Impermanent loss is the gap between two portfolios: the one that would simply have held your coins, and the one that put them into a liquidity pool. If the price of one half of the pool doubles while the other stands still, that gap comes to 5.72 percent. €150 from holding turns into €141.42 in the pool. The effect is no more than that, and it hangs on a single quantity: the ratio of the two prices to each other.
Providing liquidity earns you a share of the pool’s trading fees. Whether it pays off turns on one question: whether those fees close the gap. This piece works both sides against each other, with figures you can check yourself.
What impermanent loss in a liquidity pool really is
Liquidity pool: a pot of two tokens that anyone can swap against without needing a counterparty. Instead of an order book with buyers and sellers, a formula sets the price. Anyone who deposits tokens becomes a liquidity provider and no longer holds two coins, but a share of the pot.
Impermanent loss: the difference between the value of that share and the value of the coins had you not deposited them. The gap arises from price moves alone, not from fees, not from a hack and not from a flaw in the protocol.
The name misleads, because nothing is lost at first. As long as the price ratio of the two tokens returns to where it stood at entry, the gap disappears entirely. That is why it is called impermanent. Withdraw while the ratio is displaced, though, and you make it permanent.
Only the ratio matters here, not the direction and not the absolute size. If one half of the pool rises 50 percent while the other stands still, the cost is the same as in the reverse case. If both rise 50 percent, it costs nothing at all, because the ratio has not changed.
How an automated market maker tracks the ratio inside the pool
Automated market maker (AMM): the program that derives the price in the pool from the two balances. In the classic case, as used by Uniswap v2 and most of its imitators, the rule is that the product of the two balances stays constant. Put token A in, take token B out, and the price shifts until the product holds again.
When the outside price of a pool token rises, it is briefly too cheap inside the pool. Traders then step in, buy it out of the pool and sell it dearer elsewhere. This tracking from outside is not a side effect but the mechanism itself: the pool only follows the market because somebody exploits the gap. Whatever value walks out of the pool in the process is carried by the liquidity provider.
In practice that means the pool always sells you whatever is rising and buys whatever is falling. At the end of a strong price rise you hold less of the token that rose and more of the other one. That reshuffling is exactly what costs the gap against simply holding. Anyone who places a market order on a centralised exchange knows the related effect from a different angle: the price gap between the order expected and the order filled.
Pools run on decentralised trading venues, which work without an intermediary. How these differ from a classic exchange is set out in our explainer on decentralised crypto exchanges. The best known pairs contain ether; where the price currently stands is shown on the Ethereum price prediction page.
The formula behind impermanent loss in one sentence
Call the price ratio at the end divided by the price ratio at the start k. The value of your pool share then equals the holding value multiplied by twice the square root of k, divided by the sum of one and k. The gap against holding is that factor minus one.
The same result appears in a paper on the quality of centralised and decentralised trading venues, written there as the difference between two returns: half the sum of the price ratio and one, minus the square root of the price ratio. The authors note that this expression turns to zero at a single point only, namely at an unchanged ratio, and is otherwise always positive. It can be read in the study on centralised and decentralised trading venues.
What counts in it for you: there is no parameter for duration, pool size or trading volume. Two weeks and two years in the pool cost exactly the same at the same closing ratio. The gap is a function of the price, nothing else.
Our own calculation: how the price ratio drives the loss
The values below are calculated from the formula, for a pair with equal halves at entry. The second column gives the price change of one half while the other stays unchanged. The third column shows what percentage of the holding value is missing at the end.
| Price ratio | Price change of one half | Gap against holding |
|---|---|---|
| 1.00 | unchanged | 0.00 percent |
| 1.10 | up 10 percent | 0.11 percent |
| 1.25 | up 25 percent | 0.62 percent |
| 1.50 | up 50 percent | 2.02 percent |
| 2.00 | up 100 percent | 5.72 percent |
| 3.00 | up 200 percent | 13.40 percent |
| 4.00 | up 300 percent | 20.00 percent |
| 5.00 | up 400 percent | 25.46 percent |
| 10.00 | up 900 percent | 42.50 percent |
The lower end stands out. Up to a price gain of 25 percent the gap stays below one percent, and at a price move of ten percent it sits at a thousandth of the stake. In that zone impermanent loss is barely an issue, and any halfway active fee rate covers it several times over.
Above that the curve turns steep. Between up 100 and up 400 percent the gap quadruples, from 5.72 to 25.46 percent. Put a young token with large price potential into a pool, and you pay for that token’s success with a noticeable slice of the gain.
€100 in an ETH pair: €8.58 behind simply holding
A worked example makes the percentage tangible. You put €100 into a pair of ether and a dollar stablecoin, so €50 in each half. The ether price then doubles while the stablecoin stays at one dollar.
