the 1 ETH/1,000 USDC scenario, the $3,000-ETH scenario, the $10,000-deposit scenario — is a hypothetical construction the outlets use to demonstrate the formula. None is drawn from a specific pool’s actual transaction history, and no source in this evidence audited a real pool’s impermanent loss over time.
The claims about Uniswap v3 LP profitability, Bancor’s specific protection terms, and institutional options-hedging products for impermanent loss each rest on a single outlet’s account. This page has not independently checked them against Bancor’s or Uniswap’s own documentation, and readers relying on those specific figures should treat them as single-sourced.
Sources
Every fact above is attributed to one of these reports. Where they disagree, the article says so.
