Impermanent Loss (Divergence Loss)
01 · Concept — what problem does it solve?
An 's pool share automatically rebalances against the trend: as a token pumps, the pool sells it; as it dumps, the pool buys more. So an LP always ends up holding less of the winner and more of the loser than if they had just held — that shortfall versus holding is . "Impermanent" because it vanishes if price returns to entry.
It is exactly the short-gamma inventory loss from the TradFi Market Making primer — realized via arbitrageurs who do the rebalancing at the LP's expense.
In plain English
If you deposit two assets into a pool and their prices drift apart, you can end up with less value than if you'd just held them in your wallet. That gap is the loss. It's called "impermanent" because it shrinks back toward zero if prices return to where you started — and the trading fees you earn can offset whatever is left. Withdraw before that happens and it stops being impermanent.
02 · Mechanics
- Driver: price divergence from entry ratio, in either direction. Symmetric: 2× up hurts the same as 2× down (−5.7%).
- Volatility link: expected IL grows with realized variance — LPs are short volatility; fees are the option premium they collect.
- Profitability condition:
fees earned > IL realized. High-volume/low-volatility pairs (stable pairs) are best; volatile, drifting pairs are worst. - v3 amplification: concentration multiplies both fees and IL; a narrow range is a leveraged short straddle.
03 · Formulas
// P = current_price / entry_price
V_hodl = ½(1 + P) normalized
V_lp = √P
IL(P) = V_lp/V_hodl − 1 = 2√P/(1+P) − 1
// reference points
P=1.25 → −0.6% P=2 → −5.7%
P=1.5 → −2.0% P=3 → −13.4%
P=4 → −20.0% P=5 → −25.5%
04 · Edge cases & risks
- Should you actually LP? — fees offset IL only if volume is high enough. High-volume, low-volatility pairs (ETH/USDC on a 0.05% tier, pairs) regularly out-earn IL. Low-volume, high-drift pairs almost never do. Before entering, estimate daily fees earned vs the historical IL for that volatility level; most retail LPs on volatile pairs would have earned more holding.
- LVR refinement — modern research (loss-versus-rebalancing) separates IL into hedgeable inventory drift + unhedgeable losses to arbitrageurs. LVR is the true cost of LPing.
- IL can exceed fees forever — in trending markets no fee tier compensates.
An LP holds a 50/50 pool position. One asset's price doubles relative to the other. Approximately how much impermanent loss versus simply holding?
An LP's pair diverges sharply, then the price returns exactly to where they entered. What happens to the impermanent loss?
An LP withdraws from a 50/50 pool while the price ratio sits at 4× its entry. What is true of their impermanent loss?
A 50/50 LP position's price ratio moves to 4× entry. Ignoring fees, what is the divergence loss versus simply holding?