Impermanent loss compares the value of providing liquidity with holding the same starting assets outside the pool. Its name does not guarantee that a difference will reverse. This example uses a full-range, constant-product, initially equal-value position with no fees or incentives. A stated benchmark and denominator are essential to interpreting the result.
The position gains value against its starting amount while trailing holding by about 5.72%. Reference prices are hypothetical.
BTKWIN.COM · EDUCATIONAL EXAMPLEDefine the comparison before calling something a loss
Start with one unit of an asset priced at one hundred reference units and one hundred units of a second asset assumed to remain worth one reference unit each. Combined starting value is two hundred. If the first asset’s price doubles to two hundred, simply holding the original quantities gives three hundred.
That holding portfolio is the benchmark, not merely the initial investment and not the best trade selected with hindsight. Compare both strategies at the same ending timestamp and using the same prices. Otherwise a reported difference can reflect valuation choices rather than the effect being examined.
The Uniswap v2 returns documentation discusses liquidity returns relative to holding. The calculation here is deliberately narrower than every real pool: full range, constant product, initially 50/50 by value and no trading fees or incentives.
Follow how the position’s composition changes
When one asset becomes more valuable relative to the other, trading and arbitrage can remove some of it from the pool and add the counterpart. The provider consequently holds less of the asset that rose and more of the other one than the original wallet would have held.
In the example, the initial quantity product is one multiplied by one hundred, or one hundred. After the external price doubles, assume the pool rebalances toward the new ratio. Quantities satisfying that product and a reference-asset-to-volatile-asset ratio of two hundred are approximately 0.7071 and 141.4214.
Value the first quantity at two hundred: approximately 141.42 reference units. Adding the counterpart’s 141.42 gives approximately 282.84. The holding portfolio remains one asset worth two hundred plus one hundred reference units, totaling three hundred. The difference is approximately 17.16.
Keep the two percentages separate
Divide the 17.16 difference by the holding value of three hundred to obtain approximately 5.72% underperformance. Alternatively, divide the position’s 82.84 gain by its starting value of two hundred to obtain approximately 41.42% growth. These ratios answer different questions and can both be correct.
| Hypothetical item | Start | Holding at doubled price | Pool before fees |
|---|---|---|---|
| First-asset quantity | 1 | 1 | About 0.7071 |
| Reference-asset quantity | 100 | 100 | About 141.42 |
| Reference value | 200 | 300 | About 282.84 |
The position is worth more than its starting value in this rising-price example, yet less than the specified alternative. Calling the entire difference a realized cash loss would obscure that distinction. State whether the calculation measures benchmark underperformance, a change from initial value or actual cash proceeds after exit.
What if the price falls instead?
Return to the same starting assets and halve the first asset’s price from one hundred to fifty, keeping the counterpart stable. The same model gives approximately 1.4142 units of the first asset and 70.7107 reference units. Their combined value is approximately 141.42.
Holding the original quantities would instead be worth 150. The gap is approximately 8.58, again about 5.72% of the holding benchmark. The similar relative gap under doubling and halving does not make their absolute outcomes similar: the falling-price position is below its original two hundred.
When both assets move, their relative price change drives this model’s compositional comparison. Their cash valuations can still change together. A small divergence from holding does not mean stable cash value, and two volatile assets do not become a stable-value position merely by moving in parallel.
The word impermanent does not promise recovery
If the original price ratio returns exactly in the simplified no-fee model, the theoretical rebalancing gap disappears. But whether and when that happens is unknown. Leaving a position open maintains exposure to the assets, contract and market conditions; waiting does not create an obligation for prices to return.
Real flows can also complicate the benchmark. Adding liquidity or withdrawing partway requires dated quantities and corresponding holding comparisons. The number of position-representing tokens can remain unchanged while the underlying composition changes. Evaluate actual asset entitlements rather than assuming a constant token count means a constant basket.
The concentrated-liquidity guide explains positions with chosen ranges, including inactive out-of-range liquidity. Do not apply the full-range result unchanged to a narrow position. Its composition and fee eligibility depend on price relative to its particular range.
Add fees without hiding the benchmark
Record the network, pool, assets, quantities, prices and timestamp at entry. At review, use actual position quantities and simultaneous prices, keeping earned fees separate where they are not already included. If an interface includes fees in the position value, adding them again overstates returns.
In the rising-price example, an independent hypothetical ten reference units of fees outside the quoted position value increase 282.84 to 292.84 before other costs. The position still trails holding at three hundred by 7.16. Four units of entry and exit costs then leave 288.84.
These figures do not predict a fee yield or assume prices remain unchanged while exiting. When comparing cash exits, apply appropriate conversion costs consistently to both paths. A holding portfolio valued before sale is not directly comparable with a pool position valued after converting everything to cash.
Interpret yield displays and stable-asset pairs carefully
An interface’s yield can describe fees only, incentives at a current price or a short period annualized. Read the definition and whether asset-value changes are included. Positive fee income can coexist with a negative total result or underperformance against holding without any arithmetic contradiction.
A pair of assets normally maintaining similar values still needs assessment of redemption, issuer, liquidity and contract risks. A loss of value in one asset can change the position’s composition materially. The impermanent-loss calculation does not measure every source of possible loss.
Use the comparison to identify how a changing basket differs from a stated holding alternative and how much net fee income would offset the gap in a scenario. It does not forecast price or choose a suitable investment. Preserve actual quantities, dated valuations, costs and excluded factors so that the result can be reviewed rather than reduced to a yield headline.
Continue reading
English content and examples reviewed: 27 October 2026. Read the Arabic edition.
