How to use it
- Pick the pool model: constant product (with a weight for token A) or a two-coin stable pool (with an amplification value).
- Enter your deposit in CAD.
- Enter how much token A's price changes relative to token B, as a percentage.
- Enter an illustrative fee APR and the number of days.
- Compare the pool value with the hold value, and note the fee APR needed to break even.
What impermanent loss measures
In an automated market maker, arbitrage traders rebalance the pool whenever prices move elsewhere. If token A rises, the pool ends up holding less A and more B; if A falls, more A and less B. Compared with keeping your original tokens in a wallet, you always finish with more of whichever asset did worse.
Impermanent loss is the percentage by which the pool position trails that simple hold, before fees. It is “impermanent” only in the sense that it disappears if prices return exactly to where they were when you deposited; withdraw after a move and it is realized. It is measured against holding, not against your starting CAD value, so a pool position can show impermanent loss and still be up in dollars.
Constant-product pools
For a 50/50 constant-product pool, the loss depends only on the ratio r between token A's new and old price relative to token B: pool ÷ hold = 2√r ÷ (1 + r). The loss is symmetric in ratio terms, so halving and doubling both cost 5.72%.
Weighted pools soften the effect for the heavier token. With an 80/20 weighting, a doubling of token A costs 3.27% instead of 5.72%, and a halving costs 4.28%. The general formula is pool ÷ hold = r^w ÷ (w × r + 1 − w), where w is token A's weight.
| Price change of A against B | Ratio r | Impermanent loss |
|---|---|---|
| −75% | 0.25 | −20.00% |
| −50% | 0.5 | −5.72% |
| −25% | 0.75 | −1.03% |
| +25% | 1.25 | −0.62% |
| +50% | 1.5 | −2.02% |
| +100% | 2 | −5.72% |
| +200% | 3 | −13.40% |
| +400% | 5 | −25.46% |
Stable pools: why higher amplification can mean more loss
Pools for two assets meant to trade at the same price use an amplified curve that keeps the pool price close to 1:1 across a wide range of balances. The calculator solves that curve numerically for a two-coin pool. While both coins hold their peg, impermanent loss is negligible. When one coin depegs, the picture changes.
A higher amplification (A) keeps the pool price near 1:1 for longer, so arbitrage drains more of the sound coin before the pool price catches up. For a coin trading at 0.90 of its partner, the loss is 1.91% with A = 10, 3.86% with A = 100 and 4.78% with A = 1,000, while a plain 50/50 constant-product pool would lose only 0.14%. In a severe depeg to 0.50, an A = 100 pool trails holding by 30.16%. See stablecoin depeg risk.
Worked example: fees against loss
Illustrative inputs: $10,000 in a 50/50 constant-product pool, token A doubles against token B, a 10% fee APR, 365 days. Holding would be worth $15,000.00. The pool before fees is worth $14,142.14, an impermanent loss of $857.86 (5.72%). Fees at 10% a year on the pool value add $1,414.21, for a total of $15,556.35, which is $556.35 ahead of holding. The fee APR needed just to break even over that year is 6.07%.
In a stable pool with A = 100, a $10,000 deposit where one coin falls 10% and fees run at an illustrative 4% for a year ends at $9,498.33, against $9,500.00 for holding. The fees barely cover the loss, and the position is down in CAD either way.
Fee income here is simple: fee APR × time, applied to the pool value before fees. Real fee income varies with trading volume and your share of the pool. Concentrated-liquidity positions behave differently again: their loss is larger within the chosen range, and they stop earning fees outside it.
What the calculator leaves out
It does not model gas to enter and exit, reward tokens, smart contract risk, oracle risk in pools that rely on external price feeds, or the chance that one token goes to zero. For farming with reward tokens and gas, use the yield farming calculator.
For Canadian taxes, CRA lists exchanging one crypto-asset for another as a disposition, but it has not published guidance on depositing into or withdrawing from liquidity pools. Keep detailed records of each deposit and withdrawal, and see capital vs business income.