Impermanent Loss, With Actual Numbers

Impermanent loss is the gap between what a liquidity position is worth and what the same two assets would be worth if you had simply held them. That is the whole definition. Most of the confusion around impermanent loss comes from stories people attach to it afterwards — that it is temporary, that fees always cover it, that it only bites if you panic and withdraw. None of those are part of the definition.

What the definition does give you is something measurable before you deposit a cent. The loss depends on how far the two prices diverge, not on how long you stay. The arithmetic below uses one standard two-asset pool and clearly labelled illustrative numbers, so you can see where the loss is created and what it would take to offset it.

• The loss is relative, not absolute. No one invoices you for it. It is the difference between your position and the same assets held outside the pool.
• The size of the move sets the size of the loss. A 2x move in one asset produces about 5.7% of divergence in a standard 50/50 pool; a 4x move produces 20%.
• Time is not the variable. A position held for a day and one held for a year at the same end prices carry the same divergence loss. Only the fees differ.
• Fees are the offset, and they are not guaranteed. Sometimes cumulative fees exceed the loss, sometimes they do not. You can compute the break-even before depositing.

What creates the loss

A constant-product pool has to keep the product of its two balances constant, which forces it to trade against the market at every price change. When one asset rises, arbitrageurs buy it out of the pool and leave the other asset behind, so the position ends up holding less of the winner and more of the loser.

The pool sells what is rising

This is not a bug or a mispricing. It is what market making is: you are the counterparty to people who want to swap. The pool sells the appreciating asset because that is the only way to keep the invariant intact, and it does so continuously without asking you.

The consequence is structural. Any position holding two assets in a fixed proportion will underperform a straightforward holding of those same assets whenever their prices move apart. The pool does not lose money to a hack or a bad trade; it loses the difference between a rebalanced portfolio and a static one.

Why the word impermanent misleads

The loss is called impermanent because it reverses if the price ratio returns to where it started. That is true and almost useless. If one asset doubles and stays doubled, the loss is as permanent as anything in this market, and waiting does not undo it — it only gives fees more time to accumulate against a gap that is not closing.

The size of the gap depends on the pool’s shape, not on its fee tier. The table below is a rough map of where divergence comes from in common designs.

Impermanent loss, computed for a 2x move

A 50/50 pool holding 1 ETH and 2,000 USDC at an ETH price of $2,000 is worth $4,000. The alternative is holding exactly those 1 ETH and 2,000 USDC outside the pool. Every figure below is illustrative arithmetic, not a forecast of any asset.

Because the pool’s balances must multiply to the same constant, the composition slides along a fixed curve. At any price P, the position holds 1 divided by the square root of k in ETH and 2,000 multiplied by the square root of k in USDC, where k is P divided by $2,000.

Two things are worth staring at. First, a doubling and a halving produce the same percentage loss, 5.72%, because the formula depends on the ratio rather than the direction. Second, the loss is mild for small moves and then accelerates hard: about 1% at a 25% move, 5.72% at a 100% move, 20% at a 300% move.

The loss does not arrive as a fee. It arrives as a position that is quietly worth less than the one you decided not to open.

None of this requires the price to crash. A position can lose to holding in a rally just as easily as in a drawdown, which is the part most first-year users miss.

What fee income has to beat

Fees are the only thing standing between the divergence loss and a net loss, and they accumulate on a different schedule. The loss is set by the end price; fees are set by volume over time.

The break-even, in days

If the gap is 5.72% of the position and the pool pays an illustrative 0.05% of position value per day in fees, break-even is roughly 114 days of uninterrupted volume. If the price moves 4x instead, the gap is 20% and the same fee rate needs about 400 days, which assumes volume does not fall — a strong assumption in a market that has just moved violently.

That comparison is the argument in one line. A large price move creates a loss that normal-volume fees may never catch. A small move creates a loss that a busy pool clears in weeks. Neither outcome is guaranteed, and incentive tokens change the arithmetic without changing the mechanics.

Concentrated liquidity makes impermanent loss larger

Concentrating liquidity into a narrow price range multiplies the fee rate you earn and multiplies the divergence loss over the same price move. There is no free lunch in the range width. You are picking a point on a curve that trades fee density against divergence.

A narrow range behaves like a leveraged position. Because almost all the capital sits near the current price, a move of a few percent shifts the composition far faster than in a full-range pool. The upside is real: for the same capital you may earn several times the fees while price stays inside the range.

The failure mode is equally mechanical. Once price exits the range, the position is 100% in the weaker asset, stops earning fees entirely, and still carries the full divergence loss of the move. The range did not protect you; it concentrated the bet.