A concrete example
In an ideal equal-value constant-product pool, a doubling of relative price creates about 5.72% divergence before fees.
In context
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.
The related mechanism, visually
- 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.
Explore the full explanation
Impermanent loss with a worked example
Impermanent loss measures how a liquidity-provider position differs from simply holding its initial assets as relative prices change.