Awarded once after a correct answer.
Compare providing liquidity with simply holding
Useful first : Liquidity pools and automated market makers
Reading path · 28 / 41 · Intermediate
Impermanent loss measures how a liquidity-provider position differs from simply holding its initial assets as relative prices change.
The essentials
Impermanent loss measures how a liquidity-provider position differs from simply holding its initial assets as relative prices change. It is a comparison of strategies, not necessarily a negative return in currency terms. Trading fees can offset the difference but need not do so.
How it works
For an idealised equal-value, full-range constant-product pool without fees, the relative value is 2 × sqrt(r) / (1 + r), where r is the price ratio change. If one asset doubles relative to the other, the pool position is about 94.28% of the hold strategy: a 5.72% shortfall before fees.
What to watch
This formula does not directly describe concentrated liquidity, weighted pools or lending positions. A price returning to the starting ratio can remove the modelled divergence, but there is no guarantee it will return. Withdrawal realises the position at that time; the label impermanent should not be interpreted as a promise of recovery.
Understand the details
Divergence loss compares the pool position with holding the same initial assets outside the pool. In a fee-free 50/50 constant-product model, arbitrage changes the quantities held as the relative price moves. The provider ends up with less of the asset that appreciated and more of the other asset.
Boundaries and common mistakes
The word impermanent can mislead: withdrawal realizes the difference at that moment, and prices may never return. Fees may offset the gap but are uncertain. Concentrated liquidity changes the exposure and can leave a position entirely in one asset outside its range. Compare like-for-like values and include fees separately.
The mechanism at a glance
- 01Same starting assets
- 02Relative price changes
- 03Pool rebalances quantities
- 04Compare with holding
Read these as connected concepts, not necessarily consecutive steps.
Read the explanation
Divergence loss compares the pool position with holding the same initial assets outside the pool. In a fee-free 50/50 constant-product model, arbitrage changes the quantities held as the relative price moves. The provider ends up with less of the asset that appreciated and more of the other asset.
Put the mechanism into context
Start with 1 X worth 100 and 100 stable units. If X doubles to 200, simply holding is worth 300. In the idealized fee-free pool, the position becomes approximately 0.7071 X and 141.42 stable units, worth 282.84.
Apply it in the workshop →What this mechanism does not guarantee
The word impermanent can mislead: withdrawal realizes the difference at that moment, and prices may never return. Fees may offset the gap but are uncertain. Concentrated liquidity changes the exposure and can leave a position entirely in one asset outside its range. Compare like-for-like values and include fees separately.
The distinction that changes the analysis
Measure both alternatives at the same final prices and with the same starting assets. A pool can gain in euro value while still underperforming holding. Fees belong in a separate line so you can see whether they offset that relative difference.
Explain it yourself
Revisit the case above. Name what is established, what remains to be checked and the evidence needed to conclude. A strong answer addresses both sides of the diagram.
Apply the lesson to a case
Start with 1 X worth 100 and 100 stable units. If X doubles to 200, simply holding is worth 300. In the idealized fee-free pool, the position becomes approximately 0.7071 X and 141.42 stable units, worth 282.84.
It is above the initial 200 but below holding by 17.16, or about 5.72% of 300. Divergence loss is relative underperformance, not necessarily an absolute loss. State the benchmark clearly and avoid presenting the result as a forecast for all pool designs.
Terms in this lesson
- Impermanent loss
- The value shortfall of certain liquidity-provider positions relative to holding the original assets after relative prices change.
Prepare a correction note
Describe the passage and the proposed correction. This creates a local note for you to share; it sends nothing. Do not include personal or confidential information.