What do fees have to earn before liquidity providing breaks even?
Impermanent loss is only half a sentence. The full one is: an LP is long fee income and short volatility, and whether that trade worked out is a subtraction anybody can perform. Most people never perform it.
The one equation
LP outcome versus holding = fees earned − impermanent loss
Both terms have to be measured over the same period, on the same capital, against the same benchmark — the hold portfolio. Nothing else belongs in the comparison.
Where the fee side comes from
Fees are a share of volume, split by pool ownership:
your fee income = volume × fee tier × your share of the pool
Worked. A pool holds $4,000,000; your $40,000 position is 1% of it. The pool trades $2,000,000 a day at a 0.30% fee.
daily pool fees = 2,000,000 × 0.003 = $6,000 your share = $60/day
Daily return on your capital = 60 ÷ 40,000 = 0.15%. Over 30 days: $1,800, or 4.5% of the position.
Annualising that naively gives about 54.75% — and the size of that number is exactly why the next step matters.
Now subtract
Suppose over the same 30 days ETH doubled. From the previous lesson, IL at r = 2 is 5.72% of the hold value, and the hold value is $60,000:
IL in dollars = 60,000 × 0.0572 = $3,431
Net versus holding = 1,800 − 3,431 = −$1,631.
An LP earning fees at an apparent 54% annualised rate finished $1,631 behind a wallet that did nothing, in a month when the position's nominal value rose by more than $18,000. Every number in that sentence is real and none of them contradict each other. This is why the advertised APY on a liquidity pool is not a return: it is one term of a subtraction whose other term is unknown until the period ends.
The break-even condition
Rearranged, the requirement is:
volume × fee tier × share ≥ hold value × [1 − 2√r/(1+r)]
Which produces three structural observations:
- Fee income scales with volume; the loss scales with price divergence. They are different variables and there is no mechanism forcing them to match.
- The loss term is convex in r. A big move can outrun a great many days of fees.
- Adding capital raises your dollar fees roughly in proportion, and your rate is set by the pool, not by you: fees per dollar deposited depend on volume against total liquidity. Your own deposit raises your share; what dilutes you is everybody else's, and an attractive yield is exactly what attracts them. Unit 4 makes this general.
Concentrated liquidity: same trade, amplified
Newer AMM designs let an LP place liquidity only within a chosen price range rather than across the whole curve. Inside the range, capital efficiency rises — the same dollars provide far more depth, so they earn a larger share of the fees. But the exposure amplifies in exactly the same proportion: divergence loss within the range is magnified, and once the price exits the range the position sits entirely in one asset and earns nothing until price returns. It converts a passive position into one that requires active management, without changing the underlying subtraction. It is a different point on the risk curve, not an escape from it.
The honest summary
Providing liquidity is a short-volatility position with a fee coupon. That is a recognisable structure — the same shape as writing options, which the derivatives domain covers in its own terms. It can be profitable. It can lose against simply holding. And it carries every risk from Unit 1 on top: the pool is a smart contract, and smart contracts have been drained to zero.
This course does not suggest providing liquidity, and takes no view on whether any pool's fees compensate its risk. It gives you the subtraction so that you can never again read an APY as if it were an answer.
Try it now
- Take a 30-day window on the chart below, Measure it to get r, compute the IL from the closed form and convert it to dollars on a $40,000 position.
- Find a real pool's 24-hour volume and total liquidity on a public analytics site. Compute the fee income on a hypothetical 1% share over the same 30 days, then run the subtraction against the IL from step 1.
- Solve for the volume that would have been required to break even in your window. Compare it with the pool's actual volume — and note that you could only have known this afterwards. Measure a different 30-day window on the chart and the required volume changes completely.