Had you only held, the €50 of ether would have become €100, which together with the unchanged €50 makes €150.00. In the pool, €141.42 stands at the end. The gap is €8.58, or precisely those 5.72 percent. Those €8.58 have not vanished; they sit in the pockets of the traders who kept levelling the pool out along the way.
The counter-calculation belongs with it: over the same period the pool collected trading fees, and your share of them is yours. In a pool throwing off a 25 percent fee yield on an annual basis, €8.58 would be earned after roughly 83 days. Whether your pool carries that rate shows only in its actual trading volume, not in a marketing figure.
Why the weighting at entry shifts the calculation
The values in the table hold for a pair with two equally large halves. Pools with a different weighting, 80 to 20 for instance, spread the effect differently: the smaller half is reshuffled more heavily, the larger one barely at all. A pool made up 80 percent of one token behaves closer to simply holding that token, and brings in fewer fees for it.
Trading fees and fee yield set against the loss
Fee yield: the share of trading fees attributable to the capital you deposited, extrapolated to a year. It comes out of the pool’s trading volume, the fee tier and the share you hold of the pool. It is not a promise but a look back: if volume falls, it falls with it.
From the formula and an assumed fee yield you can read off how long a pool has to run for the fees to cover the gap. The values below are derived from the same calculation, with capital active throughout:
- Price up 50 percent, gap 2.02 percent: at a 10 percent fee yield, around 74 days; at 25 percent, around 29 days.
- Price doubled, gap 5.72 percent: at 10 percent, around 209 days; at 25 percent, around 83 days; at 50 percent, around 42 days.
- Price tripled, gap 13.40 percent: at a 25 percent fee yield, around 196 days.
- Price up tenfold, gap 42.50 percent: even a 50 percent fee yield needs more than 300 days.
- Price unchanged: no gap, and every bit of fee yield stays as profit.
This calculation is deliberately generous, because it assumes a fee yield that holds steady across the whole period, and that is the least likely part of it. High rates mostly arise in a pool’s first weeks, when volume is large and the liquidity deposited is still small. After that they fall, often sharply.
Then there are costs that appear in no rate at all: the network fee on depositing, on harvesting the rewards and on the way out. On small amounts they eat a double-digit percentage of the yield. If you would rather look for a platform with stated terms, the comparison of staking and yield platforms lists the usual providers with their conditions.
Doubling and halving cost exactly the same share
This point surprises most people and sits directly in the formula: a price ratio of 2 and a price ratio of 0.5 produce the same gap. Worked through for several values:
- Up 25 percent and down 20 percent: both 0.62 percent.
- Up 50 percent and down 33 percent: both 2.02 percent.
- Up 100 percent and down 50 percent: both 5.72 percent.
- Up 300 percent and down 75 percent: both 20.00 percent.
Something uncomfortable follows for practice: a pool does not protect you against falling prices. On the way down, the gap against holding is added to the price loss. If you deposit into a pair because you expect a quiet sideways phase, you have read the formula correctly. If you deposit because you want to cushion a slump, you have read it wrongly.
Concentrated liquidity on Uniswap v3 sharpens the effect
Concentrated liquidity: liquidity that works only within a price range you choose yourself, instead of being spread across the whole curve. Uniswap’s developer documentation describes the core as liquidity allocated within a custom price range, and cites as an example an older dollar pool that used only around half a percent of its capital for trading between $0.99 and $1.01. Draw the range tightly and you get far more depth at that point out of the same capital, earning correspondingly more in fees.
The price for that stands in the same documentation: once the price leaves the range, the liquidity is no longer active and earns no more fees. The position then consists entirely of one of the two tokens. If the price returns into the range, it becomes active again. The details are in the documentation on concentrated liquidity; where the protocol token currently stands is shown on the Uniswap price prediction page.
For the calculation that means the narrow range leverages both sides. Inside the range the fee yield is a multiple, but so is the gap against holding. A position with half the range width behaves, at the same price move, like a far larger stake in a classic pool. And as soon as the price breaks out, it earns nothing more while the gap remains.
The table shows directly which pairs are quiet. Two dollar stablecoins such as USDC and USDT normally move by fractions of a percent against each other; the price ratio stays close to one, and so the gap stays close to zero. The same holds for a pair of ether and an ether sitting in a staking protocol, or for a pair of BTC and a wrapped version of the same coin.
The catch: these very pairs carry the lowest fees, because there is little room between them. Quiet and lucrative do not come in the same pool. On top of that, stablecoin pairs keep a risk of their own that the formula does not capture: if one of the two tokens loses its peg to the dollar, the ratio shifts suddenly and sharply, and the effect then bites with full force.
Rewards from liquidity programmes can turn the equation around, though with deadlines of their own. That such entitlements can lapse is shown by the case of a programme in which every claim below a minimum amount expired on a fixed date.
