Impermanent loss in plain terms, and why the name misleads
Impermanent loss is the gap between what an LP position is worth and what the same two assets would have been worth if simply held. It is not a fee, nobody charges it, and it is not reliably impermanent. This entry explains where the gap comes from, gives the arithmetic that produces it, and states plainly what fee income would have to do to cover it.
- Question
- Why is an LP position often worth less than the same two assets held outright, and how large is that gap for a given move in the price ratio?
- Balances used
- The price ratio at entry and at exit, the pool invariant, the fee parameter, and where applicable the interval a concentrated position covers.
- Out of reach
- Whether any particular position came out ahead, since that depends on fee flow through it and on what the provider would otherwise have done.
- What would overturn it
- A constant-product position that matches a simple hold across a large price divergence with no fee income, which the arithmetic does not permit.
- Confidence
- Firm. The gap is a closed-form consequence of the constant-product formula and can be derived in a few lines.
The short answer
Impermanent loss is the difference between the value of a liquidity position and the value the same two assets would have had if the provider had simply held them. It appears whenever the price ratio between the two assets changes, it grows with the size of that change, and it is symmetric: a doubling and a halving of the ratio produce the same gap.
It is not a fee. Nobody bills it, no counterparty receives it as a charge, and it does not appear as a line item anywhere. It is the arithmetic consequence of holding a position that automatically sells whichever asset is rising and buys whichever is falling.
Two things follow. Fee income is the only thing working against it, and fee income is not guaranteed to be enough. A provider can be up in absolute terms and still have done worse than doing nothing, which is the comparison that matters when deciding whether the position was worth holding.
Where the gap comes from
A constant-product pool must keep its two reserves at a fixed product. When the external price of one asset rises, the pool's quote lags, so arbitrage traders buy the underpriced asset from the pool until the quote catches up. Every one of those trades takes the rising asset out and puts the other asset in.
The provider's share therefore ends up containing less of whatever went up and more of whatever went down. That is exactly the opposite of what a holder experiences, and it is not a malfunction: it is what supplying a two-sided quote means. The pool is obliged to sell into strength and buy into weakness, and the provider owns a slice of that obligation.
Seen from the other direction, the gap is the payment the provider makes to the arbitrage traders who keep the pool's price aligned with the rest of the market. That alignment is a service the pool needs, and the provider funds it. Fees are the compensation offered in exchange, which is why the two quantities always have to be considered together.
Where the value actually goes
The gap is not destroyed and it is not taken by the venue. It is transferred to the traders who corrected the pool's price. Each arbitrage trade buys from the pool below the wider market price or sells to it above, and the difference accumulates in those traders' hands rather than evaporating.
Understanding that removes a lot of the mystique. There is no hidden fee schedule and no adversary specific to liquidity provision. There is an ordinary trade happening repeatedly, in which the pool is systematically on the losing side of every price correction because it is obliged to quote both ways at a price derived from stale reserves.
It also explains why the gap grows with volatility rather than with time. A pair whose ratio wanders and returns generates many corrections that largely cancel, leaving a small gap and a lot of fee income. A pair whose ratio moves decisively in one direction generates corrections that all point the same way, and the gap is the sum of them.
Why the exposure is often described as short volatility
A liquidity position gains a steady trickle of fees and loses as the price ratio moves in either direction. That payoff shape is familiar from options markets, and practitioners often describe an LP position as being short volatility for exactly that reason.
The comparison is useful as intuition and should not be pushed too far. The position has no expiry, no premium quoted up front and no counterparty obliged to deliver anything. What it shares with the analogy is the important part: a small regular income set against an exposure that hurts more the further the price travels.
The arithmetic behind it
For a full-range constant-product position, write r for the ratio of the exit price to the entry price, measuring one asset against the other. The value of the position relative to holding is twice the square root of r, divided by one plus r. Subtract one and you have the gap.
Three properties of that expression are worth internalising. It equals one when r is one, so no divergence means no gap. It is always at or below one, so the position never beats holding on price alone, before fees. And it is symmetric under replacing r with its reciprocal, so an asset doubling and an asset halving hurt identically.
