What Is Impermanent Loss?

In brief

• Impermanent loss (IL) compares an LP position with a specific benchmark: holding the assets and quantities originally deposited.
• It is a relative shortfall, not necessarily a fall in the LP position’s dollar value.
• In an ideal no-fee constant-product pool, the gap depends on the relative price change between the two assets. The pool automatically ends with less of the relative winner and more of the relative loser.
• Withdrawing does not create the economic shortfall, but it locks in the pool’s current asset mix. A later price reversal can no longer repair an exited position.
• Fees, incentives, gas, active range management and token prices must be added separately to judge an LP’s actual return.
• Loss-versus-rebalancing (LVR) is related but uses a dynamic rebalancing strategy as the benchmark. It should not be used as a synonym for IL.

The live Liquidity pools article explains pool inventory and shares; Automated market makers explains pricing rules; Slippage explains trader execution. This page focuses on the LP’s hold-versus-pool comparison.

The benchmark matters

Suppose an LP deposits one token A and 1,000 units of token B when A is worth 1,000 B. The deposit is worth 2,000 B. Later, A doubles to 2,000 B.

If the LP had simply held the original assets, the basket would now be worth 3,000 B. In a no-fee 50/50 constant-product pool, arbitrage changes the reserves until the pool reflects the new relative price. The LP’s share would be worth about 2,828 B. The pool position gained in absolute terms, but it trailed holding by about 172 B, or 5.72%.

That distinction is essential:

• absolute return: the LP position rose from 2,000 B to about 2,828 B;
• impermanent loss: it underperformed the 3,000 B hold benchmark by about 5.72%;
• net LP result: the pool value plus fees and incentives, minus costs, compared with whichever benchmark the analyst states.

The familiar constant-product IL expression for a relative price ratio (r), before fees, is:

[ \mathrm{IL}(r)=\frac{2\sqrt{r}}{1+r}-1 ]

For (r=2), the result is approximately (-5.72%). The same formula gives the same shortfall when the relative price halves because either direction makes the assets diverge. It is not a forecast: real positions include fees, changing liquidity, gas, routing, and possibly a concentrated range.

Why the pool changes the asset mix

Uniswap v2’s constant-product design keeps reserve product (x \cdot y) from decreasing after a swap. When outside markets value token A more highly than the pool does, arbitrageurs buy A from the pool and pay in B until further arbitrage no longer covers fees and execution costs. The pool therefore sells the relative winner as its price rises.

This is not a bookkeeping mistake. It is how the AMM follows prices elsewhere. LPs supply the inventory that makes those trades possible and receive fees for doing so. The same reserve movement produces price impact for traders and inventory rebalancing for LPs.

Different pool curves create different exposures. A StableSwap-style curve may offer lower impact near parity for like-priced assets, but it does not remove loss if one asset breaks its peg or becomes impaired. Weighted pools compare against a correspondingly weighted hold basket, not automatically a 50/50 basket.

Why “impermanent” is a dangerous name

In the idealized no-fee constant-product example, if the relative price returns exactly to its starting point while the LP remains in the same position, the hold-versus-pool gap returns to zero. That reversible endpoint gave IL its name.

Real outcomes are less tidy:

• If the LP withdraws while prices differ, the returned mix is fixed. A later reversal does not rebalance the wallet back into the old quantities.
• One token may never recover because of a depeg, exploit, governance failure, or collapse in demand.
• Fees and incentives make the net result path-dependent even when the simple no-fee IL benchmark is not.
• Re-entering a pool establishes a new position and benchmark; it does not undo the old trade history.
• Taxes, gas, rebalancing costs, and hedges can change the investor’s result without changing the mathematical IL measure.

It is therefore more precise to call IL an opportunity cost versus holding. Withdrawing realizes the current inventory choice, but the economic shortfall exists before withdrawal whenever the marked-to-market pool share trails the stated hold basket.

Concentrated liquidity sharpens the exposure

Uniswap v3 introduced price ranges, and v4 retains concentrated liquidity. Capital is active only between an LP’s chosen lower and upper prices. A narrow range can provide much more liquidity near the current price per dollar committed, which can increase fee earning capacity while the position remains active.

The tradeoff is stronger inventory conversion over a smaller price interval:

• as price moves through the range, the position shifts from one token toward the other;
• at one boundary it can be entirely token A, and at the other entirely token B;
• once price leaves the range, the position is inactive and earns no swap fees until price re-enters;
• a narrow range can therefore accumulate the underperforming asset faster than a full-range position.

There is no single “Uniswap v3 IL percentage” without the entry price, range, current price, deposited mix and fee history. Comparing concentrated positions solely by headline APR hides both out-of-range time and inventory risk.

Fees do not erase the comparison

Swap fees compensate LPs for making inventory available. They can exceed IL over a chosen period, exactly offset it, or fall short. High historical fee APR can reflect volatile flow that also creates larger adverse selection and range-management costs.

A sound performance calculation keeps the lines separate:

1. value of the current LP inventory;
2. fees actually earned;
3. token incentives, if any;
4. gas and management costs;
5. value of the original hold basket over the same period.

Calling an LP “profitable” without naming the benchmark is ambiguous. A position can earn positive fees and gain in dollars while still underperforming holding.

IL versus LVR

IL is an endpoint comparison with a static hold basket. Loss-versus-rebalancing (LVR), formalized by Milionis, Moallemi, Roughgarden and Zhang, compares the AMM with a hypothetical strategy that holds the same changing inventory but trades at an external reference price rather than at stale pool prices.

LVR isolates an adverse-selection cost: arbitrageurs trade against an AMM after the outside price has moved, capturing value that a continuously rebalancing benchmark would not give away. It depends on the price path and can accumulate even if the price later returns to its starting point. IL and LVR can be connected under model assumptions, but they answer different questions and should remain separate in beginner material.

Risks that are not impermanent loss

IL is not a catch-all term for an LP losing money. Separate risks include:

• token loss: either asset falls in value, depegs, rebases, freezes, or is malicious;
• smart-contract loss: a bug or compromised component moves pool funds;
• oracle or lending liquidation: an LP token used as collateral may be liquidated elsewhere;
• slippage and MEV: execution can be worse when entering, rebalancing, or exiting;
• incentive-token dilution: nominal rewards may fall in price or be emitted faster than demand;
• inactive liquidity: an out-of-range position earns no swap fees, even though it still has market exposure.

Lending pools that do not make markets do not have this curve-driven inventory effect. Their primary risks are borrower solvency, utilization, oracle behavior and liquidation. “Pool” does not automatically mean “impermanent loss.”