Impermanent Loss (Divergence Loss)

01 · Concept — what problem does it solve?

An LP'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 loss. "Impermanent" because it vanishes if price returns to entry; permanent the moment you withdraw at a diverged price.

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.

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, stablecoin 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; "impermanent" is marketing.