The expression is also concave, which means the gap grows slowly at first and then accelerates. Small moves cost almost nothing, which is why providers on stable pairs rarely think about it, and large moves cost a great deal, which is why providers on volatile pairs sometimes discover it all at once.
The gap at different divergences
| Price ratio change | Position vs holding | Gap | Reading |
|---|---|---|---|
| 1.25x or 0.80x | 99.38% | 0.62% | Negligible; ordinary fee flow covers it easily |
| 1.50x or 0.67x | 97.98% | 2.02% | Noticeable; needs sustained fee income to offset |
| 2.00x or 0.50x | 94.28% | 5.72% | Material; a common outcome on volatile pairs |
| 3.00x or 0.33x | 86.60% | 13.40% | Large; fee income rarely closes this alone |
| 4.00x or 0.25x | 80.00% | 20.00% | Severe; the position holds mostly the weaker asset |
| 5.00x or 0.20x | 74.54% | 25.46% | Severe; holding would have been far better |
| 10.0x or 0.10x | 57.50% | 42.50% | Extreme; typical of a pair that moved decisively |
The right-hand column is a reading of the arithmetic rather than a claim about how often each row occurs. This desk does not publish frequencies it has not measured, and the distribution of price divergence across Solana pairs is not something a table like this can supply.
Why the name misleads
The word impermanent describes a property the gap has while the position is open: if the price ratio returns to its entry value, the gap closes. That is true and it is the reason the term was coined. It is also the reason the term does so much damage.
Nothing forces the ratio to return. On a pair where one asset has fundamentally repriced, the ratio is not oscillating around a mean waiting to come home; it has moved. The gap is then permanent in every sense a provider cares about, and it becomes realised the moment the position is closed.
The name also implies the gap is a temporary inconvenience rather than a structural feature of the position. It is structural. Any position that provides a two-sided quote across a moving price carries it, and the only question is how large it gets and whether fee income offsets it.
Divergence loss is the better term because it names the cause. Some venues and documentation have moved to it. This entry uses the older phrase because that is what readers search for, while noting that the phrase has misled a great many people into treating a real exposure as an accounting curiosity.
What fee income has to cover
Set the two quantities side by side. The gap is a function of price divergence, which the provider does not control and cannot predict. Fee income is a function of the fee rate, which is a published pool parameter documented by venues such as Raydium, multiplied by flow through the position, which the provider also does not control. Both are outside the provider's hands, and the position is profitable relative to holding only when the second exceeds the first.
That framing removes a lot of confusion. Providing liquidity is not a yield product with an occasional drawback. It is a trade: you supply a two-sided quote and accept the rebalancing that comes with it, in exchange for a share of the fees paid by whoever uses that quote.
Whether the trade is a good one depends entirely on the pair and the period, and the honest answer for any specific case is that it is not knowable in advance. Anyone quoting an expected return is either describing a past period or making it up, and this desk publishes no yield figures for exactly that reason.
The one thing that can be said generally is that fee income scales with flow. A position sitting where nothing routes earns nothing while carrying the full exposure, which is why providers care about where activity actually lands. It is also why the reserve side and the activity side keep meeting: analysts who study routed flow, including operators of an automated Solana volume bot, are looking at the same venue and range data that decides whether a position is earning at all.
Concentrated ranges amplify it
A concentrated position behaves like a much larger full-range position while the price is inside its interval. That amplification applies to both sides of the trade: more fee accrual per unit of capital, and more rebalancing per unit of price movement.
When the price leaves the interval entirely, the position has been fully converted into one asset, which is the behaviour Orca's developer documentation describes for a position whose range the price has crossed. At that point it is no longer a liquidity position at all; it is a holding of a single token that has stopped earning. Whether that outcome is welcome depends on which asset it converted into and what happens next, neither of which the position controls.
The narrower the range, the more pronounced both effects become. A very tight range around the current price can accrue fees quickly and can also be exited by a single ordinary move. Providers who choose narrow ranges are taking an active position on where the price will stay, whether or not they describe it that way.
The comparison that matters
The useful question is never whether a position went up in nominal terms. It is whether it did better than holding the two assets untouched over the same period. Any assessment that skips that comparison will call a position successful in a rising market when doing nothing would have been better.
