Impermanent Loss Explained (With Real Numbers)

What is impermanent loss?

Impermanent loss is the difference in value between providing two assets to a liquidity pool and simply holding those same two assets in your wallet. It appears when the two assets change price relative to each other, because the pool automatically rebalances by selling the asset that rose and buying the one that fell.

Notice what the definition does not say. It doesn't say you lose money — you can finish with more dollars than you started with and still have suffered impermanent loss, because the comparison is against holding, not against zero. It also doesn't say anything was taken from you. Nobody stole anything; the pool did exactly what it was designed to do.

The word "impermanent" is doing real work. While your capital sits in the pool and prices are diverged, the gap is unrealised — it exists only as a comparison to a path you didn't take. If the two assets drift back to their original ratio, the gap closes to zero on its own. The instant you withdraw, though, whatever gap exists at that moment becomes permanent. Some people prefer the term divergence loss for exactly this reason: it names the cause rather than promising the loss will go away.

Why it happens: the rebalancing problem

A constant-product AMM keeps the product of its two reserves fixed, which forces it to hold less of whichever asset is rising and more of whichever is falling. Arbitrage traders enforce this rebalancing, and the pool is effectively selling winners and buying losers on your behalf.

A standard automated market maker pool holds two assets and obeys a simple rule: x × y = k. The quantity of asset X multiplied by the quantity of asset Y stays constant as people trade. Price is just the ratio between the two reserves.

Now suppose the market price of one asset doubles somewhere else. The pool doesn't know that — it only knows its own ratio. So its price is briefly wrong, and an arbitrage trader steps in to buy the now-underpriced asset from the pool until the pool's ratio matches the market. That trade is profitable for the arbitrageur, and the profit comes out of the pool's value.

Zoom out and the pattern is stark. The pool systematically sells the asset that is going up and buys the asset that is going down. That is the opposite of what a directional investor wants, and it's the mechanical source of impermanent loss. You are, in effect, being paid trading fees to provide a continuous rebalancing service to the market.

One important consequence: impermanent loss is symmetric. It does not matter which asset moves or in which direction — only how far the two prices diverge. An asset halving produces exactly the same loss percentage as it doubling.

The formula and the loss table

For a standard 50/50 constant-product pool, impermanent loss = 2 × √p ÷ (1 + p) − 1, where p is the ratio of the new price to the original price of one asset against the other. A 2× price move produces roughly 5.7% loss, a 4× move produces 20%, and a 10× move produces about 42.5%.

The formula is short enough to memorise:

Because the formula depends only on p, the same table applies to every 50/50 constant-product pool on every chain. This is the reference table worth committing to memory:

Two things stand out. First, the curve is gentle at the start and brutal at the tail — small moves cost almost nothing, which is why stable pairs are so forgiving. Second, note the symmetry column: "2× or −50%" produce identical loss, confirming that direction is irrelevant.

A full worked example

Deposit $5,000 of XLM and $5,000 of USDC into a 50/50 pool at $0.40 per XLM. If XLM doubles to $0.80, the position is worth $14,142 while simply holding would have been worth $15,000 — a shortfall of $858, or 5.72%, exactly as the formula predicts.

Let's do it step by step so nothing is hidden.

Step 1 — The deposit

XLM is at $0.40. You deposit 12,500 XLM ($5,000) and 5,000 USDC ($5,000), for a $10,000 position. The pool's constant is k = 12,500 × 5,000 = 62,500,000.

Step 2 — The price moves

XLM doubles to $0.80. Arbitrageurs trade against the pool until its internal ratio matches. Solving x × y = k with a price of 0.80 gives new reserves of 8,838.83 XLM and 7,071.07 USDC. The pool sold roughly 3,661 XLM into the rally on your behalf.

Step 3 — Compare the two outcomes

Here is the part people miss: the LP position still made money. It went from $10,000 to $14,142 — a 41% gain. The "loss" is that holding would have returned 50%. If you'd been paid more than $858 in trading fees and rewards over that period, providing liquidity was the better decision outright.

And if XLM later fell back to $0.40, the pool would rebalance again and the entire $858 gap would vanish. That is the "impermanent" part, made concrete.

