Liquidity Provision and Impermanent Loss

Providing liquidity is not the same as holding two assets unchanged. A pool changes the provider's asset mix as relative prices move. The term impermanent loss describes a comparison with a hold-only benchmark under specified assumptions. It does not always mean a cash loss, and it does not promise that the difference will disappear.

Education only. Crypto assets can lose substantial value or become worthless. No lesson requires buying an asset, depositing money or sharing real passwords, private keys or recovery words.

What a liquidity provider contributes

Think of a community library in Melbourne where neighbours donate books and share the small late-return fees. The more they put in, the larger their share.

A liquidity provider (LP) deposits both tokens of a pair in equal value, for example 1 ETH and 2,000 USDC at an invented price of 2,000. The contract issues LP tokens as a receipt for their share. Uniswap's documentation describes these as pro-rata shares that can be redeemed for the reserves at any time. Fees are added to the pool, so when the LP redeems, their share includes fees collected.

Here the library analogy breaks down. A donated book stays the same book, but every swap changes a pool's balance, so what you withdraw can differ greatly from what you put in. That change has a name.

A liquidity provider deposits assets into a pool under its rules and receives an accounting interest or position representing a share of the pool. A withdrawal generally returns the asset mix the position then represents, not necessarily the original quantities. Fees, ranges and position structure depend on the version. Do not compare a displayed yield with a savings account without examining how the principal can change.

Follow a relative price change

Use a full-range, two-asset constant-product pool, ignoring fees and costs. Initially it holds ten practice coins priced at USD 100 and 1,000 stable quote units assumed worth USD 1. Its value is USD 2,000 and product k is 10,000. If the coin's outside price rises to USD 200 and arbitrage brings the pool ratio into line, x becomes approximately 7.0711 and y approximately 1,414.2136.

The pool has fewer rising coins and more quote units. At the new price, each side is worth about USD 1,414.21, giving total value USD 2,828.43. The assumptions include a stable quote value and adjustment to the outside price. Real pools may differ because of fees, ranges, other flows and market conditions. This example isolates the rebalancing effect rather than forecasting a live position.

Compare with holding the original assets

If the original ten coins and 1,000 quote units had simply been held, their value at USD 200 per coin would be USD 3,000. The pool value is approximately USD 171.57 lower. Relative to the hold-only benchmark, that is about 5.72 percent less. This is the illustrated impermanent loss before fees and costs.

Notice that the pool still gained USD 828.43 compared with the initial USD 2,000. A position can rise in cash value while underperforming the hold-only alternative. Always state the benchmark and denominator. Comparing only with the starting cash would answer a different question and could hide the opportunity cost. If the quote asset also changes value, the benchmark and pool calculation must both reflect that change.

Full-range constant-product illustration. Stable quote, no fees, no incentives and no costs are assumed.

Imagine two friends in Rome keeping a joint box split 50/50 by value between euros and a fast-moving stock. Each time the stock rises, the rule forces them to sell some, so they end up holding less of it than if they had left it alone.

Open diagram at original size ↗

Read diagram as text

Initial assets: USD 2,000. After the illustrated price doubles, pool value: approximately USD 2,828.43. Holding the original assets: USD 3,000.

The pool gains against initial cash but trails the hold-only benchmark by about USD 171.57, or 5.72%.

The comparison assumes no fees or costs.

Fees, incentives and impermanent loss

Trading fees can offset some or all of the benchmark difference, but the result is not guaranteed. Incentive tokens may change price or be difficult to sell. Subtract entry and exit costs, network fees and other relevant charges. Compare the full net position with the same initial assets held under a fair benchmark.

The term impermanent refers to the fact that the relative difference can change as prices change before withdrawal. It is not a promise that prices will return, that losses will recover or that the provider should wait indefinitely. Asset collapse, a stablecoin depeg or a contract exploit introduces risks beyond the isolated model. A complete result distinguishes modelled rebalancing from those additional failures.

The percentage shortfall is tied to a particular benchmark and pool model. For a full-range equal-value two-asset constant-product position without fees, the relative factor can be written as 2√r ÷ (1+r), where r is the new relative price divided by the starting relative price. Subtract one for the signed difference, or subtract the factor from one for a positive shortfall percentage. At r=2, the shortfall is about 5.72% of holding.

Do not describe that as a 5.72% loss of the initial cash. In the supplied doubling example, the pool gains against initial cash and still trails simply holding the starting assets. If both assets fall in the home currency, a position can also lose against initial cash. Relative underperformance and absolute loss are separate measurements.

Concentrated liquidity needs its own analysis

In a standard pool, your liquidity is spread across every price from near zero to near infinity, and most sits where trades never happen. Uniswap's documentation gives the example of a dollar-stablecoin pair trading between US$0.99 and US$1.01, where only about 0.5% of an older-style pool's money was used.

Uniswap's version 3 introduced concentrated liquidity: an LP chooses a price range, and their money only works inside it, earning more fees per dollar there. Outside the range, the position stops earning, and as the price moves through the range it gradually turns into only one of the two tokens.

Think of a street vendor in Seoul who sets up only where the crowd is, and earns nothing once it moves on. Narrow ranges need watching and adjusting, each adjustment costs gas, and losses from price moves are sharper. Higher fees here come with more work and more risk.

Whatever the pool design, your swap waits in public before it enters a block. Some people make a business of that wait.

Within the range, the position can be more sensitive to price changes and earn fees under the version's rules. Outside the active range, it may hold predominantly or entirely one asset and stop earning trading fees until conditions or the position change. Do not apply the simple full-range percentage to every concentrated position. A displayed high APR may reflect a narrow range or a recent short period rather than a stable result. The next lesson examines lending collateral, which has a different loss mechanism: liquidation.

Try the following questions aloud or on paper before opening the worked answers. Compare your reasoning as well as your final answer.

References and further reading