What Is Impermanent Loss? Examples, Math, and When Fees Offset the Risk

Decentralized exchanges (DEXs) changed how people trade crypto. Instead of an order book, many DEXs use liquidity pools where users give tokens to a smart contract and earn trading fees. It looks simple on the surface, but there is a hidden risk.

This risk is called impermanent loss. It is not a bug in the code. It is a normal effect of how automated market makers (AMMs) work. If a person gives liquidity without understanding this, the final balance can be lower than if the same tokens were just held in a wallet.

This article explains what is impermanent loss, how it happens in AMMs, the basic math, and when trading fees can balance or even beat this loss. The language stays simple so that anyone who knows basic crypto ideas can follow.

What Is Impermanent Loss?

Impermanent loss is the difference between:

1. The value of tokens if they were just held in a wallet, and
2. The value of the same tokens after being in a liquidity pool, when prices have changed.

If the second value is lower, the liquidity provider (LP) has impermanent loss. It is called “impermanent” because it is not final until the liquidity is withdrawn. If prices move back to the original level, the loss can shrink or even disappear.

In most simple AMMs, like Uniswap v2 style pools, a user often deposits two tokens with a 50:50 value split. For example:

• 1 ETH worth 1,000 USD
• 1,000 USDC

The total deposit is 2,000 USD. If the LP had just held the tokens, the final value would follow the normal market price. Inside the pool, however, the AMM keeps a special balance rule. When the price changes, the pool adjusts the mix of tokens. The LP finishes with more of the losing token and less of the winning token.

Impermanent loss does not mean the LP always loses money in total. There are also trading fees that the pool pays to LPs. An LP can still earn a net profit if fees plus token gains are higher than impermanent loss. But impermanent loss is the hidden cost that must be compared against those fees.

How Impermanent Loss Works in AMMs

To understand impermanent loss, it helps to see how an AMM keeps prices in balance.

Most classic DEX pools, like Uniswap v2, use a constant product formula:

x × y = k

Where:

• x = amount of token A in the pool
• y = amount of token B in the pool
• k = a constant number

This rule means that the product of both token amounts always stays the same. When traders buy one token, its amount in the pool goes down. To keep x × y = k, the AMM changes the price so it becomes more expensive.

Now imagine a 50:50 ETH / USDC pool:

• At the start, ETH = 1,000 USD
• The pool holds 10 ETH and 10,000 USDC
• Total pool value is 20,000 USD

Later, the outside market price of ETH jumps to 2,000 USD. Arbitrage traders see that the DEX price is still near 1,000 USD. They buy cheap ETH from the pool and sell it on other exchanges for profit. As they do this:

• The pool loses some ETH
• The pool gains more USDC
• The price inside the pool rises until it matches the outside price

By the end of this process, the pool might hold something like:

• 7.07 ETH
• 14,142 USDC

The exact numbers come from the constant product math, but the key idea is simple:

When one token goes up in price, the pool shifts so LPs hold less of that token and more of the other one.

If the LP had just held 10 ETH and 10,000 USDC, the value would be:

• 10 ETH × 2,000 USD = 20,000 USD
• 10,000 USDC
• Total = 30,000 USD

Inside the pool, the LP now owns a share of:

• 7.07 ETH × 2,000 USD = 14,140 USD
• 14,142 USDC
• Total ≈ 28,282 USD

The LP is poorer by about 1,718 USD compared to just holding. That gap is an impermanent loss before counting fees.

If both tokens move in the same way, the loss can be smaller. For example, in a pool with two stablecoins, such as USDC / USDT, the prices do not move much against each other. So price divergence is low, and impermanent loss is usually small.

Also Read: What is Crypto Asset Management? How to Stay in Control of Your Crypto

Impermanent Loss Math in Simple Terms

This article now looks at the main formula people use to estimate impermanent loss in a 50:50 pool.

For a pool like Uniswap v2, the most common formula for impermanent loss (IL) is:

IL = 2 × √d / (1 + d) − 1

Where:

• d = new price / old price of token A, measured in token B
• √d = square root of d

This result comes from the constant product rule and the change in token mix after price movement.

What the formula says

The formula has some useful properties:

• IL depends only on how much the price moves, not on the direction.
  • A 2x increase and a 50% drop give the same IL size.

• IL is always negative, which means it is a loss compared to holding.

• For small price moves, IL is small. For large moves, IL grows fast.

Price change vs impermanent loss (50:50 pool)

The table below shows rounded values that many guides use for a 50:50 pool.

Price change of token A	Price ratio d	Approx. impermanent loss
0	1.25	−0.6%
1	1.50	−2.0%
+100% (2x)	2.00	−5.7%
+200% (3x)	3.00	−13.4%
+400% (5x)	5.00	−25.5%

Remember, these numbers also apply if the price moves down by the same factor. A 2x move up and a 50% move down both give about −5.7% impermanent loss.

A Worked Example with Numbers

Take this simple case:

• You deposit 1 ETH at 3,000 USD and 3,000 USDC
• Total deposit value: 6,000 USD
• Later, ETH doubles to 6,000 USD

If you had just held:

• 1 ETH = 6,000 USD
• 3,000 USDC
• Total = 9,000 USD

Inside the 50:50 pool, after price moves and arbitrage happen, you end up with about:

• 0.707 ETH
• 4,242 USDC

Now value is:

• 0.707 ETH × 6,000 USD = 4,242 USD
• 4,242 USDC
• Total ≈ 8,484 USD

Compare:

• 9,000 USD (hold)
• 8,484 USD (LP)

The gap is:

• 8,484 / 9,000 − 1 ≈ −5.7%

This matches the 2x line in Table 1.

