A liquidity position can rise from $2,000 to $2,828 and still leave its owner $172 behind. There is no contradiction: the same tokens, left in a wallet, would have become worth $3,000.

That difference is impermanent loss: the shortfall caused by a pool’s changing asset composition, measured against holding the original token quantities. It is not necessarily a dollar loss, a withdrawal charge or evidence that a protocol has been hacked. Understanding the comparison matters more than memorizing the name.

Providing liquidity changes what you own

In an automated market maker, traders exchange tokens against a pool. A liquidity provider, or LP, supplies assets and receives a claim on a share of the pool. As trades change its balances, the claim represents different quantities of each token.

Consider a full-range, two-token, 50/50 constant-product pool. Its fee-free model is x × y = k, where x and y are token balances. When outside prices change, arbitrage traders can trade against a stale pool price, moving the reserve ratio toward the market. The provider ends up with less of the relatively appreciating token and more of the relatively depreciating token. This is the economic cost of making those trades available.

The examples below assume continuous arbitrage to the outside price, an unchanged LP share, no fees, incentives or network costs, and a stablecoin that stays at $1. They are calculations for this specific model, not forecasts or a description of every pool.

When ETH doubles, the pool sells some ETH

Start with a position representing 1 ETH and 1,000 stablecoins when ETH costs $1,000. Both sides are worth $1,000; the total is $2,000. The scaled balances satisfy x × y = 1,000.

If ETH rises to $2,000, the new price ratio requires y ÷ x = 2,000. Solving those two equations gives approximately 0.707107 ETH and 1,414.21 stablecoins. At the new market price, each side is worth $1,414.21, for a total of $2,828.43.

Holding the initial 1 ETH and 1,000 stablecoins would instead produce $3,000. The pool is $171.57 behind, or 5.72% of the holding benchmark. It nevertheless gained $828.43 relative to the initial deposit. Calling that outcome a 5.72% loss on the original $2,000 would use the wrong denominator.

If ETH instead falls to $500, the position becomes roughly 1.414214 ETH and 707.11 stablecoins, worth $1,414.21. Holding would be worth $1,500. Here the pool loses dollars and also trails holding by $85.79, again 5.72%. Accumulating more ETH did not protect the portfolio’s dollar value.

Relative prices determine the basic calculation

Let r equal the final price of one token in the other token, divided by that relative price at deposit. For the model above, the pool’s value divided by the holding value is 2√r ÷ (1 + r). Expressed as a positive underperformance percentage, impermanent loss is [1 − 2√r ÷ (1 + r)] × 100%.

The symmetry concerns reciprocal relative-price moves, such as doubling and halving—not equal percentage gains and declines. A 50% rise and a 50% fall are not reciprocals. Different weights, stable-swap curves and bounded liquidity ranges need their own calculations.

“Impermanent” means the modelled gap can shrink if the relative price returns. It does not mean a recovery is scheduled or guaranteed. Leaving a position open preserves exposure to what happens next; it does not cancel today’s economic shortfall.

Fees must cover a dollar gap, not a headline APR

In the doubling example, $171.57 of additional net value would be needed to catch up with holding at that moment. This is a bookkeeping hurdle, not an estimate of future fees. Real fees can change pool reserves or accrue separately, depending on the implementation.

Compare the marked value of the LP claim, plus separately held fees and rewards, minus relevant costs, with the value of the original token quantities at the same time. Do not add fees twice if the position value already includes them. Value reward tokens at a realistic realizable price, allowing for vesting and sale costs.

An annualized display extrapolates assumptions about activity and capital. It cannot establish that the actual income during your holding period exceeded the actual shortfall. Nor does high volume alone establish how much eligible liquidity shares the fees.

Concentration and stablecoins change the exposure

Concentrated liquidity puts capital within chosen price bounds. As price traverses the range, balances shift; beyond a boundary, the principal position becomes one-sided. Uniswap’s documentation explains that an out-of-range position stops earning trading fees until it becomes active again. Narrow ranges can intensify inventory changes and require more management. The full-range formula above is not a calculator for a bounded position.

Stablecoin pairs can have modest relative-price movement in ordinary conditions, but a depeg changes that premise. Traders may remove the stronger asset while depositing the weakening one. A pool’s familiar dollar labels do not provide reserve backing or redemption guarantees.

Contract exploits, compromised administration and malicious tokens are additional risks. Borrowing to fund a deposit can add liquidation risk. None should be folded into the impermanent-loss formula and treated as already accounted for.

Also separate inventory underperformance from execution costs. KTX’s guides to liquidity and trade size and slippage explain why entering or selling the resulting tokens can add another cost. Eligible readers can explore markets through KTX; exchange trading and providing assets to an on-chain pool are different activities.

Five questions before comparing pool returns

If both tokens double in dollars, is there impermanent loss?

If their relative price stays unchanged, the basic model has no impermanent loss, even though the dollar values rise. The comparison tracks relative movement between the assets.

Does an LP token guarantee repayment of my deposit?

No. It represents a claim under the pool’s rules, not a promise to return the original quantities or dollar amount. Some concentrated positions use an NFT rather than a fungible LP token.

Does collecting fees reset the loss calculation?

No. A fee claim is income; it does not by itself reset the original holding benchmark. Keep a record of deposits, withdrawals and distributions to avoid rewriting the comparison.

What if I add more capital later?

Each addition has a different starting price and token mix. Track separate deposit lots or use a consistent cash-flow-adjusted benchmark rather than treating everything as the first deposit.

Is staking subject to the same mechanism?

Staking alone does not rebalance two pool reserves through swaps. Putting a staking receipt into a liquidity pool introduces a separate LP exposure, alongside the receipt’s own risks.

Educational material, not investment advice. All numerical examples are hypothetical. Liquidity provision can lose capital.

Technical references: Uniswap’s impermanent-loss explanation, concentrated-liquidity documentation, and the Balancer whitepaper. Worked examples and percentage calculations above are independently derived from the stated assumptions.