When fees outweigh the loss

Liquidity providers earn a share of every swap that passes through the pool, plus any incentive rewards the protocol pays. If those earnings over your holding period exceed the divergence loss at the moment you withdraw, your position beats holding. High-volume pools and low-volatility pairs are where this happens most reliably.

Impermanent loss is only one side of the ledger. The other side has two entries:

• Swap fees. Every trade routed through the pool pays a fee that accrues to liquidity providers pro rata. The relevant metric is not the fee rate alone but volume relative to pool size — a pool doing daily volume equal to its own TVL at a 0.30% fee is earning its providers roughly 0.30% per day before any rewards.
• Incentive rewards. Many protocols emit a reward token to liquidity providers on top of swap fees. On Stellar, Aquarius directs AQUA emissions to pools chosen by ICE voters — the mechanism our ICE voting guide covers in detail.

So the real question is never "will I suffer impermanent loss?" — you will, if the prices diverge at all. The question is "will fees plus rewards, compounded over my holding period, exceed the divergence at the moment I exit?" That reframing turns a scary-sounding risk into an ordinary expected-value calculation.

Note the interaction with compounding: rewards that are harvested and reinvested grow faster than rewards left idle, so the fee side of the ledger benefits materially from auto-compounding. Impermanent loss, meanwhile, does not compound — it's a function of the price ratio alone. Time is therefore on the fee side of the equation, which is why patient liquidity in a busy pool tends to win.

Five ways to reduce it

Choose correlated pairs whose prices track each other, favour pools with high volume relative to their size, understand that concentrated ranges amplify the effect, consider single-asset strategies that avoid pairs entirely, and size positions so a large adverse move is survivable.

In rough order of effectiveness:

• Pair correlated assets. Two dollar stablecoins, or a token and its own staked derivative, barely diverge — so p stays close to 1 and the loss stays close to zero. This is why stableswap-style pools exist and why they can run on thin fees.
• Chase volume, not TVL. A large pool with no trading pays almost nothing. Compare a pool's daily volume against its total liquidity; that ratio, times the fee, is your real fee yield.
• Respect the tail. The loss table is nearly flat up to 1.5× and steep past 3×. If you think an asset might 5×, holding it is probably the better expression of that view than pooling it.
• Consider single-asset strategies. Staking, lending, and single-sided vaults have no second asset to diverge against, so impermanent loss simply doesn't apply. You trade it for other risks — smart-contract risk, and rates that can fall.
• Size for the drawdown. Assume a 3× divergence and check whether the resulting 13.4% shortfall is survivable for that position. If it isn't, the position is too big.

Concentrated liquidity amplifies it

Concentrated liquidity lets you supply capital within a chosen price band rather than across the whole curve, which multiplies both the fees you earn and the impermanent loss you take. If price exits your band, the position ends up entirely in the weaker asset and stops earning fees altogether.

The trade is easy to state and hard to manage. By concentrating your capital into a narrow range, you provide far deeper liquidity at the prices that actually trade — so you capture a much larger share of fees per dollar deposited. The same concentration means a given price move rebalances a far larger fraction of your position, so the divergence loss scales up too.

Worse, the loss becomes less "impermanent." Once price leaves your range, you hold 100% of whichever asset performed worse and earn nothing until price returns or you rebalance. The gentle self-healing property of a full-range position is gone.

This isn't an argument against concentrated liquidity — it's an argument that it's an active strategy rather than a passive one. Our guide to Aquarius concentrated liquidity pools walks through how ranges, capital efficiency, and rewards interact on Stellar specifically.

Where does WhaleHub sit in all this? WhaleHub is a yield-optimization protocol on Stellar rather than a liquidity pool. You stake AQUA and receive BLUB, a liquid receipt token whose value floats with the market, while the protocol aggregates ICE voting power on Aquarius and auto-compounds the resulting rewards. Because staking AQUA is a single-asset action, that particular position has no second asset to diverge against — though as with any DeFi protocol, other risks including smart-contract risk and variable rewards still apply.

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Impermanent loss deserves neither the panic nor the dismissal it usually gets. It's a well-defined, precisely calculable opportunity cost that you can look up in a table before you deposit. Learn the shape of the curve — flat near the middle, vicious at the tails — check whether the pool's fee income plausibly covers the divergence you expect, and you've done most of the analysis that matters.