Since the rewards for the Moon/ETH liquidity pool went live I’ve seen many people struggling to understand the financial risks of joining a liquidity pool and even people who don’t know about impermanent loss. I’m absolutely no expert and would appreciate it if someone corrects me if I made an error somewhere, but nevertheless I would like to try and explain the math behind liquidity pools and what impermanent loss is.

Stats we start with on February 26th when the rewards for the Liquidity Pool went live:

• You join with a $16,000 stack
• Moons $0.19 from February 26th when Liquidity Pool (LP) rewards went live
• ETH $1,600 from February 26th when Liquidity Pool (LP) rewards went live
• Moons experienced a 22% gain from February 26th till now
• ETH experienced a 3% loss from February 26th till now

Example 1: You join the LP with $16,000 worth of ETH on February 26th

You have 10 ETH worth $16,000 and you want to join the Moons/ETH LP. A LP always balances both sides of the book so the $ value of each holding is exactly the same. So in this case to be able to join you basically sell half your stack of ETH for Moons to be able to join:

You hold at the start, 26th of February, 5 ETH worth $8,000 (5 * $1,600) and 42,105 Moons worth $8,000 (42,105 * $0.19).

Meanwhile Moons have increased in price with about 22% while ETH decreased in price with about 3% over the last 10 days. This changed your stack to:

37,544 Moons worth $8,702 (37,544 * $0.2318). The $0.2318 comes from the 22% increase in price since February 26th when Moons were $0.19.

5.607 ETH worth $8,702 (5.607 * $1,552). The $1,552 comes from the 3% decrease in price since February 26th when ETH was $1,600.

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Your total holdings are now $8,702 in Moons + $8,702 in ETH = $17,404 a 8.775% increase from your original value of $16,000 after joining the LP.

If you just held on to your 10 ETH you would have had 10 * $1,552 = $15,520 a 3% decrease from your original value of $16,000 if you didn't join the LP.

Joining the LP with ETH compared to holding your ETH has increased your value with $1,884 ($17,404 - $15,520) which equates to a portfolio increase of 12.14%

Example 2: You join the LP with $16,000 worth of Moons on February 26th

You have 84,210 Moons worth $16,000 and you want to join the Moons/ETH LP. A LP always balances both sides of the book so the $ value of each holding is exactly the same. So in this case to be able to join you basically sell half your stack of Moons for ETH to be able to join:

You hold at the start, 26th of February, 5 ETH worth $8,000 (5 * $1,600) and 42,105 Moons worth $8,000 (42,105 * $0.19).

Meanwhile Moons have increased in price with about 22% while ETH decreased in price with about 3% over the last 10 days. This changed your stack to:

37,544 Moons worth $8,702 (37,544 * $0.2318). The $0.2318 comes from the 22% increase in price since February 26th when Moons were $0.19.

5.607 ETH worth $8,702 (5.607 * $1,552). The $1,552 comes from the 3% decrease in price since February 26th when ETH was $1,600.

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Your total holdings are now $8,702 in Moons + $8,702 in ETH = $17,404 a 8.775% increase from your original value of $16,000 after joining the LP.

If you just held on to your 84,210 Moons you would have had 84,210 * $0.2318 = $19,520 a 22% increase from your original value of $16,000 if you didn't join the LP.

Joining the LP with Moons compared to holding your Moons has decreased your value with $2,116 ($17,404 - $19,520) which equates to a portfolio decrease of 10.84%

Example 3: Impermanent Loss explained

But what if you already had 42,105 Moons worth $8,000 and 5 ETH worth $8,000 to start with on February 26th and you joined the LP without having to swap Moons for ETH or vice versa? That’s how we will be able to explain and calculate the impermanent loss you would be experiencing.

As mentioned before with the price increase of 22% for Moons and a price decrease of 3% for ETH since February 26th you would hold these amounts in the LP:

37,544 Moons worth $8,702 (37,544 * $0.2318). The $0.2318 comes from the 22% increase in price since February 26th when Moons were $0.19.

5.607 ETH worth $8,702 (5.607 * $1,552). The $1,552 comes from the 3% decrease in price since February 26th when ETH was $1,600.

Your total holdings in the LP are now $8,702 in Moons + $8,702 in ETH = $17,404 a 8.775% increase from your original value of $16,000

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To be able to see what your impermanent loss would be you compare these numbers to ‘what if I just held?’. Let’s see those numbers:

42,105 Moons worth $9,760 (42,105 * $0.2318). The $0.2318 comes from the 22% increase in price since February 26th when Moons were $0.19.

5 ETH worth $7,760 (5 * $1,552). The $1,552 comes from the 3% decrease in price since February 26th when ETH was $1,600.

Your total holdings if you just held would have been $9,760 in Moons + $7,760 in ETH = $17,520

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Just holding versus joining the LP would have netted you $116 more. The $116 is your impermanent loss, or 0.65%.

But the fun thing about joining a LP are the rewards. So as long as your LP rewards within those 10 days since it went live exceeded $116 in value, you would still have made more by being in the LP compared to just holding.

I hope this piece of information has helped some of you understand how liquidity pools work and the maths behind it. Not only do you have to consider if you join with a stack of Moons or ETH, but also important is to try and solve if the rewards from the liquidity pool outweigh the impermanent loss you are going to experience. Because unless Moons and ETH mimic their exact price action, you will be experiencing impermanent loss.