Impermanent loss: compare a liquidity pool with holding
Impermanent loss is the shortfall of a liquidity position compared with holding the same starting tokens outside the pool, before fees and incentives. Your position can rise in dollar value and still lag behind holding. The name does not promise that the difference will disappear.
Your task: calculate both portfolios at the same prices, then decide what fees would be needed to close the gap.
Understand what changes inside the pool
The pool changes your token mix
In a simple 50/50 constant-product pool, trades change the quantities of the two assets. Arbitrage brings its price towards the wider market. As one token becomes relatively more expensive, the pool holds less of it and more of the other asset. You no longer own the original mix.
Holding is the comparison
Record the exact quantities deposited and value those unchanged quantities at today’s prices. Compare them with the current withdrawable position at those same prices. Comparing only with the original deposit answers whether you gained dollars, not whether providing liquidity beat holding.
Fees are a separate return
Trading fees and incentives can offset the shortfall, but may not. Deduct deposit, withdrawal, claim and rebalancing costs. Value reward tokens at a realistic sale price. Check whether the displayed position already includes fees so you do not add them twice.
Walkthrough: build a fair comparison
Write down the starting portfolio
Use a hypothetical deposit of 1 ETH and 1,000 USDC when ETH is $1,000 and USDC is $1. Total starting value: $2,000. Assume a full-range 50/50 constant-product pool, arbitrage equilibrium, no fees or costs, and an unchanged USDC peg. These are teaching assumptions, not a live quote.
Recalculate after the price changes
If ETH rises to $4,000, the model position becomes 0.5 ETH and 2,000 USDC. Its value is $4,000. Holding the original 1 ETH and 1,000 USDC would be worth $5,000. The pool has gained $2,000 since deposit, yet trails holding by $1,000.
Add the actual economics
The shortfall is $1,000 ÷ $5,000 = 20%, not 25% of the pool value. If separately measured fees are $180 and costs are $30, net pool value is $4,150 and the gap remains $850. In this simplified comparison, gross fees must reach $1,030 to match holding after those costs.
Worked model: the price ratio drives the gap
For this fee-free, full-range 50/50 model, r is the final relative token price divided by its initial relative price. The LP-to-holding value ratio is 2√r ÷ (1+r). At r = 4, that ratio is 0.8: the shortfall is 20%. The reserve product x × y = k is a pricing invariant, not the pool’s dollar value. If the relative price returns exactly to its starting point, this model’s divergence disappears, but costs, other losses and the possibility it never returns still matter.
Where the simple model stops working
Concentrated liquidity needs its range
A narrow price range changes the exposure. Outside the range a position can become entirely one token and stop earning trading fees until price re-enters. Do not apply the full-range formula blindly to a concentrated position; use its bounds and actual withdrawable balances.
Stablecoins are not risk-free
Two tokens tracking the same currency can diverge if one loses its peg. A pool can accumulate the weakening asset as traders remove the stronger one. Smaller historical price moves do not remove issuer, contract or liquidity risks.
An attractive APY is not the result
Annualized recent fees are not guaranteed future income. Volume, competition, range activity and incentive prices change. Impermanent loss also excludes hacks, token failure and other risks that can dominate the outcome.
Try it: compare both portfolios after a price fall
Use the same original deposit, but let ETH fall to $250 while USDC stays at $1. The model position becomes 2 ETH and 500 USDC. What are the pool and holding values? What is the percentage shortfall before fees?
Reveal the calculation
Pool: 2 × $250 + $500 = $1,000. Holding: 1 × $250 + $1,000 = $1,250. The gap is $250, or 20% of holding value. Both portfolios lost dollars from the original $2,000. The 20% figure describes their difference; it is not the pool’s total loss, which is 50% before fees.