So impermanent loss did not wipe out your money, but you gave up about 5.7% of what you could have had by just holding. To see if providing liquidity was worth it, this article must now compare this loss with trading fees.

Examples: When Fees Cover Impermanent Loss

Impermanent loss shows the cost side of liquidity providing. The benefit side is trading fees.

In many AMMs, each trade pays a small fee that goes to LPs. For example, Uniswap v2 often uses a 0.30% fee. If a pool has high trading volume, these fees can add up and offset or beat impermanent loss.

Simple Fee Versus Loss Comparison

Suppose:

• You provide 10,000 USD of liquidity in a 50:50 pool.
• Over some period, the token price moves such that IL is about −5%.
• At the same time, the pool collects trading fees that equal +8% of your deposited value.

Your rough result is:

• Fees: +800 USD
• IL: −500 USD
• Net result: +300 USD, or +3%

So even with impermanent loss, the final result is positive because fees are larger than the loss.

Example Scenarios for LP Results

This table shows simple, made-up examples to think about fees versus impermanent loss. It is not a promise of real returns.

Table 2 – Example fee vs IL outcomes for a 50:50 pool

Scenario	Impermanent loss	Fee yield in period	Net effect vs holding
Low volatility, low volume	−1%	=+0.5%	−0.5% (worse)
Low volatility, high volume	−1%	=+4%	=+3% (better)
High volatility, medium volume	−8%	=+5%	−3% (worse)
High volatility, very high volume	−8%	=+15%	=+7% (better)

The main lesson is simple:

High volume and good fees can cover impermanent loss, but price swings can still be too strong.

Real data shows that in some Uniswap v3 pools, many LPs actually underperformed a simple hold strategy, because impermanent loss was larger than fees.

Why “Impermanent” Can Become Permanent

Impermanent loss is only a potential loss while your liquidity stays in the pool. If prices go back to the original ratio, the loss shrinks. But in real markets, strong price moves often do not fully reverse.

If you withdraw when prices are far from the entry level, the loss becomes real. In that moment, it is effectively a permanent loss compared to holding.

So an LP is always making a trade-off:

• Taking price risk and earning fees
• Or holding tokens and skipping the fee income

Good LPs track both trading volume and price trends, and they choose pools where expected fees are likely to outpace expected impermanent loss.

Also Read: How Liquidity Tokens Work

How To Reduce Impermanent Loss Risk

There is no way to fully avoid impermanent loss in a classic AMM for volatile assets. Still, there are several ways to reduce the risk or make it more acceptable.

1. Choose More Stable Pairs

The more the prices of the two tokens diverge, the higher the impermanent loss. So one simple rule is:

• Use pools where both tokens move in a similar way, or
• Use at least one stablecoin

Examples:

• USDC/USDT, DAI/USDC: very low price movement between tokens, so IL is usually very small.

• ETH/stETH or similar pairs: both sides track the same underlying asset, so divergence is often low.

2. Understand Concentrated Liquidity

Newer AMMs, such as Uniswap v3, let LPs provide liquidity only inside a price range. This is called concentrated liquidity. It has two effects:

• Fees can be much higher because the same capital is used more often.

• Impermanent loss can also be larger, since liquidity is more focused and reacts more strongly to price moves.

If you do not follow the market closely, very tight ranges can be risky. A simple approach is to:

• Use wider ranges at first

• Watch how the position behaves over time

• Move to tighter ranges only after more experience

3. Start with Small Amounts

If impermanent loss is new for a person, it is safer to start with a small deposit. This allows the LP to:

• Learn how the pool works

• See how price changes affect the token mix

• Watch fees come in over days or weeks

Many sites also provide impermanent loss calculators. These tools let users plug in price change scenarios and see the expected IL percentage for different pool types, such as 50:50 or 80:20.

4. Spread Risk Across Pools and Assets

Not all liquidity has to sit in one volatile pair. A more balanced plan might:

• Put some funds in stablecoin pools with low IL

• Put some in blue-chip token pairs like ETH/stablecoin

• Keep some tokens in a wallet or staking, without AMM risk

This reduces the chance that one bad move in a single pool will hurt the whole portfolio.

5. Use Tools that Offer Impermanent Loss Protection

Some DeFi platforms try to offer impermanent loss protection (ILP). In such designs:

• The protocol tracks how much potential IL an LP has

• Over time, part of the protocol’s income or token rewards is used to cover that loss if needed

ILP has its own rules and risks, but for some users, it is attractive because it softens the worst outcomes of strong price moves.

In every case, it is important to read the documentation of the chosen protocol and understand where ILP payments come from and what limits exist.

Conclusion

Impermanent loss is not a trick or a scam. It is a natural result of how AMMs work. When the price of one token in a pool moves away from the other, the pool rebalances. The LP ends up with a different token mix than if the tokens were just held. This can be good or bad in raw value terms, but compared to simple holding, the difference is usually a loss.

This article showed what is impermanent loss, how the constant product rule works, and how the standard formula gives a clear picture for 50:50 pools. It also walked through simple examples that compare LP results with a hold strategy, and it showed how trading fees play a key role. In some pools, high fees and volume can fully cover impermanent loss and still leave profit. In others, especially with high volatility and weak volume, LPs may do worse than holders.

Before giving liquidity, it helps to think in a structured way:

• How much can prices move between these two tokens?
• How strong is trading volume, and what fee rate applies?
• Do tools like IL calculators and past data suggest that fees will likely beat IL?

If the answers look positive, liquidity provision may be a fair bet. If not, simple holding or other strategies may be safer. With a clear view of impermanent loss, AMMs become less mysterious, and each person can decide if this trade-off of risk and reward is right for their own crypto plan.