The Highly Regarded guide to Impermanent Loss

I saw a post here recently which mostly failed to simplify Impermanent loss. It tried to convert everything to USD to make things more "real" to people.

I know us smooth brains are programmed to think in USD for everything, but it actually just makes understanding liquidity pools harder.

The only thing you need to know to understand a liquidity pool is the simple formula:

Coin 1 amoint x Coin 2 amount = A number that never changes

Example: 10 BTC and 100 ETH are in a pool. (Look it's our favourite coins). That pool has 10 x 100 = 1000 total liqudity (never changes). If you come in with a trade of 1 BTC for 10 ETH, the pool would now contain:

9 BTC and 110ETH = 9 x 110 = 990 liquidity

You can see the liquidity would change if that transaction took place, but this can't be allowed to happen or our magic formula would be broken. That's where "slippage" comes in. Slippage happens when the pool isn't big enough to handle your order, so it fucks you a little bit on the transaction rate to maintain the same total liquidity.

In our example if say, you want to exchange 1 BTC for ETH, the pool will have 11 BTC after you make that transaction meaning the pool needs to have:

1000 liquidity / 11 BTC = 91 ETH

remaining after the transaction. This means you get 100 - 91 = 9 ETH for your 1 BTC. Slippage gets less impactful the smaller transaction you're making compared to the LP pool total.

So I lied a bit before. There is one scenario total liquidity changes - when you fund or liquidate a pool. When you do this, you take owernship of a percentage of the pool's total liquidity. So if you consider the example of 10 BTC and 100 ETH and you add 5 BTC and 50 ETH, you now own 33% of the pool which now has 15 * 150 = 2250 liqudity.

If someone else now exchanges 5 BTC for ETH using the pool, the pool will have:

20 BTC and 2250/20 = 112.5 ETH

Now you decide to withdraw your liqudity and you get your percentage of the pool back:

20*0.33 = 6.7 BTC and 112.5*0.33 = 37.5 ETH

This means you gained 1.7 BTC and lost 12.5 ETH. The problem is at the new rate of exchange (1 BTC = 5.625 ETH), you've lost value overall - you lost 12.5 ETH which is currently worth 12.5 / 5.625 = 2.2 BTC - more than the 1.7 BTC you've gained. You'll lose overall value if the pool ratio changes in either direction - the best case for you is completely stable exchange rates.

This is impermanent loss and it was all explained without mentioning USD.