Impermanent loss: compare a liquidity pool with holding

Impermanent loss is a shortfall against holding the tokens you put into a liquidity pool, valued at the same later prices. A position can gain dollar value and still trail that holding benchmark.

To check it, keep the original token quantities, the current position quantities and one common set of prices. Record fees and costs separately. A deposit receipt and a current dashboard total alone cannot show the difference.

The example below is a model of a two-asset, full-range, 50/50 constant-product pool with no fees. It is not a forecast, a live pool quote or a reason to move funds. Do not apply its percentage directly to a concentrated Uniswap v3 range or a managed vault.

Choose the comparison before calculating the loss

Balancer describes impermanent loss as the opportunity cost of adding liquidity instead of holding the individual assets. The relevant price movement is one token’s price relative to the other. Both dollar prices rising together by the same proportion does not create that relative-price change.

Write down the two alternatives:

• Holding: the quantities you originally deposited, priced now.
• Pool: the quantities your share currently represents, priced now, with the treatment of fees made explicit.

Use the same time, currency and token identities for both. Do not substitute the original dollar deposit for the holding benchmark. That answers a different question about change in dollar value.

If you first need to identify a position, use the Uniswap v3 position guide. That article checks ownership, amounts and fee records; use this comparison once you have identified the position.

Follow a model where the two answers differ

Assume an illustrative pool starts with 2 units of asset A and 200 units of asset B. Asset B is the unit of account; assume each B is worth $1 throughout this example. A starts at 100 B. The pool therefore starts at $400, with equal value on each side.

Ignore fees, costs and changes in ownership share. For clarity, the calculation uses the whole model pool. A fixed fraction of it would scale every amount and value by the same fraction.

Now suppose the outside price of A becomes 400 B. Trading has brought the pool to that price. In the Uniswap v2 constant-product model, the reserves satisfy x * y = k, where x and y are the two asset quantities. With no fees, our starting product is 2 * 200 = 400.

At the later price, y / x = 400. Solving the two equations gives x = 1 and y = 400. The pool now holds less A and more B.

Both alternatives below use the later prices: A = $400 and B = $1. The $400 initial deposit was valued earlier, when A = $100.

Alternative at later prices	Quantity of A	Quantity of B	Later value
Hold the original quantities	2	200	$1,000
Model pool after repricing	1	400	$800

The pool value rose from $400 to $800. Holding the initial quantities would instead be worth $1,000. The pool is $200 behind that benchmark, or 200 / 1,000 = 20%.

The percentage uses the holding value as its denominator. Dividing the same $200 by the $400 initial deposit gives 50%, but that is not the impermanent-loss percentage in this comparison. Neither number is a current return estimate for a real pool.

Use the ratio formula only inside its assumptions

For this fee-free, full-range 50/50 model, let r be the later relative price divided by the starting relative price. The signed difference from holding is:

2 * sqrt(r) / (1 + r) - 1

Here r = 400 / 100 = 4, so the result is -0.20. Expressed as the size of the shortfall, that is 20%. The formula is not saying that 20% of the original dollar deposit was removed.

A small worksheet makes the direction and denominator easier to check:

Relative-price ratio r	Pool value as a share of holding	Shortfall from holding
1	100%	0%
2	94.28%	5.72%
4	80%	20%
0.25	80%	20%

The last row shows why a fall can also create a shortfall. In this model, a fourfold rise and a fall to one quarter have the same percentage gap against their respective holding benchmarks. Their dollar outcomes are not the same.

Check the pool design before using any calculator. Different weights, concentrated ranges, changes to your share and strategies that rebalance or compound require different inputs. A familiar pair of token symbols does not establish that this model applies.

Keep fees, rewards and costs in separate records

The Uniswap glossary frames impermanent loss relative to holding. It is not a complete account of what a liquidity provider earns or spends. A fee-free comparison deliberately omits fee income.

For a real position, first establish what its displayed value includes. Depending on the pool design, fees may be included in pool balances or accounted for separately. Uniswap’s v3 fee documentation explains that accrued fees are collected separately rather than automatically reinvested in a position. Do not add a separate fee row if the total you are using already includes it.

Record reward assets and their valuation separately too. A quoted APR does not prove that earned rewards or fees cover the gap over your own holding period. Transaction costs and other actual expenses belong in the net outcome, using a consistent scope for both alternatives.

For example, adding a hypothetical $30 of separate fees to the model’s $800 gives $830 before costs. That still trails the $1,000 holding benchmark by $170. This is an accounting illustration, not a prediction of fee income. If fees are already in the $800 figure, adding $30 again would be wrong.

Build a comparison you can revisit without withdrawing

Make a dated record with these fields:

1. Pool identity, chain and position identifier.
2. The period being compared and the original quantities of both assets.
3. Later quantities represented by the same position or ownership share.
4. The prices and quote time used to value both alternatives.
5. Fees and rewards, stating whether they are included in the position total.
6. Deposits, withdrawals, collected fees and costs during that period.

A position with additional deposits or withdrawals cannot be reconciled by pretending it had only the first deposit. Separate those flows before interpreting a difference. If an original quantity or fee treatment is missing, mark the result incomplete rather than reporting a precise percentage.

A portfolio total can help locate holdings, but it does not show what the original quantities would be worth now. If two screens show different quantities or coverage, use the balance reconciliation guide first. Neither a rising chart nor a current balance proves performance against holding.

In the simplified model, a return to the starting relative price closes the fee-free gap. The word impermanent does not promise that prices will return, or that costs and other losses will reverse. The useful result is a comparison with stated inputs and limitations, not an instruction to wait, withdraw or add liquidity.