You’ve deposited two tokens into a pool, you’re collecting a slice of every swap’s fee, and the dashboard says you’re up. Life is good — until you do the math on what you’d have if you’d just held the two tokens in your wallet and done nothing. Suddenly the pool looks like the worse deal. You didn’t get hacked. No fee ate your stack. You ran straight into the LP’s signature risk: impermanent loss.
This is the last big idea of the topic, and it’s the one that separates LPs who know what they’re doing from LPs who get quietly bled. Let’s name the cost, derive it, and figure out when the fees make it worth paying anyway.
Before you read — take a guess
You provide liquidity to an ETH/USDC pool, then ETH's price rises sharply. Compared with simply holding your original ETH and USDC in your wallet, your pool position is now worth…
The setup: arbitrage rebalances your pool
Recall from the last lessons that a constant-product pool prices ETH purely from its own reserves, and arbitrageurs keep that price glued to the wider market. That spring is great for traders — and it’s exactly what costs you as an LP.
Say you LP into an ETH/USDC pool. ETH’s market price climbs on some exchange. Now your pool is quoting ETH too cheap, so arbitrageurs buy ETH out of your pool until its price catches up. When ETH instead falls, your pool quotes it too expensive, so they sell ETH into your pool. Either way the pattern is identical and brutal:
- The pool sells you the winner (hands out ETH while ETH is climbing).
- The pool buys you the loser (soaks up ETH while ETH is sinking).
You’re the counterparty to every one of those rebalancing trades, and they always go the “wrong” way for you. The end result: your pool position is worth less than if you’d just held (HODL’d) the two tokens untouched in your wallet. That shortfall — pool value minus HODL value — is impermanent loss (IL).
HODL: the thing you're measured against
HODL (crypto-speak for “hold”) is the do-nothing baseline: keep the exact tokens you started with, make zero trades. Impermanent loss is never measured against your dollar deposit — it’s measured against that HODL alternative. You can be up in dollars and still have impermanent loss, because holding would have made you even more.
Why “impermanent”? The loss can vanish
Here’s the saving grace baked into the name. The loss is only on paper while prices sit away from where you entered. If ETH wanders off and then comes back to your entry ratio, the arbitrage flow reverses, the pool rebalances back, and the gap closes to zero. The loss was unrealized the whole time — impermanent.
It only becomes permanent the moment you withdraw while prices are dislocated. Pull your liquidity at a price far from entry and you crystallize the shortfall; it’s no longer a paper gap, it’s a realized loss you carry out the door.
Plenty of people argue the honest name is divergence loss: the loss is a function of how far prices have diverged from entry, and calling it “impermanent” oversells how reliably it reverses. Don’t bank on a round trip — a token that 5בs and stays there hands you very permanent-feeling IL.
Pin down what makes the loss 'impermanent' — and what makes it real.
Pick the right option for each blank, then check.
Impermanent loss is the gap between your pool value and simply the tokens. It exists only while the price is your entry ratio, and it shrinks to if the price returns to where you entered. The loss becomes permanent only when you , which is why some call it instead.
The formula: how big is the gap?
For a standard 50/50 constant-product pool, impermanent loss has a clean closed form. Let r be the price ratio — the volatile asset’s new price divided by its old price (the other side is a USD stablecoin, so its price stays put). Then:
A few things to read straight off it:
- The result is always ≤ 0 (it’s a loss or zero, never a gain vs HODL). At r = 1 — price unchanged — it’s exactly 0.
- It’s symmetric in r and 1/r: a 2× move and a halving (r = 2 and r = 0.5) give the same IL. The pool doesn’t care which token won, only how far prices spread.
- It grows with the size of the move in either direction. Small wiggles barely register; big divergences bite hard.
- Price ratio (r)
- 2.00×
- Impermanent loss
- −5.72%
- HODL value
- $15,000
- LP value
- $14,142
- Gap vs. HODL
- $858
- Fees earned
- +$0
- Net vs. HODL
- −5.72%
Impermanent loss wins
Drag the price ratio r. The HODL value (just holding both tokens) pulls ahead of the LP value (your pool position) the further r moves from 1 — in either direction. The shaded gap between them is impermanent loss; at r = 1 it's zero. Bump the fees slider and watch fees fight back against the gap.
Here’s the curve as a table. Each IL figure is just the formula evaluated at that r — check a couple yourself:
| Price ratio r | Move | Impermanent loss |
|---|---|---|
| 1.00 | flat | 0.0% |
| 1.25 | +25% | −0.62% |
| 1.50 | +50% | −2.0% |
| 2.00 | 2× | −5.72% |
| 3.00 | 3× | −13.4% |
| 4.00 | 4× | −20.0% |
| 5.00 | 5× | −25.5% |
| 0.50 | −50% (½×) | −5.72% |
| 0.25 | −75% (¼×) | −20.0% |
Notice the symmetry in action: r = 2 and r = 0.5 both give −5.72%, and r = 4 and r = 0.25 both give −20.0%. Up or down, the spread is what matters.
Yes and no — and this is the misconception that trips up almost everyone. Impermanent loss does not mean your position went down in dollars. In the doubling example below, the LP walks away with about $14,142 on a $10,000 deposit — clearly up. The “loss” is purely the gap versus HODLing, which would have been $15,000. So IL is an opportunity cost, not a hole in your balance. You can be richer than when you started and still have suffered IL — and, crucially, the trading fees you earned can outweigh that gap entirely. “I have impermanent loss” and “I lost money” are two different sentences.
