FOLLOW THE MECHANISM
- 1Start
Record the exact initial quantities as the hold benchmark.
- 2Rebalance
Arbitrage changes pool inventory as relative prices move.
- 3Compare
Value the pool and original basket at the same ending prices.
A conceptual sequence. Real implementations can add steps, intermediaries, and conditions.
Choose the comparison first
The phrase impermanent loss usually describes how an LP position performs relative to simply holding the same starting token quantities. Divergence loss is a clearer name because the difference need not disappear. It is not the same as a decline in dollar value. Both strategies might gain, or both might lose, while one outperforms the other. The benchmark must use the same starting assets, time interval and valuation currency, or the comparison cannot isolate the effect of pool inventory changes.
Derive the full-range result
For a 50:50 constant-product pool with no fees, no new deposits and arbitrage that aligns the pool with an outside price, let r be the ending price divided by the starting price. The LP value divided by the hold value is 2√r ÷ (1 + r). Subtract one to express relative divergence. This comes from combining x × y = k with the new reserve ratio. It is an original algebraic comparison of the model, not a measured yield or an estimate for a live position.
An illustrative doubling
Start with one A worth 100 B and 100 B, for total value 200 B. If A’s price doubles, holding gives 300 B. The no-fee pool’s corresponding inventory is approximately 0.7071 A and 141.42 B, worth 282.84 B. The pool gained 41.42%, yet it trails holding by 17.16 B, or about 5.72% of the hold benchmark. A rising portfolio can therefore experience divergence loss. The word loss alone hides which comparison is being made.
Fees and ranges complicate the outcome
Trading fees can offset some or all benchmark underperformance, but that requires actual volume and fee accrual. Incentive tokens are a separate uncertain source of value. Concentrated liquidity changes the inventory path and can leave the position entirely in one asset outside its range, so the simple formula does not apply unchanged. Transaction costs, rebalancing, token failures and correlated price moves also matter. If relative prices return to the starting ratio, the ideal no-fee full-range divergence closes; nothing guarantees that path.
MAKE IT CONCRETE
A useful boundary check
At r = 1 the formula gives zero divergence. At r = 4, the pool is worth 80% of the hold benchmark before fees, a 20% relative difference.
FAILURE PATHS & COMMON MISREADINGS
Where the model can break
- Impermanent does not mean guaranteed to recover.
- The 50:50 formula is not valid for every concentrated-liquidity position.
KEEP EXPLORING