Liquidity-provider returns: fees, inventory and impermanent loss

A liquidity pool can collect trading fees while its providers finish with less value than they would have had by simply keeping their original tokens. There is no contradiction: fees are one component of the result, while the pool continually changes the assets a provider owns.

To understand a liquidity-provider return, keep two comparisons separate: the position's gain or loss since entry, and its performance against holding the same starting inventory. A positive return can still trail that benchmark.

The pool changes your inventory

Consider the full-range, constant-product design described in the Uniswap v2 whitepaper. Ignoring fees, reserves follow x × y = k. Trading changes the quantities of the two tokens while preserving their product. A provider owns a proportional claim on those reserves, rather than a promise to receive the original quantities back.

When one token becomes more valuable relative to the other, arbitrage trading changes the pool's balance toward the new relative price. The provider ends up with less of the appreciating token and more of its counterpart. This inventory change is central to the comparison with holding. It is different from the execution question covered in swap slippage and price impact.

A hypothetical price doubling

Assume a fee-free pool contains 10 units of token A and 1,000 units of token B. Token A initially costs 100 B, so each side has equal value and the pool is worth 2,000 B. Treat this whole pool as the example position. No one adds or removes liquidity, B is our accounting unit, and arbitrage aligns the pool with an external price of 200 B per A.

The product remains 10,000. The new reserves must satisfy both A × B = 10,000 and B / A = 200. Therefore A becomes approximately 7.0711 and B becomes 1,414.2136.

The pool gained approximately 41.42% from its starting value. Holding gained 50%. The pool is approximately 5.72% below the holding benchmark: 2,828.4271 / 3,000 − 1. That last percentage uses the final holding value as its denominator; it is not a 5.72% loss of the initial deposit.

Uniswap's return explanation describes this relative shortfall as impermanent loss, also called divergence loss. In this simplified model it disappears if the relative price returns to its starting point while the position remains unchanged. The name does not promise that prices will return or that selling the position restores the shortfall. Nor does it describe every cause of loss in an actual pool.

Fees must be measured alongside the assets

Fees can offset a shortfall against holding, but a fee percentage displayed beside a pool does not demonstrate that they have done so. The result depends on actual trading, the provider's share of active liquidity, the applicable fee rules and the prices at which all remaining tokens are valued.

The Uniswap fee documentation distinguishes swap fees from protocol fees. It also explains that v2 adds fees to reserves, while v3 and v4 record claimable position fees separately. Consequently, a return calculation must avoid either omitting uncollected fees or counting reinvested fees twice. Incentive tokens, if any, belong on a separate line with their own valuation and realization assumptions.

For a personal worksheet, record the original token quantities, final withdrawable quantities, collected and uncollected fees, external cash flows, and transaction costs. Value both the position and the original-token benchmark at the same endpoint prices. Comparing returns on the same clock matters just as much here as in an ordinary portfolio comparison.

Concentrated liquidity changes the calculation

The example above is not a formula for every automated market maker. Under Uniswap's concentrated-liquidity design, a position has chosen lower and upper price bounds. Its principal inventory can become entirely one token when the price leaves that interval, and it stops earning swap fees while inactive. Previously earned fees remain a separate accounting item.

A narrow interval can deploy more liquidity around a price, but it also makes those boundaries more relevant. Moving the range changes the strategy and may require transactions or trades. A useful report therefore shows range changes and time spent inactive, as well as fee income. The question is what the complete position delivered after its inventory changed, compared with the clearly stated alternative of holding.