Worked case study / Follow the assumptions
The pool gained. Holding still did better.
A positive CAD return and an impermanent loss can happen at the same time. The missing piece is the comparison with simply holding the original tokens.
50/50 by value / full-range constant-product model
Only A doubles
Hold$1,500
Pool$1,414.21
Both double
Hold$2,000
Pool$2,000.00
Only A halves
Hold$750
Pool$707.11
One starting basket, two ways to hold it
Begin with CAD 1,000 split equally between two fictional tokens, A and B. Both initially cost CAD 1, so the basket contains 500 A and 500 B. One version stays in a wallet. The other supplies a full range 50/50 constant product pool with no fees. We compare their final CAD values using the same final token prices.
Keeping the tokens in a wallet leaves their amounts unchanged. The pool changes its token amounts as prices change relative to each other. This example assumes the pool has adjusted to the final price ratio in the wider market. It leaves out entry costs, exit costs and rewards to make that difference easier to see.
A doubles, B stays unchanged
Let A rise to CAD 2 while B remains at CAD 1. The untouched basket is worth CAD 1,500: CAD 1,000 of A plus CAD 500 of B. The modelled pool position is worth about CAD 1,414.21. It has gained CAD 414.21 against the original deposit, yet it is CAD 85.79 behind holding.
Relative to the CAD 1,500 holding benchmark, that shortfall is about 5.72%. This is the model's impermanent loss. It is not a 5.72% fall from the initial CAD 1,000. Comparing with the starting deposit would give a different percentage.
The pool position now corresponds to roughly 353.553 A and 707.107 B in this simplified setup. Compared with holding, it contains less of the token that appreciated and more of the unchanged token. Both sides have equal CAD value at the new prices.
The relative price move matters
If both tokens instead double, their relative price stays unchanged. Holding and the modelled pool are each worth CAD 2,000. The CAD value has grown, but there is no gap between the pool and holding in this model.
If A halves to CAD 0.50 and B stays at CAD 1, holding finishes at CAD 750 and the pool at about CAD 707.11. The relative shortfall is again about 5.72%, although the CAD outcomes are very different from the first path. In this model, doubling the price ratio and halving it create the same percentage gap.
| Independent final-price path | Holding | Pool before fees | Pool minus holding |
|---|---|---|---|
| A doubles; B unchanged | CAD 1,500.00 | CAD 1,414.21 | −CAD 85.79 |
| Both double | CAD 2,000.00 | CAD 2,000.00 | CAD 0.00 |
| A halves; B unchanged | CAD 750.00 | CAD 707.11 | −CAD 42.89 |
How much would fees change the first comparison?
Return to the path where only A doubles. Add hypothetical fee income of CAD 100 to the final pool value. The result is CAD 1,514.21, around CAD 14.21 ahead of holding before any other costs. In this simple additive comparison, CAD 85.79 of fee income would approximately close the original gap.
The CAD 100 is an input, not an earnings estimate. Nothing here predicts trading volume, the position's share of fees, how fee assets change in value or how long the position remains open. An annual percentage yield cannot be inferred from a final fee amount without additional assumptions.
Keep both comparisons visible
Use the calculator to compare the final pool value with the initial deposit and the value of keeping the original tokens. The first shows the CAD gain or loss on the deposit. The second shows how far ahead of or behind holding the pool is. Both still leave out some costs and risks of supplying liquidity.
This example does not model concentrated liquidity, custom weights, liquidation, protocol failures or a stablecoin losing its peg. The word impermanent also does not promise that the gap will disappear. A later price-ratio reversal could change the comparison, while withdrawing at the modelled endpoint fixes that endpoint's token quantities for the next decision.