Why the loss is called impermanent and when it turns permanent
As long as your share sits in the pool, the gap is an arithmetical figure. If the price ratio returns to its entry value, it dissolves completely, however far it had run up in the meantime. A pair that goes from one to four and back to one costs nothing at the end.
It turns permanent the moment you close the position. You then receive the two tokens paid out in the displaced ratio, and what is missing is missing. The same happens with a position on a narrow range if you close it outside that range.
A plain consequence for the moment of exit follows: close immediately after a strong move and you realise the largest gap. Wait until the ratio has calmed and you pay less, but you carry the price risk of both tokens, and the risk of the protocol itself, for longer.
Tax in Germany: the deposit, the rewards and the exit
The tax treatment does not follow the economic logic of the pool but German income tax law, and it breaks into three separate events: the deposit, the running inflow and the exit. Each is assessed on its own, and none of them knows the term impermanent loss.
The order is particularly awkward: a gap against holding is not a loss for tax purposes as long as no event realises it, while rewards from the pool are valued at the moment they arrive. A taxable inflow can therefore arise while the position as a whole sits at a loss. Which event is classified how in Germany, and what records the tax office wants to see, we set out in our piece on liquidity pools and tax of July 10, 2026.
In practice the documentation matters most of all. A pool position produces many small events that no exchange itemises for you: the deposit, the reshuffling by the pool, rewards in small tranches, network fees, the exit. Without a complete record, neither a gain nor a loss can be evidenced at the end of the year.
What an impermanent loss calculator does and where it goes wrong
Calculators on the web take two prices and output the gap as a percentage. That part they handle reliably, because it is exactly the formula above. For a quick sense of scale it is enough.
Three things these tools typically do not deliver. First, the actual fee yield of your pool over the period you held it, because that hangs on volume and on your share. Second, the network fees for entry, harvest and exit. Third, the time a position on a narrow range spent outside that range and therefore earned nothing. A result of “minus 5.72 percent” says nothing, then, about whether your trade won or lost.
The interface terms you will meet in the apps
Protocol interfaces are almost entirely in English, and the terms there do not map onto everyday language. These six come up most often. An impermanent loss calculator works out the gap from two prices. Fee APR is the fee yield on an annual basis; APY is the same number with reinvestment assumed, and therefore always the larger of the two. The fee tier is the pool’s fee level, meaning the rate every swap there costs. The range is the price range of a position with concentrated liquidity. The LP token is the receipt for your share of the pool, which you hand back on the way out. And the price ratio is precisely that ratio of prices which appears in the formula above as k.
Know that mapping and you can read a pool’s interface in half a minute: the fee tier and fee APR say what comes in, the range says how long the capital stays active, and the price ratio says what it costs.
The calculation only becomes solid once you assemble the four quantities: the gap from the formula, the fees collected, the network costs and the time with capital active. Only then is it settled whether the pool brought in more than simply holding.
Our assessment of liquidity provision for private investors
In this newsroom’s view, providing liquidity is arithmetically attractive for private investors in exactly one case: pairs whose price ratio stays stable. The evidence is in the table above. Below a price move of 25 percent the gap stays under one percent, and there a double-digit fee yield covers the effect within a few weeks. At a price ratio of four, by contrast, 20 percent is missing, and hardly any pool brings that back.
Against it stands the fact that the most lucrative part of the market is precisely the volatile one. High fee rates arise with young, sharply swinging tokens, meaning exactly where the price ratio runs furthest. Seek out those rates and you buy the gap along with them. Add to that the risk of a flaw in the protocol, and the fact that decentralised trading venues hold no BaFin licence and offer no investor protection: if something goes wrong there is no counterparty and no compensation. A total loss of the amount deposited is possible.
Impermanent loss: it only costs more than 5 percent once the price doubles
- Before depositing, work through the formula to see what gap you are accepting at a doubling and at a halving. The table above gives the yardstick: 2.02 percent at up 50, 5.72 percent at up 100, 20.00 percent at up 300 percent. If the expected fee yield sits below that, the trade cannot be won on the arithmetic. If you are looking instead for a yield without a price ratio, the providers are listed in the comparison of lending providers.
- Record four values for every position: the entry prices of both tokens, the date, the fees collected and all network costs. Those four values later carry the tax return and the answer to whether the trade was worth it. The tools for that are in the comparison of tax software.
- Before entering, compare a plain purchase on a licensed exchange with the pool. If you want to hold the coin anyway, buying without a pool is the route with no gap and no protocol risk; an overview of licensed trading venues is in the exchange comparison.
(As of October 18, 2026. This article is not investment advice. Prices and fee structures change; check the terms with the provider before you buy.)
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