What impermanent loss compares
Impermanent loss describes a difference between the value of a liquidity position and the value of holding its original assets as relative prices change. It is a comparison against a benchmark, not simply another name for an asset price falling. A pool position can rise in dollar value and still trail the holding benchmark. The result depends on the pool design, price path, fees and other conditions.
The example below uses a full-range, equal-value, two-asset constant-product pool. It ignores fees and assumes arbitrage aligns the pool with an external price. These assumptions make the arithmetic transparent. They do not describe every concentrated-liquidity, weighted or stable-asset pool. The word impermanent should not be read as a promise that an unfavorable result will reverse.
Start with an explicit hypothetical position
Suppose a pool holds 10 units of asset A and 1,000 units of asset B. Assume B is worth $1 and A initially costs $100. The pool value is $2,000, and the constant product is 10,000. For simplicity, imagine a participant owns the entire economic position. A fractional share would scale the dollar amounts while leaving the comparison percentage unchanged.
Now assume the external price of A doubles to $200 while B remains at $1. With no fees, the new reserve quantities satisfy two conditions: A × B = 10,000 and B ÷ A = 200. Solving gives approximately 7.0711 A and 1,414.21 B. The pool now holds less of the asset that increased in relative price.
Compare the two ending values
At the new prices, the pool is worth approximately 7.0711 × $200 + 1,414.21 × $1 = $2,828.43. Holding the original 10 A and 1,000 B would be worth $3,000. The pool is approximately $171.57 behind that benchmark, or 5.72%. Both values exceed the original $2,000, which illustrates why a positive dollar return does not eliminate the comparison loss.
For this particular model, the value ratio is 2 × square root of r ÷ (1 + r), where r is the new relative price divided by the original relative price. Subtracting one gives the proportional difference from holding. At r = 2, the difference is about −5.72%. This is a derivation for the stated assumptions, not a universal calculator for any pool displaying two tokens.
Add fees without hiding the benchmark
Suppose the same hypothetical position also accumulates $100 of net fees, with every other assumption unchanged. Its illustrative ending total becomes $2,928.43, still $71.57 below holding. If fees were $200, the total would exceed the $3,000 holding benchmark before other costs. This shows what it means for fees to offset the comparison loss; it does not establish that a particular level of fees will occur.
Real accounting can be more complicated because fees may change pool reserves, positions may be rebalanced, and transaction expenses can be paid in another asset. Keep the benchmark consistent. Compare the same starting assets over the same period, record withdrawals and additions, and state whether values include fees, rewards and costs.
Why concentrated positions need a different calculation
A position active only within a selected price range does not have the same inventory path as a full-range position. It can move out of range and become concentrated in one asset. Its fee earning behavior also depends on where trading occurs and the protocol’s rules. The simple formula above should therefore not be pasted into an analysis of a concentrated position without checking the actual design.
Balancer’s educational material and Uniswap’s liquidity documentation describe why pool construction matters. An equal-value illustration cannot automatically stand in for a weighted pool, a stable-asset pool or a multi-asset arrangement. The protocol version, chosen range or weights, and valuation method belong next to any reported result.
Questions that make an explanation useful
What did the participant start with? What benchmark is being used? Which price ratio changed? What is the ending composition? Are fees included? What costs or risks are omitted? Answering these questions makes a claim about liquidity returns much more informative than quoting an annual percentage alone.
Continue with the parent guide to understand how this inventory exposure fits alongside smart-contract, oracle, governance and liquidity risks. The mathematical example here explains one mechanism. It does not determine whether providing liquidity is suitable for an individual reader.
Sources & further reading
Educational content. Examples are illustrative. Protocols, products and rules can change; consult the linked documentation for current details.