Module 9: DeFi Deep Dive
Impermanent Loss
Chapter 4 of 14 · about 6 minutes
4.1 Earning fees and still losing
Mint deposited 1 ETH and 3,000 USDC into an ETH/USDC pool, worth $6,000 total with ETH at $3,000. Over the next few months, ETH doubled to $6,000. Mint had earned $400 in fees and was excited to withdraw.
The withdrawal returned about 0.71 ETH and 4,243 USDC, worth about $8,485, plus the $400 in fees: $8,885 in total.
Then Mint did the comparison. If Mint had simply held the 1 ETH and 3,000 USDC, they would be worth $9,000.
"I earned $400 in fees," said Mint, "and still ended up $115 worse than doing nothing?"
"That's impermanent loss," said Hash. "It's the most important concept for anyone providing liquidity, and the most misunderstood."
4.2 What impermanent loss is
Impermanent loss (IL) is the difference between the value of an LP position and the value of simply holding the same tokens outside the pool, caused by price changes.
It happens because of the arbitrage described in Chapter 3. As ETH's price rose, arbitrageurs bought ETH from the pool at prices below the market, until the pool's price matched. The pool automatically sold ETH as it rose, leaving Mint with less ETH and more USDC. When ETH falls, the opposite happens: the pool buys ETH as it falls, leaving the LP with more of the falling asset.
In effect, an LP in a constant product pool is always selling the asset that's rising and buying the asset that's falling.
4.3 Mint's position, step by step
| Start | After ETH doubles | |
|---|---|---|
| ETH price | $3,000 | $6,000 |
| ETH in Mint's share of the pool | 1.000 | ~0.707 |
| USDC in Mint's share of the pool | 3,000 | ~4,243 |
| Value of LP position | $6,000 | ~$8,485 |
| Value if Mint had just held | $6,000 | $9,000 |
| Impermanent loss | ~$515, or ~5.7% | |
| Fees earned | $400 | |
| Net result versus holding | ~−$115 |
Mint still made money compared with the start: from $6,000 to about $8,885. But compared with doing nothing, the LP position did worse.
Chapter 4 · Impermanent loss
As one asset's price doubles, a holder's portfolio tracks the gain fully, while a liquidity provider's position lags because the pool sold the rising asset along the way. The shortfall is impermanent loss, roughly 5.7% here, which trading fees must offset to make LPing worthwhile.
4.4 The impermanent loss formula
For a standard 50/50 constant product pool, impermanent loss depends only on how much the price ratio between the two tokens has changed.
IL = 2 × √r ÷ (1 + r) − 1, where r is the new price divided by the original price.
| Price change of one token versus the other | Impermanent loss |
|---|---|
| ×1.25 (up 25%) | 0.6% |
| ×1.5 (up 50%) | 2.0% |
| ×2 (up 100%) | 5.7% |
| ×3 (up 200%) | 13.4% |
| ×4 (up 300%) | 20.0% |
| ×5 (up 400%) | 25.5% |
| ×0.5 (down 50%) | 5.7% |
| ×0.25 (down 75%) | 20.0% |
Three important patterns:
Direction doesn't matter. A doubling and a halving cause the same impermanent loss.
Small moves cause small losses; big moves cause big losses. Loss grows quickly as prices diverge.
Only relative price matters. If ETH and the other token both double, the ratio doesn't change, and there's no impermanent loss.
4.5 Why "impermanent"?
The loss is called "impermanent" because if prices return to exactly where they were when you deposited, the loss disappears. But that's a misleading name. If you withdraw while prices have moved, the loss becomes permanent. And prices in crypto often don't return.
"So it's impermanent the way a missed train is impermanent," said Node. "Only if another one comes along at exactly the same time."
Many people now prefer terms like divergence loss, which describes what actually causes it.
4.6 Can fees cover it?
The real question for an LP is whether fees and incentives outweigh impermanent loss over the period.
Take a $100 position (split 50/50 at the start) and fees of 20% of that starting value, or $20, over the year. The hold value is 50 × (1 + r), where r is the new price divided by the old. The LP value, before fees, is 100 × √r. The net is the LP value plus fees, compared with holding.
| Scenario over a year | ETH price change | Hold value | LP value | Plus $20 fees | Net vs holding |
|---|---|---|---|---|---|
| Sideways market | ×1.0 | $100 | $100 | $120 | +$20 |
| Moderate rise | ×1.5 | $125 | $122 | $142 | +$17 |
| Doubling | ×2 | $150 | $141 | $161 | +$11 |
| Tripling | ×3 | $200 | $173 | $193 | −$7 |
| Major crash | ×0.25 | $62.50 | $50 | $70 | +$8 |
(Simplified: fees are a flat 20% of the starting value, ignoring compounding and costs.)
In sideways, choppy markets, LPs tend to do well: fees accumulate and prices don't diverge much. In strong trends, impermanent loss can overwhelm fees.
4.7 Concentrated liquidity amplifies it
In concentrated pools (Chapter 2), capital is used more intensely within the range. That multiplies fee income, but also multiplies impermanent loss for the same price move. A narrow range can suffer impermanent loss many times larger than a full-range position for the same price change, and if price leaves the range, the LP ends up holding entirely the less valuable token.
4.8 Loss to arbitrage
Researchers have developed a more precise way to measure the cost LPs pay to arbitrageurs, sometimes called loss-versus-rebalancing (LVR). Instead of comparing with simply holding, it compares the LP with a hypothetical trader who rebalanced the same portfolio at true market prices. The key insight is the same: in volatile markets, LPs systematically lose value to arbitrageurs, and fees must compensate for that. Some newer DEX designs try to reduce this loss, for example by capturing part of the arbitrage value for LPs.
4.9 Reducing impermanent loss
| Approach | How it helps | Trade-off |
|---|---|---|
| Correlated pairs, like two stablecoins or ETH and liquid staking ETH | Prices barely diverge, so little IL | Lower fees; depeg risk |
| Pools with high volume relative to TVL | More fees to offset IL | Volume can fall |
| Wider ranges in concentrated pools | Less amplified IL | Lower fees per dollar |
| Avoiding pools with tokens you expect to trend strongly | Avoids large divergence | Missed fee opportunities |
| Incentives | Extra rewards offset IL | Temporary; reward tokens may fall in value |
4.10 Try it yourself
Use an online impermanent loss calculator, or the formula in section 4.4, to calculate IL for an ETH/USDC position if ETH moves +20%, +80%, −40%, and −70%. Then find a real ETH/USDC pool's fee APR and estimate how many months of fees it would take to cover each loss.
Key takeaways from this chapter
- Impermanent loss is the difference between an LP position's value and simply holding the same tokens.
- It's caused by arbitrage: pools sell rising assets and buy falling assets as prices move.
- In a 50/50 constant product pool, a doubling or halving of relative price causes about 5.7% IL; a 4x move causes 20%.
- Direction doesn't matter; only the change in relative price does.
- The loss becomes permanent if you withdraw after prices move.
- LPs profit when fees and incentives exceed IL, usually in sideways markets.
- Concentrated liquidity amplifies IL; correlated pairs and high-volume pools reduce it.