Impermanent Loss In Crypto: How To Calculate & Avoid It

The formulas used by automated market makers (programs that set prices in liquidity pools) can lead to impermanent loss. Understanding how this formula works can be helpful in knowing how supply and demand affect pool prices.

The most common algorithm used is called the constant product formula, which multiplies the quantity of each token in the pair by the other token’s quantity. This result is called a constant product, and the algorithm uses this number to calculate token prices.

Constant Product Formula: x * y = k

• X is the quantity of the first token in a pair.
• Y is the quantity of the second token.
• K is the (constant) product.

Here’s a simple example using MATIC and ETH. Grab a calculator or spreadsheet if you want to follow along.

Exchange prices:

• MATIC exchange value: $0.85
• ETH exchange value: $1327.80

Pool deposit:

• 2,343.2 MATIC ($1,991.72 exchange value)
• 1.5 ETH ($1,991.70 exchange value)

The constant product is 3,514.80 (2,343.2 * 1.5). This number remains constant, even as swaps occur.

Let’s say someone swaps 100 MATIC to buy ETH. The supply of MATIC in the pool increased (and ETH decreased).

Divide 3514.80 by 2443.2 (the new MATIC supply) to get the amount of ETH remaining in the pool.

3514.80 / 2443.2 = 1.4386 ETH remaining

The ETH buyer gets the difference between the starting quantity of ETH and the calculated amount remaining in the pool.

1.5 (starting ETH) - 1.4386 (ETH remaining) = 0.0614 ETH (the amount that goes to the buyer)

The pool supply is now:

• 2443.2 MATIC ($2,076.72 exchange value)
• 1.4386 ETH ($1,910.17 exchange value)

Now, let’s say ETH goes up to $1,500, while MATIC remains the same at $0.85.

Here’s the value of the original deposit:

• 2343.2 MATIC ($1,991.72 exchange value)
• 1.5 ETH ($2,250 exchange value)
• Total value: $4,241.72

And here’s the value of the remaining tokens after the swap.

• 2443.2 MATIC ($2,076.72 exchange value)
• 1.4386 ETH ($2,157.90 exchange value)
• Total value: $4,234.62

This example results in an impermanent loss of $7.10 (4,234.62 - 4,241.72) after the swap based on the exchange prices for MATIC and ETH.

If we repeated the same swap (another 100 MATIC for ETH), the next swap would give the buyer 0.048 ETH compared to 0.07 ETH on the first swap. Increased demand for ETH in the pool decreases the exchange rate with MATIC.

ETH is getting spendy in this example pool, but there’s likely an arbitrage play in which a trader can swap ETH to the pool to pick up MATIC they can sell elsewhere for a profit. The arbitrage trade would bring pool prices closer to the outside market by reducing the supply of MATIC (raising the price) and increasing the supply of ETH (reducing the ETH price).

This example shows how the AMM works on Uniswap. Some protocols, like Balancer and Bancor, use different algorithms to balance pools.

The Role of Liquidity Providers

When you deposit tokens into a liquidity pool, you’re a liquidity provider. You’ll earn a fee for swaps that occur in the pool. Some DeFi protocols, like Curve, also provide liquidity pool tokens to liquidity providers.

Traders drive the prices in a pool. Uneven demand causes one token to rise in value and the other to fall in value. But these price divergences create an opportunity for arbitrage. Keen traders can scoop up undervalued tokens and sell them on outside exchanges. The increased demand for these underpriced tokens in the pool helps bring the pool price closer to exchange prices. Advanced traders often use bots to search for DEX arbitrage opportunities.

To calculate impermanent loss, you need a few figures.

• Starting token balance: Take notes or screenshots when you deposit to a liquidity pool.
• Ending token balance: You can preview the withdrawal on most DEXs (without withdrawing).
• Exchange prices for the tokens in the pool: Check an exchange for current prices.

Here are the steps:

Step 1:Multiply your starting token quantities by the current exchange prices.

