Liquidity pools: fees, inventory and divergence loss

Liquidity provision is a changing inventory

An automated market maker holds reserves and allows swaps according to a rule. In a basic constant-product model, reserve quantities x and y satisfy x × y = k, ignoring fees for the simplified calculation. Uniswap’s documentation distinguishes this early model from concentrated-liquidity designs. A liquidity provider supplies inventory that changes as traders exchange one asset for the other.

The position is therefore not simply two tokens earning interest. When one asset rises relative to the other, arbitrage trades adjust the pool’s inventory. The provider ends with less of the appreciating asset and more of the other one than an unchanged wallet would hold. Fee income must be evaluated against this inventory effect.

Work through the no-fee benchmark

Suppose a pool initially holds 10 units of token A and 1,000 units of a dollar token. Token A is worth $100, so the pool is worth $2,000 and k equals 10,000. If the external price doubles to $200 and arbitrage aligns the pool, its reserves satisfy y ÷ x = 200 and x × y = 10,000. Solving gives about 7.071 A and 1,414.214 dollar tokens.

The pool is then worth approximately $2,828.43. Simply holding the original assets would be worth $3,000. The $171.57 difference is about 5.72% of the hold benchmark. The pool still gained in dollar value, but underperformed holding. Loss relative to a benchmark is not the same as an absolute negative return.

Add fees without erasing the benchmark

Trading fees can offset some or all of that relative loss, but the amount depends on volume, fee rules, the provider’s share and price path. Quoting a fee rate does not establish the net return. A pool with high volume might also face adverse selection when better-informed traders trade against stale relative prices.

For a practice ledger, separate starting assets, ending assets, collected fees, incentives, gas and management costs. Value all components at the same endpoint prices. If fees are retained in reserves, avoid adding them a second time. If rewards remain unclaimed, distinguish marked value from cash realized through a sale. Consistent accounting matters more than an impressive annualized dashboard number.

Concentrated ranges change the exposure

Concentrated-liquidity systems allow capital to operate within a chosen price interval. The Uniswap v3 whitepaper describes liquidity over bounded ranges rather than uniformly over every possible price. This can increase capital efficiency while making the inventory response more concentrated. A position outside its active range can become entirely one of the two assets and stop earning trading fees until price returns, under the relevant pool mechanics.

Narrower is not automatically better. Compare a narrow range and a broad range under the same hypothetical price path, including the cost and timing of repositioning. Frequent resets can create transaction expenses and crystallize inventory changes. A backtest that moves a range instantly at a historical price may omit the main difficulty of implementing the strategy.

Define the objective before measuring success

A provider might compare results with holding both assets, holding only the quote asset, or a target rebalancing policy. These benchmarks answer different questions. Choose one before observing the outcome and retain the alternatives as context. Otherwise a losing strategy can be made to look successful merely by switching comparisons afterward.

Also stress token impairment, pool-contract failure and an inability to exit. Divergence-loss arithmetic assumes functioning assets and a working market; it is not a full risk estimate. A small calculated benchmark shortfall does not cap the possible principal loss. The examples here isolate mechanisms for education and deliberately omit a recommendation to provide liquidity in any particular pool.

A second practice path can end at the original price after a large intermediate excursion. Compare the passive holding result with a provider who repeatedly moved a concentrated range. Identical starting and ending prices do not imply identical outcomes once trading fees, inventory resets and transaction expenses are introduced. Path dependence should therefore be visible in the research design, not hidden inside an endpoint return chart.

Measure fees against the right alternative

A pool position can earn fees and still lag the assets that were deposited. Suppose a fictional starting basket is worth $10,000. At the review date, simply holding that basket would be worth $10,500. The pool inventory is worth $10,200 before separately counted fees; fees add $300, and network and rebalancing costs subtract $50. Net value is $10,450: a $450 gain from the starting value, but $50 less than holding.

Both comparisons matter, and neither should be hidden. “The position made money” describes the change from the starting value. “The position underperformed holding” describes a different benchmark. In this example, the fees needed to match holding were $350: the $300 inventory gap plus $50 of expenses. If your chosen pool’s fee accounting already includes earned fees in the reported position value, do not add them again.

Use a cash-flow record with dates for deposits, withdrawals, fees and rebalancing. Adding capital halfway through the period changes the interpretation of a simple start-to-finish percentage. Keep the benchmark funded on the same dates so that the comparison measures the liquidity-provision decision rather than an accidental difference in timing.

A narrow range is an inventory commitment

Concentrated-liquidity designs let liquidity providers choose a price interval. When the price leaves that interval, the position can become entirely one of the pair’s assets and stop earning trading fees until it is active again. Uniswap documents how active ranges behave. Capital efficiency inside a range is not a promise of a better total outcome.

Imagine that the price moves steadily through your entire range while you are away. Before considering a new range, describe the inventory you now own. Would you be comfortable holding it without the fee label attached? Moving the range can require trading into a new mix, paying costs and choosing a fresh exposure. It does not erase the path that produced the existing inventory.

For practice, compare two price paths that end at the same level: one moves directly there, while the other repeatedly crosses the range. Their fee opportunities and management decisions need not be identical. A single ending price is therefore insufficient to reconstruct the lived result. Record time in range, trading activity, costs and the rules used for any changes rather than evaluating the position from an attractive annualized fee snapshot.