Compare providing liquidity with simply holding
By the end, explain the diagram in your own words, solve the case and justify the correction.
Prerequisites : Liquidity pools and automated market makers
Level 2 · Intermediate →Reading path · 28 / 35 · 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
- Same starting assets
- Relative price changes
- Pool rebalances quantities
- Compare with holding
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.