A worked comparison, illustrative
The same period, two ways of holding
Illustrative figuresEvery number here is invented for teaching and describes no real position, pool or period. A provider supplies 10 units of token A and 1,000 units of token B to a pool quoting 100 B per A. Total value at entry, denominated in B, is 2,000.
Over the period, A rises to 200 B, a ratio change of 2.0x. The full-range position rebalances so that the provider's share is now roughly 7.07 A and 1,414 B. Valued at the new price, that is about 2,828 B.
Simply holding the original 10 A and 1,000 B would have produced 2,000 plus 1,000, which is 3,000 B. The position is worth about 172 B less than holding, which is the 5.72 per cent shown in the table above.
Suppose fee income over the same period, from flow that happened to route through this pool, came to 60 B. The position is then about 112 B behind holding despite having gained 888 B in nominal terms. A provider who only looked at the nominal gain would record this as a success. Against the alternative of doing nothing, it was not.
Checking your own position
- Record the price ratio at entry, because without it no comparison against holding can be made later.
- Record the exact amounts deposited, not their value, so the hold alternative can be reconstructed at any later price.
- Track fee income separately from the position value, because a venue that keeps fees in reserves blends the two.
- Recompute the hold alternative at the moment you assess the position, not at the price you remember.
- On concentrated venues, check whether the price is inside the range before assuming the position is still earning.
- State the result honestly, including periods where the position underperformed holding, since that is the only way the record is useful.
What this entry is not
It is not a claim that providing liquidity is a bad idea, and it is not a claim that it is a good one. It is a description of a mechanism that is frequently presented in reassuring language and deserves plain language instead.
It is also not a complete account of the risks involved. A liquidity position is exposed to everything the two assets are exposed to, plus the mechanics described here, plus whatever risks attach to the specific program holding the funds. Any one of those can dominate the others.
Nothing here is financial advice, and nothing here should be read as an estimate of what any position would earn. Providing liquidity can leave a position worth less than holding the two assets, in some periods substantially less, and that outcome is a normal consequence of the design rather than a failure of it.
Questions this entry gets asked
Is impermanent loss an actual loss?
It is a real difference in outcome, measured against a specific alternative: holding the two assets untouched. It is not a charge and no counterparty receives it. If you exit while the price ratio is back where it started, the gap is close to zero. If you exit after divergence, the gap is realised and is as real as any other outcome.
Why is it called impermanent?
Because the gap disappears if the price ratio returns to where it was at entry, so while a position is open the loss is unrealised and reversible in principle. The name has been widely criticised because there is no mechanism forcing a return, and many providers exit while the gap is wide. Divergence loss is the more accurate term and some venues now use it.
Does a stable pair avoid it?
It reduces the exposure rather than removing it. Two assets designed to track the same value diverge less, so the gap stays small in normal conditions. When one of them stops tracking, the pool rebalances into the weaker asset exactly as it would with any other pair, and the position ends up holding predominantly whichever side lost its peg.
Do fees make up for it?
Sometimes, and there is no rule that says they must. Fee income depends on flow through the position, which the provider does not control, while the gap depends on price divergence, which the provider also does not control. Any framing that presents fees as automatic compensation is describing a hope rather than a mechanism.
Is it worse on concentrated positions?
For the same price move, yes, in the sense that a narrow range concentrates the same rebalancing into a smaller price interval and converts the position fully into one asset once the price exits. The trade-off is higher fee accrual while the price stays inside the range. Neither side of that trade-off is guaranteed to dominate.
Can it be hedged away?
Positions can be constructed that offset some of the exposure, and doing so introduces its own costs and its own risks. This desk describes the mechanism rather than recommending any response to it, and treats the question of what a provider should do as outside what reserve analysis can answer.
Where does the value actually go?
To the traders who took the other side. As the price moved, the pool sold the rising asset too cheaply and bought the falling one too expensively relative to the eventual price, and arbitrage captured that difference. The gap is not destroyed value; it is value transferred to whoever kept the pool aligned with the wider market.
Filed in Pools by The Depth Ledger Desk. Every quantity inside a worked example on this page is invented for teaching and describes no real pool. Nothing here is advice about what to buy, sell or supply, and liquidity provision can end with a position worth less than holding the two assets. Terms used above are defined in the liquidity glossary.