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Encyclopedia DeFi · Entry 54

Impermanent loss: comparing pool inventory with simply holding

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DeFi
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Key facts

Key facts for Impermanent loss: comparing pool inventory with simply holding
FactDetailSource
BenchmarkThe comparison is with holding the original quantities.[1]
ModelThe simple formula assumes full-range equal-value constant-product liquidity.[1]
FeesSwap fees can offset some shortfall but do not guarantee a profit.[1][2]
01

Derive a concrete fourfold-price example

Start with 1 A and 100 B when A costs 100 B. Ignore fees and assume arbitrage moves the pool to the external price. If A rises to 400 B, the product remains 100 and the new balances are 0.5 A and 200 B: their ratio is 400 B per A.

The pool position is now worth 400 B. Holding the original assets would instead be worth 500 B: 1 A at 400 B plus 100 B. The pool underperforms holding by 100 ÷ 500 = 20%, even though its value increased from the initial 200 B.

02

Relative loss is different from cash loss

The comparison needs both a benchmark and a valuation asset. A position can rise in value while falling behind holding, as above. It can also decline in value while collecting fees. Calling all fees profit ignores the inventory that produced them.

The word impermanent describes the possibility that the relative price returns. It does not promise that it will return or that waiting repairs a position. A withdrawal realizes the current inventory, and later market movements occur outside that pool position.

03

Do not apply one formula to every position

The expression assumes no fees, no deposits or withdrawals, continuous repricing to the outside market and a full-range 50:50 value setup. Real results also depend on gas, token behavior, fee income and the exact execution path.

A concentrated range can become entirely one asset and needs a range-specific calculation. A leveraged position adds borrowing and liquidation exposure. State these boundaries whenever quoting a loss percentage so that a compact answer does not silently change the model.

Direct answers

Questions people ask

Is impermanent loss the same as a hacked pool?

No. It describes an inventory-versus-holding comparison under normal market making. Contract exploitation is a different source of loss and is not captured by the formula.

Inspect the evidence

The answer and key facts have stable claim links. These records retain the scope and qualification when reused.

Impermanent loss is the shortfall of an AMM liquidity position relative to holding its original assets, under a specified price comparison. In a fee-free, full-range, equal-value constant-product pool it is 2√r ÷ (1 + r) − 1, where r is the relative price change. Fees and other costs must be assessed separately.

Scope: DeFi. Verification: verified · 2026-10-02T15:08:18.373Z.

Link to this claim
Benchmark: The comparison is with holding the original quantities.

Scope: DeFi. Verification: verified · 2026-10-02T15:08:18.373Z.

Link to this claim
Model: The simple formula assumes full-range equal-value constant-product liquidity.

Scope: DeFi. Verification: verified · 2026-10-02T15:08:18.373Z.

Link to this claim
Fees: Swap fees can offset some shortfall but do not guarantee a profit.

Scope: DeFi. Verification: verified · 2026-10-02T15:08:18.373Z.

Link to this claim
Revision history
  1. — First publication after primary-source research and independent automated verification.

Source register

Sources and references

Retrieval dates and locators are recorded individually.
  1. Understanding returnsUniswap

    The no-fee full-range constant-product comparison with holding both tokens.

    Locator: Risks; Why is my liquidity worth less than I put in? · Version / scope: Uniswap v2 · Retrieved: 2026-10-02Open source
  2. Uniswap v2 pair sourceUniswap

    Reserve accounting, LP shares, fee-adjusted invariant and optional protocol fee.

    Locator: mint; burn; swap; _mintFee · Version / scope: v2-core v1.0.1 · Retrieved: 2026-10-02Open source
  3. Introducing Uniswap v3Uniswap Labs

    Range-based liquidity, inactive positions and position-specific accounting.

    Locator: Concentrated Liquidity; Active Liquidity; Non-Fungible Liquidity · Version / scope: 2021-03-23 announcement · Retrieved: 2026-10-02Open source
How this article was made

Research and drafting use AI assistance. A separate automated review checks claims against primary sources; no external expert or named human review is implied. Publication, substantive editing, source retrieval and verification are recorded separately. This version was independently checked by an automated reviewer on 2 October 2026.

Editorial method and corrections

Degrees of Satoshi editorial project. “Impermanent loss: comparing pool inventory with simply holding.” Published 2026-10-02; updated 2026-10-02. https://degreesofsatoshi.com/encyclopedia/impermanent-loss/