Impermanent loss

Impermanent loss is an AMM liquidity position's shortfall versus holding the same deposited assets. Learn the constant-product formula, benchmark, fee trade-off, and risks.

For educational purposes only; not investment advice. Liquidity provision can lose money and can underperform holding the deposited assets.

Direct answer

Impermanent loss is the value shortfall of an automated-market-maker liquidity position compared with simply holding the same quantities of the deposited tokens over the same period. It is a benchmark-relative opportunity cost, not necessarily a negative account return: an LP position can rise in dollar value and still trail the hold portfolio.

Arbitrage trades change the pool’s token mix as relative market prices move. A full-range constant-product LP ends up with less of the outperforming token and more of the underperforming token. Swap fees and incentives can offset that shortfall, but they are separate return components and do not make the loss impossible.

The word “impermanent” does not mean harmless or guaranteed to reverse. In the simplified full-range model the gap returns to zero if the relative price returns to its entry level, but prices may not return, and withdrawing, rebalancing, fees, token failures, or contract losses can make the economic result permanent.

New / initial price2x

50/50 LP vs holding

-5.72%

LP relative value: 94.28%

Outputs are educational approximations. They exclude venue rules, taxes, latency, oracle behavior, and other protocol-specific parameters unless shown.

How it works

For a fee-free, full-range, 50/50 constant-product pool, reserves satisfy x * y = k. Suppose the relative price of one token becomes r times its entry price. Arbitrage changes the reserves until the pool price tracks the external price, subject to trading costs.

Compared with holding the initially deposited quantities, the LP value ratio is 2 * sqrt(r) / (1 + r). The benchmark-relative return called impermanent loss is therefore:

IL(r) = 2 * sqrt(r) / (1 + r) - 1

At r = 1, the result is 0%. At r = 2 or r = 0.5, it is about -5.72%; at r = 4 or r = 0.25, it is -20%. The symmetry concerns the relative price ratio, not the investor’s dollar profit or loss.

This formula excludes fees, incentives, gas, taxes, price impact on exit, and changes to the pool design. Concentrated ranges, unequal weights, stable-swap curves, more than two tokens, and active rebalancing require their own position-level calculation. For multiple deposits or withdrawals, build a separate matched hold benchmark for each cash flow.

Example

At 2,000 USDC/ETH, an LP deposits 1 ETH and 2,000 USDC into a full-range pool. The deposited value is 4,000 USDC. Ignore fees and assume the position represents the whole pool.

ETH then rises to 4,000 USDC/ETH. After arbitrage, the pool holds about 0.7071 ETH and 2,828.43 USDC, worth 5,656.85 USDC at the new market price.

Holding the original assets would be worth 1 ETH + 2,000 USDC = 6,000 USDC. The LP trails that benchmark by 343.15 USDC, or about 5.72%, even though its own value increased. This is why “loss” means underperformance versus holding, not necessarily a fall below the initial deposit.

If the position also earned 400 USDC in fees and cost 30 USDC in gas, its simplified net value would be 26.85 USDC above the hold benchmark. Fee income can offset impermanent loss in a realized result, but future volume, competition, and price paths are unknown.

Risks

Benchmark error: changing valuation times, token quantities, price sources, or denomination can create a false result.
Fee uncertainty: displayed APR and historical volume do not guarantee that future fees will cover inventory underperformance.
Concentrated-range risk: a position can become single-sided and stop earning swap fees while it is out of range.
Asset risk: depegs, token collapse, transfer restrictions, and redemption failures are distinct from impermanent loss and can be much larger.
Protocol risk: contract bugs, malicious tokens, oracle failures, admin powers, upgrades, interfaces, and bridges can cause additional loss or block exit.
Cost and incentive risk: gas, swaps, taxes, management fees, and falling or illiquid reward tokens reduce realizable returns.
Path and management risk: volatility, adverse selection, repeated rebalancing, and poorly timed range changes can matter even when start and end prices look similar.

Common misconceptions

Myth 1: There is no loss until the LP withdraws

Withdrawal realizes a particular token mix, but the position’s redeemable value and its shortfall versus holding already change as trades occur.

Myth 2: Fees always cover impermanent loss

Coverage depends on fee rates, active liquidity, volume, price path, holding period, and costs. There is no guaranteed break-even point.

Myth 3: If both tokens rise, impermanent loss is impossible

The metric depends on their relative price. Both can rise in dollar terms while one outperforms the other, leaving the LP behind the matched hold portfolio.

Myth 4: Stablecoin pools have no impermanent loss

Small relative moves may produce a small gap, but it is not automatically zero. A depeg can also leave LPs concentrated in the weaker asset, alongside credit and redemption risk.

Sources

What is Impermanent Loss? - Uniswap Labs (accessed: 2026-08-20)
Uniswap v2 Core - Uniswap Labs (accessed: 2026-08-20)
Uniswap v3 Core - Uniswap Labs (accessed: 2026-08-20)
What are the risks when providing liquidity? - Uniswap Labs (accessed: 2026-08-20)