A worked dollar example: ETH doubles
Numbers make it concrete. You deposit $10,000 split 50/50 at ETH = $2000:
- $5,000 of ETH = 2.5 ETH
- $5,000 of USDC = 5,000 USDC
The pool’s constant is k = 2.5 × 5,000 = 12,500. Now ETH doubles to $4000, so r = 2.
HODL value — if you’d just held the original tokens:
LP value — the pool rebalanced. Arbitrageurs bought ETH out of the pool until its quoted price hit $4000, which means the new reserves keep k = 12,500 while the ratio reflects the new price. Solving the constant-product math leaves the pool holding about 1.7678 ETH and 7,071 USDC:
So:
| HODL | LP position | |
|---|---|---|
| ETH held | 2.5 | 1.7678 |
| USDC held | 5,000 | 7,071 |
| Total value | $15,000 | $14,142 |
The LP ends up $858 short of HODLing — and $858 / $15,000 = −5.72%, exactly what the formula predicts for r = 2. The story in one line: as ETH climbed, the pool sold your ETH on the way up, so you rode the rally on a shrinking ETH stake. Great for the arbitrageur, a drag for you.
Fees: the other side of the ledger
If IL were the whole story, nobody would ever LP. It isn’t. IL is the cost of being the pool’s counterparty; trading fees (plus any liquidity-mining rewards) are the compensation. Every swap pays the pool a fee, and you collect your pro-rata slice for the whole time you’re in. The only question that matters for an LP is:
Do my accumulated fees (+ rewards) beat my impermanent loss?
Roughly, your performance versus HODL is:
(IL is negative, so it subtracts.) Worked verdict: suppose over your time in the pool ETH doubled (IL = −5.72%) but the pool’s volume earned you +8% in fees. Then:
You finish about 2.28% ahead of HODLing — the fees more than covered the IL, so being an LP beat doing nothing. Flip it: if fees had only come to +3%, you’d net 3% − 5.72% ≈ −2.72% versus HODL, and you’d have been better off just holding. Same IL, opposite verdict — fee income is the deciding variable, and it’s why high-volume pools are where LPs actually want to be.
Sort each pool by how much impermanent loss risk an LP is taking on.
Place each item in the right group.
- Memecoin / ETH
- BTC / USDC
- USDC / DAI (two dollar stablecoins)
- USDC / USDT (two dollar stablecoins)
- ETH / USDC
When IL is small, when it’s large
The formula is symmetric and grows with divergence, so the rule of thumb writes itself: IL tracks how far the two assets’ prices pull apart.
- Small IL — correlated, mean-reverting, or stable-stable pairs. Two dollar stablecoins like USDC/USDT barely move against each other; r hovers near 1, so IL ≈ 0. That’s precisely why stablecoin pools are so popular with LPs: almost pure fee income, almost no divergence loss. Pairs of tightly correlated assets (or assets that mean-revert) get the same benefit.
- Large IL — volatile, one-directional assets. Pair a token against a dollar and let it run, and IL piles up fast. A token that 5בs leaves the LP 25.5% behind HODL (r = 5), and a sustained one-way trend means the pool never round-trips back to wipe the loss out. Fees have to be enormous to cover that.
The misconception to bust
“Impermanent loss means I lost money.” No. IL is the gap versus HODLing, not a drop in your balance — an opportunity cost. You can still be up in dollar terms (the LP in our example finished at $14,142, well above the $10,000 deposit). And because fees run the other way, your real, net outcome can easily beat HODL even with IL on the books. Judge an LP position by fees minus IL, never by IL alone.
Key Takeaways
What to remember
- Impermanent loss (IL) is the shortfall between your pool position and simply HODLing the two tokens — it appears because arbitrageurs rebalance the pool, selling you the winner and buying the loser.
- It’s “impermanent” because it vanishes if the price returns to your entry ratio; it becomes permanent (realized) only when you withdraw while prices are dislocated. Some prefer the name divergence loss.
- For a 50/50 constant-product pool, IL is , where r is the new-over-old price ratio. It’s always ≤ 0, symmetric in r vs 1/r (a 2× and a ½× both give −5.72%), and grows with the size of the move in either direction.
- IL is an opportunity cost, not a dollar loss — you can be up in dollars and still trail HODL.
- Fees are the counterweight. Your net result ≈ fees% + IL%; if fee income beats IL, LPing wins. IL is tiny for stable-stable / correlated pairs and large for volatile, one-directional assets.
Big picture
Impermanent loss at a glance
- Impermanent loss
- Why it happens
- Arbitrageurs rebalance the pool
- Pool sells the winner, buys the loser
- Pool value trails HODL
- Why 'impermanent'
- Vanishes if price returns to entry
- Realized only on withdrawal
- Aka divergence loss
- How big
- IL(r) = 2√r / (1+r) − 1
- Symmetric: r and 1/r match
- Grows with the move's size
- The counterweight
- Fees compensate the LP
- Net ≈ fees% + IL%
- Stable pairs: tiny IL
- Why it happens
Lesson 5 check
You LP $10,000 into an ETH/USDC pool at ETH = $2000. ETH doubles. Roughly what is your impermanent loss versus HODLing — and are you up or down in dollars?
Check your answer to continue.
That’s the last teaching lesson of the topic — you now know what an AMM is, the x·y=k formula that prices it, how pools and LP tokens work, how slippage hits big trades, and the impermanent loss that LPs quietly pay. The only thing left is to prove it: the final exam pulls all five lessons together into one graded run. Take a breath, then go earn the pass.