(Token A quantity * Token A exchange price) + (Token B quantity * Token B exchange price)

Step 2:Multiply your ending token quantities by the current exchange prices.

(Token A quantity * Token A exchange price) + (Token B quantity * Token B exchange price)

The token quantities have likely changed since you started. On Uniswap, you can preview the token quantity by clicking on “remove liquidity” and then moving the slider to 100%.

Step 3:Subtract the result from Step 1 from the result from Step 2.

Subtract the total value you would have had from the value you have now.

Step 4:Add your earnings, including fees and liquidity mining tokens (if applicable).

Many online calculators don’t include fees or mining tokens in the calculation, but fees are a primary incentive to invest in liquidity pools. Fees and liquidity mining tokens awarded by some platforms, such as Curve, help offset any impermanent loss.

That’s it. If the final number is negative, you have an impermanent loss and would have done better by holding your tokens in a wallet. If positive, you’re earning more than holding your tokens in a wallet.

The previous section illustrates impermanent loss in action.

There are several ways to reduce the risk of impermanent loss.

• Low volatility tokens: Providing liquidity for stablecoin pairs is the easiest way to avoid impermanent loss. You can also consider equivalent tokens, like ETH and WETH, which won’t differ in price volatility. Expect a smaller fee in exchange for added safety.
• Join larger pools: A large pool can handle big swaps without much price impact.
• Set a trading range: Uniswap lets you set a trading range for your position. Tighter trading ranges bring more safety, but positions may require more maintenance as prices move.
• Change the liquidity ratio: Protocols like Balancer let you choose a ratio other than 50/50 for deposited tokens. Setting a more volatile token as a lower percentage of your position reduces the risk of impermanent loss.
• Use a single-sided pool (with insurance): Bancor offers single-sided positions for liquidity pools, matching the deposit with Bancor’s BNT tokens (which are burned when you pull your liquidity). Bancor takes 15% of your earned fees in exchange for a guarantee that you have at least the same number of tokens when you pull your liquidity.
• Just wait: If you’re providing liquidity for high-demand tokens on a high-traffic platform, your impermanent loss may be temporary. Arbitrage players may trade the price divergence, bringing the pool’s token prices closer to exchange prices.

Impermanent loss protection is a type of insurance you can use to be sure you exit a position with at least the same number of tokens with which you started. Bancor is the best-known option. The platform takes 15% of the trading fees earned by liquidity providers to fund an insurance pool that keeps liquidity providers whole.

Yes, sometimes. In-demand tokens attract arbitrage traders who can help bring token prices in a liquidity pool in line with exchange prices for the tokens.

It’s possible to have a gain while also having an impermanent loss. The math behind impermanent loss considers what you would have made if you just held your tokens compared to the value if you exited your position.

Impermanent loss refers to investments in which you would have earned more by holding the crypto assets rather than deploying the assets in a liquidity pool. Yield farming can include several income strategies, ranging from lending to staking, with providing liquidity among the most common strategies.

Whiteboard Crypto offers a handy calculator you can find here.

To calculate impermanent loss you can follow these steps.

• Step 1: Multiply your starting token quantities by the current exchange prices.
• Step 2:Multiply your ending token quantities by the current exchange prices.
• Step 3: Subtract the result from Step 1 from the result from Step 2.

A negative result is an impermanent loss.

While impermanent loss is usually associated with liquidity pools, a similar loss can occur in staking if your stake is slashed due to improper validator behavior. In this case, you may have been in a better position by not staking.

Impermanent loss isn’t a risk when providing liquidity for a stablecoin pair. But if pairing a stablecoin with a volatile asset, the quantity of each token in the pair changes as swaps occur, potentially causing impermanent loss.

It’s best to discuss the tax implications or liquidity pool positions with a trusted tax advisor. Some crypto tax firms treat a liquidity pool deposit as a sale, which may create a capital gains liability. However, this take is not directly related to impermanent loss and instead comes from the transfer of assets.