How this calculator works
The model keeps a two-token geometric-mean invariant with fixed value weights. Arbitrage rebalances pool quantities as external prices change. The pool value is compared with simply retaining the initially deposited quantities. Both token prices may move. Reverse modes scale a dollar shortfall into a deposit or solve the future A price for a target loss. Price inversion has two branches, so specify whether A rises or falls relative to B. Fees, liquidity additions, rewards, concentrated liquidity ranges and protocol-specific adjustments are excluded.
Formula
Held = D[w(PA1/PA0) + (1-w)(PB1/PB0)]. Pool = D(PA1/PA0)^w(PB1/PB0)^(1-w). Loss magnitude = 1 - Pool/Held. At w = 0.5 this becomes 1 - 2sqrt(q)/(1+q).
Worked example
For a $1,000 50/50 deposit, a fourfold A price with B unchanged gives $2,500 if held and $2,000 in the pool, a 20% divergence loss. If both prices double, both strategies become $2,000 and the loss is zero.
Advertisement
Frequently asked questions
Can the pool value rise while impermanent loss is positive?
Yes. Loss here is relative to holding the same starting assets, not necessarily a loss against the initial deposit.
Does this model Uniswap concentrated liquidity?
No. A bounded liquidity range changes the payoff and can leave the position entirely in one asset.
Can trading fees offset the loss?
They can affect the overall result, but this tool deliberately compares price-driven values before fees and incentives.