Impermanent loss explained, with numbers

Impermanent loss is the most misunderstood concept in DeFi, and the name is largely responsible. Here is what actually happens, with arithmetic.

The mechanism

Supplying liquidity to an automated market maker means depositing two assets, usually in equal value. The pool maintains a mathematical relationship between the two balances, and traders arbitrage it against the wider market.

The consequence: the pool automatically sells whichever asset is rising and buys whichever is falling. You end up holding more of the loser and less of the winner — the opposite of what you would have chosen.

A worked example

Suppose ETH is $2,000 and you deposit into an ETH/USDC pool:

• 1 ETH ($2,000) + 2,000 USDC = $4,000 deposited

ETH then doubles to $4,000. Arbitrageurs buy the now-underpriced ETH from your pool until it matches the market, leaving you with roughly:

• 0.707 ETH ($2,828) + 2,828 USDC = $5,657

Had you simply held the original assets:

• 1 ETH ($4,000) + 2,000 USDC = $6,000

The gap — $343, about 5.7% — is impermanent loss. You still made money; you made less than doing nothing.

How it scales

Two things to notice. It applies to divergence in either direction — the asset halving costs the same as it doubling. And it grows non-linearly, so volatile pairs are punished disproportionately.

Why the name is wrong

“Impermanent” means the loss reverses if prices return to their original ratio. That is true and nearly irrelevant.

There is no reason prices must return, and the moment you withdraw, the loss is realised and completely permanent. Many liquidity providers have discovered this after the fact, having assumed the word meant the loss was somehow not real.

A more honest name would be divergence loss, which is what it actually measures.

When providing liquidity still makes sense

The bet you are making is that trading fees exceed the divergence loss. That can be true:

• Correlated pairs. Two stablecoins barely diverge, so the loss is negligible. This is why those pools pay less — the risk being compensated is smaller.
• High-volume, range-bound markets. Lots of fees, little net divergence.
• Assets you intend to hold in that ratio anyway. If you would hold both regardless, the rebalancing matters less.

It generally does not make sense for a volatile asset you are bullish on. If you expect one asset to rise substantially, providing liquidity guarantees you capture less of that rise than simply holding it.

Before you supply liquidity

• How correlated are the two assets? Uncorrelated pairs diverge most.
• What fee income does the pool actually generate — historically, not projected?
• Would I be happy holding both assets in a shifting ratio?
• Am I bullish on one of them? If so, why am I in a structure that sells it as it rises?

What to read next

Next: how to read on-chain data.