Liquidity-Provider Fee APR

Install and import

bash

npm install fintech-algorithms

import { feeApr } from "fintech-algorithms/digital-assets-and-on-chain-finance/liquidity-and-liquidation/liquidity-provider-fee-apr";

Signature

feeApr(data, config)

Annualised fee return for a liquidity position. Meaningful only net of impermanent loss: a headline APR quoted against a divergent pair routinely describes a losing position.

Parameters

Name	Type	Notes
`data`	`PositionInput`	Position state — balances, prices, and the protocol parameters the calculation depends on.
`config`	`ProtocolConfig`	Protocol-specific thresholds and factors. These differ per protocol and per asset, so a figure computed under the wrong config is confidently wrong.

Returns

{ status, value, components, diagnostics }

The result with every component, so a position's state can be reconciled against the protocol's own interface.

Errors

When a required protocol parameter is missing — reported as a status rather than thrown

Complexity: time O(assets), space O(assets).

Worked example

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input

data

{
  "rows": [
    {
      "timestamp": "2026-01-01T00:00:00Z",
      "duration_days": 1,
      "volume": 2500000,
      "fee_rate": 0.003,
      "lp_share": 0.02,
      "lp_capital": 1000000
    },
    {
      "timestamp": "2026-01-02T00:00:00Z",
      "duration_days": 1,
      "volume": 2738636.056514657,
      "fee_rate": 0.003,
      "lp_share": 0.02,
      "lp_capital": 1000000
    },
    {
      "timestamp": "2026-01-03T00:00:00Z",
      "duration_days": 1,
      "volume": 2930007.3153574164,
      "fee_rate": 0.003,
      "lp_share": 0.02,
      "lp_capital": 1000000
    }
  ]
}

config

{
  "annualization_days": 365,
  "protocol_fee_share": 0,
  "capital_basis": "time_weighted"
}

Call

feeApr(data, config)

Returns

object with 11 fields: elapsed_days, gross_volume, lp_fee_income, time_weighted_average_capital, capital_denominator, capital_basis, protocol_fee_share, simple_fee_apr, …

{
  "elapsed_days": 365,
  "gross_volume": 912500000,
  "lp_fee_income": 54750,
  "time_weighted_average_capital": 1000000,
  "capital_denominator": 1000000,
  "capital_basis": "time_weighted",
  "protocol_fee_share": 0,
  "simple_fee_apr": 0.05475,
  "period_fee_return": 0.05475,
  "annualization_days": 365,
  "trace": [
    {
      "index": 0,
      "timestamp": "2026-01-01T00:00:00Z",
      "volume": 2500000,
      "lp_capital": 1000000,
      "daily_fee_income": 150,
      "cumulative_fee_income": 150,
      "running_apr": 0.05475
    },
    {
      "index": 1,
      "timestamp": "2026-01-02T00:00:00Z",
      "volume": 2738636.056514657,
      "lp_capital": 1000000,
      "daily_fee_income": 164.3181633909,
      "cumulative_fee_income": 314.3181633909,
      "running_apr": 0.0573630648
    },
    {
      "index": 2,
      "timestamp": "2026-01-03T00:00:00Z",
      "volume": 2930007.3153574164,
      "lp_capital": 1000000,
      "daily_fee_income": 175.8004389214,
      "cumulative_fee_income": 490.1186023123,
      "running_apr": 0.0596310966
    }
  ]
}

Other exports

This module also exports impermanentLoss, healthFactor, liquidationPrice, liquidationWaterfall, runTopic. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.

Diagrams

Liquidity-Provider Fee APR — boundary audit

Liquidity-Provider Fee APR — calculation map

Liquidity-Provider Fee APR — diagnostic deep dive

Liquidity-Provider Fee APR — family handoff

Liquidity-Provider Fee APR — parameter sensitivity

Liquidity-Provider Fee APR — scenario suite

How it works

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References

Uniswap v2 Core — Uniswap; Hayden Adams, Noah Zinsmeister, and Dan Robinson
Uniswap v3 Core — Uniswap; Hayden Adams, Noah Zinsmeister, Moody Salem, River Keefer, and Dan Robinson
UniswapV3Pool.sol — Uniswap; Uniswap Labs and protocol contributors
Evidence boundary